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UBC Theses and Dissertations

Computational studies of laser-matter interactions Silva, Luiz da 1984

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COMPUTATIONAL STUDIES OF LASER-MATTER INTERACTIONS  by  LUIZ|DA SILVA B.A.Sc,  A  T H E S I S T H E  University  S U B M I T T E D  of British  IN  R E Q U I R E M E N T M A S T E R  O F  C o l u m b i a , 1982  P A R T I A L  F U L F I L M E N T  F O R  D E G R E E  T H E  A P P L I E D  O F  S C I E N C E  in T H E  F A C U L T Y  O F  G R A D U A T E  D E P A R T M E N T  We  O F  P H Y S I C S  a c c e p t t h i s t h e s i s as c o n f i r m i n g to the required  T H E  S T U D I E S  U N I V E R S I T Y  O F  October ©  Luiz D a  standard  B R I T I S H  C O L U M B I A  1984 Silva,  1984  O F  In p r e s e n t i n g  this  thesis i n partial  fulfilment of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y of B r i t i s h Columbia, I agree that it  freely  the Library shall  a v a i l a b l e f o r r e f e r e n c e and study.  agree t h a t p e r m i s s i o n f o r extensive for  financial  copying o r p u b l i c a t i o n of t h i s  gain  Department  of  ^V\y  <g3 \ C i ^  The U n i v e r s i t y o f B r i t i s h  Columbia  1956 Main Mall  Van c o u v e r ,  Canada  V6T 1Y3  (3/81)  Q c \ -  It i s thesis  s h a l l n o t b e a l l o w e d w i t h o u t my  permission.  DE-6  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my  understood that  Date  I further  copying o f t h i s  d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  \ 6 / S 4 -  written  il Abstract  Using a one-dimensional hydrodynamic matter  interactions  for the  mass  compared cup  the  with previous  agreement.  explained  investigated.  ablation rate and  measurements.  good  was  by  T h e  T h e  results  particular,  calculated  stronger  and  that  an expanding plasma an estimate  scaling targets.  ionization state was  laws  was  conducted  and  obtained from  intensity  measured  of X-ray  intensity  lateral  by  radiation  energy  scalings  By  from  transport  These  ion calorimeter  wavelength scaling observed in the  effects  suggest  results  significantly larger t h a n the laser focal spot.  a constant  wavelength  ablation pressure have been calculated.  experimental  considering the  numerical  In  c o m p u t e r code, the ablation process in  the  can  were  scaling  laws  results  were  and  found  lead  plasma. to  an  measuring  A n the  be  results  ablation  shock  T h i s yielded scaling laws in good agreement  check o n the  velocity  through  with the simulation  is  area  modelling the ion recombination process  independent  in  Moreover,  of the error i n t r o d u c e d in ion m e a s u r e m e n t s b y  calculated.  Faraday to  experimental hot  laser-  assuming  ablation planar results.  in  pressure  aluminum  Ui Table of Contents  A B S T R A C T T A B L E  ii  O F C O N T E N T S  L I S T  O F F I G U R E S  L I S T  O F T A B L E S  iii v vi  A C K N O W L E D G E M E N T S C H A P T E R  I  vii  I N T R O D U C T I O N  1  1-1 N u m e r i c a l S i m u l a t i o n o f L a s e r - M a t t e r 1-2  Scope  I- 3  Thesis Outline  C H A P T E R II-1  II  4  M E D U S A  H Y D R O D Y N A M I C  of Laser-Matter  C O D E  5  Interactions  5  Radiation  7  Absorption of Laser  7  (ii)  9  II-l-B  Resonance  Absorption  Parametric Energy  Processes i n Plasmas  12  Transport  14  (i) T h e r m a l c o n d u c t i o n  14  (ii)  15  (iii) II-l-C  H o t electron transport Radiation  transport  16  E q u a t i o n of State i n the Shock-Compressed Solid  16  Medusa  19  Numerical  Formulation in  II-2-A  Equations of Motion  19  II-2-B  Energy  20  II-2-C  M e t h o d of Solution  II- 3  Recent  Equation  lion-Local  II-3-B  Radiation  II-2-C  Post-Processor  l  III  23  Additions  II-3-A  C H A P T E R III-  3  (i) I n v e r s e B r e m s s t r a h l u n g A b s o r p t i o n  (iii)  II- 2  1  of Thesis Work  Physics  II-1-A  Interactions  M A S S  Numerical  24  Thermodynamic  Equilibrium  24  Transport  A B L A T I O N  25 28 R A T E  Simulations using  A N DA B L A T I O N  Medusa  P R E S S U R E  30 30  Iv III-l-A  Simulation  III-4-B  C a l c u l a t e d Intensity  III- l - C III-2  Parameters  Calculated wavelength Experimental  31  Scaling of m  and  P bi  33  a  a n d Pau  34  Results  38  III-2-A  Ion Expansion Measurements  III- 2 - B  M e a s u r e d Intensity  III- 3  m  Scaling of  38  a n d Wavelength  Scaling of m  a n d P  o 0  j  40  C o m p a r i s o n of Scalings  C H A P T E R  IV  P R O C E S S E S  42  A F F E C T I N G  T H E S C A L I N G  L A W S  48  IV- 1  T w o D i m e n s i o n a l Effects  48  IV-2  Ion Recombination in an Expanding Plasma  50  IV- 2-A IV- 2-B  M e t h o d  IV-2-C IV-3  Theory  51  of Solution  Simulation  Effects  54  of the Ion Current  of X-ray  Radiation o n the Scaling Measurements  IV-3-A  Contribution of X-ray  IV-3-B  Radiation  C H A P T E R  V  S H O C K  to the Ion Calorimeter Measurements  .  61  Ablation  64  W A V E  M E A S U R E M E N T S  66  Scaling of Shock  V-2  Experimental  V-3  Wavelength  V-4  Discussion of Results V I  Energy  61  Driven  V-l  C H A P T E R  54  Velocity  with Ablation Pressure  Measurements  Scaling of Ablation Pressure  S U M M A R Y  67 67 75 70  A N D C O N C L U S I O N S  79  VI-1  Summary  79  VI-2  N e w Contributions  80  VI-3  Future  87  A P P E N D I X  A  Work M E D U S A  P O S T - P R O C E S S O R  A-l  C o m m a n d s  A-2  Three-Dimensional Plot  A-3  Auxilary  A-4  Final  A P P E N D L X  B  89 C o m m a n d s  C o m m a n d s  90 92  Comments M E D U S A  88  93 I N P U T  P A R A M E T E R S  94  List of Figures  II-l  Schematic  representation  o f laser driven  IV-2  Schematic  representation  of resonance  II-3  Developement  II-4 R e g i o n s II-5 III-l  Target  of a Shock  absorption  11 17  calculations  as f u n c t i o n o f time  27  a n ds p a c e  29  Laser pulse used in simulations  III-2 N u m e r i c a l  32  zoning used in the computer simulations  III-3 C a l c u l a t e d  intensity  III-4 C a l c u l a t e d  wavelength  scaling of mass  III-5 C a l c u l a t e d  wavelength  scaling of ablation pressure  III-6 NG-34  Laser  scalings of m a n d Pu  35  a  ablation rate  37  a tb e s t f o c u s  41  wavelength  scaling of mass  III- 9  wavelength  scaling of ablation pressure  Ablation pressure  Initial density,temperature  IV-2  Calculated  IV-3  Measured  IV-4  Average  charge  IV-5  Average  charge state vs density  IV-6  v  Faraday Faraday  ablation rate  43 44  46  as f u n c t i o n o f t i m e  IV- 1  p  36  39  III-8 M e a s u r e d Measured  33  System  III-7 F o c a l s p o t i m a g e  111-10  6  Front  in radiation transport density  ablation  a n dcharge state profiles  55  c u ptrace  56  C u ptrace  57  state vs time  59  vs distance between  detector  V-l  Trajectories  V-2  Pressure  V-3  Experimental  V-4  Streak  V-5  Shock  V-6  Ablation Pressure  V-7  Streak record o f target  V-8  Shock  A-l  Three-Dimensional work  60 a n dtarget  62  Medusa  of shock propagation in aluminum from  scaling o f the  shock velocity  transit  Medusa  simulations  setup for measuring shock velocity  record of target transit  from  time  time  [X  L  rear  surface  luminescence  = 0.53/zm)  vs Laser rear  Intensity  b o x  (Xjj  66 68 69 71 73  ( A j , = 0.53/im)  surface, shock luminescence  in aluminum  simulation  = 0.27/im)  74 76  77 90  vl L i s t of Tables  III-  l  IV- 1 B-l  General Radiated  Scaling Law X-ray  M e d u s a Input  Parameters  energy  as a f u n c t i o n o f laser i n t e n s i t y a n d w a v e l e n g t h  Parameters  45 63 93  Acknowledgements  I  would  throughout of  like  this  assistance  in  to  work. the  Ng.  and  K w a n for the  by  Joe  I am  Kwan,  was  His  my  supervisor  endless  experimental  Andrew Joe  thank  indebted to  energy  shock  Andrew  Dr. is  still  a  Ng, Daniel  N g  source  measurements  experimental ion results.  greatly  Andrew  was  Pasini,  The  for his support  and  of  A  amazement.  given Dean  by  Dean  Parfeniuk,  i n t r o d u c t i o n to  Medusa  great  deal  Parfeniuk  and  Peter  Pearson.  help.  T h e moral support and encouragement afforded by Vancouver's  also like to t h a n k  the experience a most enjoyable the  me  appreciated.  John  and help, made  Celliers,  , given to  It i s a l s o a p l e a s u r e t o a c k n o w l e d g e t h e m a n y u s e f u l d i s c u s s i o n s w i t h R o m a n I would  guidance  setbacks  one.  A  Dick  Keeler  and Alan  very special thanks  insignificant.  C h e u c k for their finest  Popil  technical  helped to  goes to A n g e l a whose  and  make  patience,  CHAPTER  I: 1  CHAPTER I  INTRODUCTION  N u m e r i c a l S i m u l a t i o n of L a s e r - M a t t e r Interactions  1-1  M o t i v a t e d primarily b y the possibility of attaining the density, temperature finement  conditions necessary  for nuclear  (including laser-plasma interactions) investigations  also  permit  the study  of many  ablation process driven b y intense  flux  levels  current  uncertainties  of non-linear parametric ablation  9  _  waves  in the theoretical  instabilities 1  3  7  '  .  8  have  pressure regime previously  also  been  strong  numerical  matter  simulations.  interactions  Even a  little  area  generally  the possibility  transport  waves  3  ~  through  generated  of state of matter  .  6  by  problems.  condution of  T h e  physics  laser-induced laser-driven  in a temperature 1 4  a n d space  physical  varying.  and  .  However,  processes  Exact,  they  at  resolving  achieved i n the m o d e l l i n g of laser-target  the many  be impractical.  Such  placed  governing  analytical  m a y easily  been  be  ex-  laser-  treatment  of  incorporated  calculations.  though the subject  more  time  of heat  shock  physics  models, greater emphasis has recently  is b e c a u s e  are inherently  such processes would into numerical  This  allows  interactions  decade.  in electron thermal  through nuclear explosions  A l t h o u g h considerable success h a s b e e n  on  This  fundamental  studied extensively  the equation  analytical  active over t h e last  results  description  accessible only  periments using steady-state,  , research o n laser-matter  2  important  limit.  Furthermore,  can be used to study  '  laser light  the free-streaming  in plasmas  1  has been extremely  The  approaching  fusion  a n d con-  than  twenty  of computer  years  employing a wide range  o l d , it  simulations  has become  of analytical,  numerical  a  of laser-produced plasmas very  large  a n d extensive  and computational  is  only  research  techniques  while  CHAPTER addressing  a vast  variety  of physics  b e e n d e v e l o p e d fall into two a n d ions are described b y the  as  wave-wave  particle  accelerations  laser-produced treat  as m a n y  O n sion,  vidual  the  in  particle  In  which  the  the  gradient  in the  different  ions  The In  are  velocity  system  well  codes  have  electrons  are g o v e r n e d  as  are  instabilities  transport  by  and  properties  two-dimensional  and  points  it  fluids,  describe  the  This  One  in can  reason  for  This  one  microballon used  in  inertial  grid points)  in the  in the  what  as  over  this  the the  is v e r y as  associated  Eulerian the  elements gradients  to maintain  the  and hence  of the  descrip-  of  a  when  fusion  fluid  materi-  case  for  a  experiments. no  averaging  Lagrangian  follow  that  description  mass  be  the with  frame  Lagrangian  would  indi-  governed by  important  element  fluid  is  code.  detailed  reference  confinement  fluid  is n e c e s s a r y  a  is t h a t  another,  region of steep density  T h i s is e x a c t l y  in  Another advantage  defining the  neglecting  system  system  expan-  or h y d r o d y n a m i c  rapid dynamics  favoured  to  is n e c e s s a r y .  thus  is k n o w n  invariant.  mixing occurs  fluid  of the  model the  is h i g h l y  is t i m e are  as  evolution  fluid.  fixed.  o f t h e p l a s m a s u c h as p l a s m a  adjacent  in the element (or  to  of the  is  scheme  gas  or  order to better  properties  filled  is s m a l l .  parametric  studied using a  treated  dynamics  is c o m m o n  coordinates, no  more  that  the  scheme  fluid.  Thus,  a n d fewer points good spatial  where  resolution  simulations.  Only the  flow  mesh points  will be  as  kinetic  macroscopic behaviour  and  it  Lagrangian  of the quantities  the  electrons  coordinate  in the  (including  waves)  state-of-the-art  one-dimensional simulations,  Lagrangian  there  plasma  shock compression can be  local  codes  particles.  interactions,  with very  is t h a t  The  fluid equations.  deuterium-tritium In  6  computer  In p a r t i c l e o r k i n e t i c c o d e s , t h e p l a s m a  interactions  electrostatic  interactions.  with the  element als  and  plasma  laser-matter  tion.  by  the other h a n d , the  appropriate  moves  10  numerous  T h e s e codes are generally u s e d to s t u d y microscopic p h e n o m e n a  wave-particle  plasmas. as  ablation  Here,  and  main groups.  The  their corresponding distribution functions which  Boltzmann equations.  such  problems.  I: 2  recently, two-dimensional h y d r o d y n a m i c simulations have b e e n feasible  technological advances  in c o m p u t e r facilities.  A  major  numerical problem which  i n m u l t i - d i m e n s i o n a l L a g r a n g i a n c o d e s is t h a t o f g r i d d i s t o r t i o n . opement  of m a n y  "sliding zone"  algorithms  p e r p e n d i c u l a r directions to follow the  fluid  1 5  ,  flow.  1  6  in which  through  the  T h i s has led to the  g r i d lines  arises devel-  are m o v e d in  Improved developments in  two  two-dimensional  CHAPTER algorithms remains  1-2  a n important  area of research.  S c o p e of T h e s i s W o r k  The  primary  objective  theoretical  understanding  performed  at T h e University  existing h y d r o d y n a m i c  of this  work  of a sequence of British  Medusa  code  experimental ( F W H M )  Columbia.  To  further  equilibrium  improve  Specifically,  o r 0.27  o n numerical  /im  an updated  recently  version  of a n  pressure  These were c o m p a r e d with the  targets  irradiated with a 2 nanosecond  at irradiances  simulations  experiments  the scalings of ablation  a n dw a v e l e n g t h .  aluminum  simulations,  <  6.0  x 10  W / c m  13  of the experiments,  2  .  non-local  thermal  ( n o n - L T E ) i o n i z a t i o n , r e c o m b i n a t i o n s i n t h ee x p a n d i n g p l a s m a as well as e n e r g y  deposition by radiation added  0.35,  interaction  wasused to calculate  scalings obtained i n planar  l a s e r p u l s e o f 0.53,  was to obtain, through numerical  of laser-matter  a n d mass ablation rate w i t h laser intensity  transport  Medusa  to t h e basic  code.  were also m o d e l l e d . Furthermore,  Such calculation routines have  to facilitate  data  analysis  calculations of t h e radiation e m i t t e d b y thep l a s m a , a n interactive p r o g r a m was  I: 8  developed.  This  w a s u s e d t o assess  t h e effect  of X-ray  a n dto  been  permit  (post-processor)  emission o n the experimental  results.  Finally, tions.  From  shock shock  propagation in aluminum  speed  measurements  made  was measured u s i n g 0.53  a n dcompared  a n d 0.27  fim  laser  conjunction with simulations, an independent measurement ofthe wavelength lation pressure wasobtained. to  identify  with light  simulaa n din  s c a l i n g o fa b -  This wascompared with that derived from i o n measurements  problems associated with the interpretation  of the ion data.  CHAPTER  1-3  Thesis Outline  I n c h a p t e r II, given.  the  a general review of the processes relevant  Particular  calculated  ablation  rate  are  intensity  and  presented  wavelength  and  scalings  compared  with  examined in chapter  IV.  Specifically  we  to  measure  the  shock  used to yield an independent are  then  measurements.  measurement  compared with Chapter  VI  the  contains  w i t h s o m e suggestions for further  pressure  results.  Several  in  the  radiation.  target  foil  of wavelength  previous  chapter  and  mass  processes  the simulation a n d experimental results  c o n s i d e r the effects of lateral e n e r g y  velocity  In  ablation  experimental  r e c o m b i n a t i o n in the e x p a n d i n g p l a s m a , a n d X-ray performed  of of the  investigations.  of the  is  chapter V,  described.  scalings of the  experimental  a summary  In  scaling laws  main  results  transport, an  The  is  numerical  e m p h a s i s is p l a c e d o n d e s c r i b i n g t h e m o d i f i c a t i o n s m a d e .  which can account for the discrepancy between  These  to laser-matter interactions  T h i s is f o l l o w e d b y a b r i e f d i s c u s s i o n o f t h e h y d r o d y n a m i c c o d e u s e d i n t h e  simulations. III  I:  are ion  experiment results  ablation obtained  are  pressure. from  and conclusions  ion  along  4  CHAPTER  CHAPTER  n  MEDUSA HYDRODYNAMIC  T h e d y n a m i c s o f laser-target and  transport  analytical quire the  processes.  models  numerical  relevant  is  Culham  O n e such hydrodynamic  a  Lagrangian  Laboratory  at  fluid  currently  code.  document  II-l  U.B.C.  and A . R . Bells by R.G. Evans  3 2  in 1980. More  additions  version  70's . A  contain  recently  3 1  was  all  pro-  developed  few modifications were  Laboratory  made.  codes which  re-  in  later  before the code  was i m -  (1982-1984), several  features  T h e m a i n objectives  Medusa  of this  and,more  chapter  importantly,  .  P h y s i c s of L a s e r - M a t t e r Interactions  physical  processes  playing  s u m m a r i z e d b y considering the three  In ways  region with  1 ,commonly  ion temperature  a  major  distinct  referred  the expanding plasma.  incident laser light. the  3 3  description would  .  published  at R u t h e r f o r d  simple,  one-dimensional simulation  describe the physical processes considered in  s o m e of the recent  The  of  employed  T h e original  have been added a n d a n u m b e r of corrections are t o briefly  Medusa  c o d e is  b y J . P . Christiansen in the early  added by R.G. Evans plemented  of most  computer  hydrodynamic  be described by  other processes, a complete  or simulations, using large  , as is t y p i c a l  of complex  a n y single process c a n usually  decoupled from  calcuations,  physics.  Medusa grams,  when  CODE  interactions involves a variety  Although  II:  role  in laser-matter  interactions  regions depicted in Figure  to as t h e c o r o n a , T h e plasma  laser  c a n refract,  light  A l t h o u g h the absorption mechanisms preferentially is e v e n t u a l l y  best  II-l.  interacts  reflect  are  and/or  in a  variety  absorb  the  heats the electron,  increased through electron-ion collisions.  5  CHAPTER  II:  F i g u r e I I - l Schematic representation of laser driven ablation, p is the target density. P is the total hydrodynamic pressure and T, and T, are ion and electron temperatures respectively.  6  CHAPTER In  t h e a b l a t i o n z o n e , r e g i o n 2, e n e r g y t r a n s p o r t  conduction carry  energy  from  the  corona to the  m e c h a n i s m s s u c h as e l e c t r o n  ablation surface.  The  heated  thermal  material  p a n d s away f r o m the ablation surface generating a large static pressure in the dense T h i s pressures drives unperturbed  In  a shock discontinuity  ( r e g i o n 3) i n t o t h e t a r g e t  ex-  target.  compresses  the  solid.  order to introduce the various  aspects of p l a s m a physics necessary  g a t i o n a b r i e f d e s c r i p t i o n o f t h e s e p r o c e s s e s is n o w  II-l-A  which  II:  in our  investi-  given.  A b s o r p t i o n of Laser R a d i a t i o n  In  this  of laser light absorption, tensities  consider the  with plasmas which  is t h e  and  most  lead to  We  in which complete  the  This  electric  processes that  field  characterize  a b s o r p t i o n of laser energy. absorption mechanism  is f o l l o w e d  our discussion by  linear excitation of p l a s m a  primary  important  is d i s c u s s e d i n d e t a i l .  absorption" waves.  section we  of the  by  a qualitative  laser light  briefly  in our  interaction  bremsstrahlung  regime  of laser  d e s c r i p t i o n of  resonantly  describing the  Inverse  the  "resonance  excites electron  processes which  in-  lead  plasma to  non-  waves.  (i) Inverse B r e m s s t r a h l u n g A b s o r p t i o n The  classical  and  most  effective  mechanism  bremsstrahlung or collisional absorption in field To  collide  with  the  ions  and  convert  which  their  In  wave in a m e d i u m  as d e s c r i b e d b y  equations reduce  to  (in  M K S  absorption  is  inverse  laser  electric  into  random  thermal  energy.  to consider the p r o p a g a t i o n of a Maxwell's  plane  equations.  z axis a n d electric  field  vector  along the  x  units)  dB ~dz~  light  oscillating in the  directed energy  the case of wave p r o p a g a t i o n along the  axis M a x w e l l ' s  laser  electrons  a n a l y z e t h e p r o c e s s i n m o r e d e t a i l it is n e c e s s a r y  electromagnetic  for  dt  [2.1]  7  CHAPTER dB  .The  induced current  u, t h r o u g h the  density  J  is r e l a t e d t o t h e e l e c t r o n d e n s i t y , n ,  e q u a t i o n of  the  and  A:L for u  field  motion  du at  + mi/ ,u = e  „  ,  -eE.  been  i n c o r p o r a t e d as a f r i c t i o n t e r m  2.4  in  described  form  E =  [2.4]  is r e l a t e d t o t h e e l e c t r i c  T o solve this s y s t e m of equations we consider the electric field to be  the plane wave  equation  [2.3]  e  e  where  velocity,  n eu,  e l e c t r o n - i o n c o l l i s i o n f r e q u e n c y , i/ ,-, h a s  the equation. by  =  Moreover, the electron velocity  m—  Here,  and electron  e  relation  w h e r e e is t h e e l e c t r o n c h a r g e . t h r o u g h the  1 d E  ,  J  E  II:  are  the  laser  E e  x  light  =  E  e x p t ( w t - k z)H L  0  frequency  a n d u s i n g e q u a t i o n [2.3]  3  =  V  and  L  wave  ?\oEavi(w t  is d e f i n e d  If w e s u b s t i t u t e t h i s c u r r e n t  into the  laser light p r o p a g a t i o n in a  plasma  field  respectively.  Solving  density  [2.6]  - k z) L  as  2 « : = P J  number  results in the current  L  w h e r e t h e p l a s m a f r e q u e n c y w„  [2.5]  x  en,. — .  [2.7]  equations we  arrive at t h e d i s p e r s i o n r e l a t i o n  for  (I) K-> I n d e r i v i n g t h i s d i s p e r s i o n r e l a t i o n w e u s e d t h e f a c t t h a t i n l a s e r g e n e r a t e d p l a s m a s , i/ et  U/'x,.  Since  ki, i s i n  general complex, the  incident  light  is a t t e n u a t e d  as  it  propagates.  < < In  8  CHAPTER fact, for w  uj£,  >  p  is e v a n e s c e n t .  v i/u)L  and  Since  e  < < 1,  is p u r e l y  the plasma frequency  imaginary  referred to as t h e  critical density, a n d  a n d as a consequence t h e wave  is a f u n c t i o n o f e l e c t r o n  that laser light c a n o n l y propagate u p to a density  at which  w  p  =  _  C  density  it is  T h i s limit  w^.  it is d e n n e d m o r e e x p l i c i t l y  n rtt  II:  apparent is u s u a l l y  as  m e u>l ~2 • e  0  T h i s e l e c t r o n d e n s i t y is w h a t d e f i n e s t h e b o u n d a r y b e t w e e n r e g i o n 1 a n d r e g i o n 2 as d e p i c t e d in Figure  II-l.  The  energy  absorption coefficient a  — • and  defines t h e spatial  t  o  )  attenuation  is g i v e n b y  - ( T ) ( j ) ( , -  /  B  of t h e laser intensity  M  ) V .  I"-"!  through the  relation  I = I exp(-az).  [2.11]  0  There  are m a n y  bremsstrahlung At  mechanisms  which  . A t low temperatures,  higher intensities, t h e s t r o n g electric  This  in turn  modifies  s o r p t i o n coefficient  can modify  simple  treatment  of  inverse  bound-bound a n d bound-free absoption c a n occur. field  the collision frequency  c a n distort i/ ; w h i c h e  (nonlinear bremsstrahlung  be f o u n d i n reference  this  ).  A  the electron velocity leads  to a intensity  detailed treatment  distribution.  dependent ab-  o f these  effects c a n  [35].  (ii) R e s o n a n c e A b s o r p t i o n A t  high  laser  sorption mechanism.  intensities  resonance absorption * 5  '  7  1  can become  an important  ab-  A n understanding of the process c a n b e gained through the following  analysis.  W h e n gradient  light  is i n c i d e n t  o n a spatially  inhomogeneous plasma  direction, Snell's law a n d the dispersion relation  (equation  at  a n angle  6 to the  [2.8]) c a n b e c o m b i n e d  9  CHAPTER to n  c  show  r  t  7  that  1  c o s 0 .  t  the  classical  Beyond  this  turning point  point,  the  wave  for the  light  wave occurs  is e v a n e s c e n t .  However,  at  a density  if the  laser  n ($)  electric  Sn  parallel to the plane in Figure and  w, p  IV-2,  the  We  electric  written  excite  energy  can  the  laser  of incidence)  resonantly  completes the  at  e  verify  field  is i n c i d e n t  plasma  transfer from  process  In  to the  waves.  rather  easily  where  Expanding  It  this  from  we  e{x)  =  =  where  8n  [2.14]  gives  Poisson's e q u a t i o n we  depicted  w h e r e u>j,  d a m p i n g of these  waves  =  that  energy.  equations  which  can  be  is t h e  e  simple  electron  result  density  illustrates  density perturbations direction of the  resonantly  A  [2.12]  eq.  [2 -  8])  .  [2.13]  the  excited only  0  e 6n.  .  [2.14]  perturbation.  two  f o r t fa  Since  [2.15]  Ve(z)  a  V n  e  ,  comparison  characteristics  of resonant  absorption:  of incidence  gradient  6.  (that  0, t h a t  For small  6,  (i)  a light w a v e w i t h a c o m p o n e n t o f its electric is E - V n  e  ^  i s , w h e r e WJJ =  0),  and  (ii)  these  the c o m p o n e n t  is t o o s m a l l a t t h e t u r n i n g ( o r r e f l e c t i o n )  the field  perturbations  w. p  d i s t i n c t f e a t u r e o f r e s o n a n c e a b s o r p t i o n is t h e d e p e n d e n c e o f t h e a b s o r p t i o n  angle  with  E V n ,  main  gradient  ,  ,  Co  are o n l y e x c i t e d b y density  =  have  e  density  (E  get  e6n  o n the  surface,  as  ,  (see  V - E =  are  the  density  Maxwell's  0  1  _ „  the  is  from  e ( i ) V - E + ( E - V ) c ( x )  in  critical  gradient  light  as  C  This  w h e n p-polarized  laser light to electron t h e r m a l  V-[ (*)E]  Now,  particular,  obliquely o n the density  can penetrate  electron  this  frequency.  field drives  e  fluctuations  =  tr  has a c o m p o n e n t paralel to the density g r a d i e n t , V n , the resulting charge seperation density  II:  of the  electric  field  point to effectively  fraction  parallel couple  to  the  energy  CHAPTER  LARGE EUECTRON PLASMA OSCILLATIONS  LIGHT AT ANGLE 6 TO KOfflAL  Figure IV-2  Schematic  REFLECTED U  S  E  R  LIGHT  representation of resonance absorption.  II:  11  CHAPTER into  the electrostatic  waves.  T h e turning point density n II-8)  "tr  As the  the angle  increases  magnitude  reduced.  tob e  field  7  [2.17]  C  n  which  law  1  = n rttCOS0.  the separation between  o f t h e electric  M a x i m u m  is d e t e r m i n e d f r o m Snell's  tT  and the dispersion relation (equation  II:  t r  and  n ,t  c a n penetrate  cr  increases.  Hence, for large  to the critical  surface  is  6  greatly  a b s o r p t i o n o f Pa 5 0 % o c c u r s a t s o m e i n t e r m e d i a t e a n g l e g i v e n b y  / e\  1/3  s i n 9 fa  where  °- [^-jr)  is t h e d e n s i t y g r a d i e n t s c a l e l e n g t h g i v e n b y  L  L  A n electrons.  =  [2.19]  n dz' K  a d v e r s e c o n s e q u e n c e o f r e s o n a n c e a b s o r p t i o n is t h e g e n e r a t i o n o f h o t o r e n e r g e t i c T h i s is d u e t o t h e p r e f e r e n t i a l h e a t i n g o f t h e e l e c t r o n s w i t h v e l o c i t i e s  to the phase velocity of the electrostatic wave.  Theoretical calculations  s u p r a t h e r m a l electrons c a n b e c h a r a c t e r i z e d b y a n effective  T  hot  where  [218]  8  II  is t h e l a s e r i n t e n s i t y  »  2  suggest that  [2.20]  050  ,  \L  these  temperature  W-^TJ^ihXL)  1.2 x  in W / c m  6 8  comparable  is t h e laser w a v e l e n g t h  in micron and T  C  is  the electron t h e r m a l t e m p e r a t u r e i n K e V . F o r t h e experimental conditions we consider this corresponds to a temperature  fa 1 K e V .  (iii) P a r a m e t r i c Processes i n P l a s m a s In  the large  regions  of underdense  plasmas  now being  generated  in  laser-target  e x p e r i m e n t s , v a r i o u s collective processes c a n p l a y a n i m p o r t a n t role i n t h e c o u p l i n g o f laser energy  to the target.  T h e f u n d a m e n t a l processes i n these  interactions  is t h e p a r a m e t r i c  CHAPTER excitation  of two  excited modes (anamolous) wave,  new  are  waves b y  purely  escape from  the  stimulated scattering of the  energy  strong  w h e r e WL  the  incident  (pump)  decay  E M  electromagnetic  process eventually  wave.  If  one  incident  the  E M  light  wave  to  the  and  w  faster  The  latter  2  which  strength  the  w  of the  T  yields  9.8  x  e  on  = 1 0  of  500 1  0  the  a  threshold  n  eV,  W / c m  e  =  for  2  the  10  2  could  be  through  waves,  conservation  of  =  k i  + k  [2.22]  L  2  the  laser  field  must  feed energy  into  for the laser  the  modes  field  the  These and  8 8  t  below  of oscillation.  as a f u n c t i o n of the p l a s m a p a r a m e t e r s  u  modes.  threshold will d e p e n d o n  natural  2  Also  waves  two  "pump"  k  conditions  the various instabilities occur.  given process the  d a m p i n g of the  ,  2  T h e frequency matching  "threshold intensity" any  , u> , k i  dissipation or d a m p i n g of these  8.8  x  1  intensities are  not  excited  little laser energy  but  3  W / c m of  1 0  1  3  10  x  for  of the  will reach the  c m  1  1 0  1  the  W / c m  expected to play because  2  -  3  for ,  typical  Z  =  parametric-decay  stability  instabilities  E M  k  intensities  4 x  2.2  laser  excited  a n d w a v e n u m b e r o f t h e l a s e r l i g h t a n d wi  the  instability,  typical  a loss m e c h a n i s m  an  [2-21]  For  two-plasmon-decay and  is  are  II-l.  Evaluation ,  excited modes  + u>2  thresholds can be calculated theoretically  namely  enhanced  wi  rate of energy  excited.  coupling and  given in Table  an  both  =  grow,  determines  are n o t  2  to  natural  requirement and  Ui  excited waves  than  to  If  UL  the region of p l a s m a densities for w h i c h  order for the  leads  wave.  requires  the frequencies a n d wave n u m b e r s of the excited waves.  in  (EM)  wave.  laser  a n d III a r e t h e f r e q u e n c y  will determine  of the  plasma and consequently become  coupling of  and momentum  incident  electrostatic,  absorption of the  it c a n  For  the  II:  2  5  W / c m  for the  2  used  strong  inverse  critical density  -  SOfim  our  role.  9.8  x  stimulated  Brillouin  in  a significant  L  instability,  stimulated are  11,  conditions  in  our  and  \  10  W / c m  3  R a m a n  scattering  experiments, T h e  1  experiment,  L  -  where the instability  2  for  scattering  instability.  laser-driven  parametric-decay  bremsstrahlung  0.532/zm  excited.  in-  Since plasma  instability  absorption only is  the  very  CHAPTER T A B L E  P a r t i a l list o f t h e  instabilities  name  which  II-l  can be driven by  process  laser light p r o p a g a t i n g in a  density  u>£, —• w  p e  + w,  at  a  n  e  ~ n  6.72  CT  instability  decay  scattering  Brillouin  n,  e  ,  w,  + w  w  pe  0  e  and  w,  ion acoustic wave  c  p e  p  (  !  + w,-  are in e V ,  L  represent  c  +w  tc  W£, -+ w ,  and  \L  —* u  WL,  scattering  w h e r e T,  p e  -+  L  at  n  at  n  at  n  ~  e  (l/4)n  c  r  10 T . ^ A2 ' 3  19  /  n  3  1  e  2  /  1 0  Z r  5  l O ^ L ^ ^ A ^  3  3  2  3 x  1  5/  <  e  ~  1  /  A ^  2  3  a  c m  -  3  , fim  the frequency  a n d scattered light  e  < (1/A)n  <  er  n  a n d /im  of the  wave,  e  x  7.5  er  x  1 0  1  2  T  <  ;  2  A ^  ' '  1  3  L  -  1  ( ^  respectively.  generated electron plasma  wave,  respectively.  II-l-B Energy Transport  In rather  laser-matter  t h a n the target  outer regions of the We  9  instability  R a m a n  w  w  2  ~  8 9  2  x  x L ~  two-plasmon-  plasma  threshold intensity W / c m  parametric-decay  II:  interactions surface.  Hence  incident  electron  transport,  laser  energy  is  deposited  in  the  corona  the mechanisms which transport the energy f r o m  p l a s m a corona to the  will consider three such energy  conduction, hot  the  ablation surface  transport  are  of considerable  importance.  mechanisms in this section: classical  and radiation  transport.  the  thermal  3  CHAPTER  II:  the heat  flux  (i) T h e r m a l c o n d u c t i o n The  classical theory  is g o v e r n e d b y F o u r i e r ' s  of thermal  conduction in a plasma assumes  law  q =  w h e r e K is t h e t h e r m a l c o n d u c t i v i t y . is d o m i n a t e d order.  by  the faster  T a k i n g this into  that  moving  account  v r  - K  T h e heat  flux,  electrons.  [2.23]  being a consequence of particle  T h e ion motion can be ignored  Spitzer calculated  the thermal  conductivity  motion,  to the  first  to be  [2.24]  where  is t h e  Z  electron LT  mean  free  ion charge  path  this  .  A , is m u c h  to  limit  flux  the heat  limit  suggest  /  that  laser  plasma  have  been  magnetic further  flux  lies  to g , t  experiments  fields  94  to  r  e  a  m  A t  ,„j.  Arguments  between  proposed  is t h e  assumption  the temperature  gradient  that  scale  flux  the  length,  gradients f o u n d i n laser generated  plasmas  may  exceed  —  [2.25]  F o r this r e a s o n it h a s b e c o m e c u s t o m a r y i n n u m e r i c a l  is u n c e r t a i n . /  result  defined b y  limit. flux  than  this  A s a consequence the calculated heat  H^treaming  w h e r e / is t h e  in  the large temperature  assumption invalid.  free-streaming limit  Inherent smaller  e  = | T / V 7 " |. H o w e v e r ,  often make the  average  0 . 1  4  2  suggests  account  using  and 0.6 /  4 3  ranges  for this  a n d ion acoustic  present  the appropriate  simple .  free-streaming  However,  from  9 5  .  This  clearly  of a  T w o  in the value  value  distribution  simulation  0.03 to 0.06.  discrepancy  turbulence  numerical  calculations  wide  for  functions variety  mechanisms  of /  remains  are an  the  of  which  self-generated area  open  to  investigations.  (ii) H o t electron t r a n s p o r t In to  the  our discussion of resonance  generation  of suprathermal  absorption  electrons.  we  indicated  T h e energy  h o w this  transport  process  mechanism  can of  lead these  CHAPTER e l e c t r o n s is p a r t i c u l a r l y the  m e a n free p a t h  c o m p l e x b e c a u s e o f their e x c e p t i o n a l l y l o n g m e a n free p a t h s .  scales  as  3  II: Since  5  [2.26]  Aire* In A n ' e  energetic electrons c a n penetrate pression.  A n accurate  be f o u n d in reference electron transport  ahead of the shock front  description o f this  a n d adversely  p h e n o m e n o n requires  [35]. I n t h e S u b - m i c r o n laser w a v e l e n g t h  affect t a r g e t  a kinetic  analysis  regime o f interest  com-  andcan here, h o t  c a n b e neglected.  (iii) Radiation transport For icant  the strongly-emitting  energy  transfer  consideration of this presented in section  ,high-Z  mechanism.  targets,  Unfortunately,  process requires  substantial  radiation like  transport  hot electron  numerical  represents  transport  modelling.  a  an  signif-  accurate  O n e s u c h m o d e l is  II-2-B.  II-l-C Equation of State in the Shock-Compressed Solid In laser-target tially  b y the local  interactions  the velocity  sound speed in the high  is c o n s i d e r a b l y h i g h e r t h a n o f the target  that  motion  respect  to the cold uncompressed material,  surface,  driven  p r e s s i o n w a v e is l a u n c h e d i n t o t h e t a r g e t speed  pressure  is p r o p o r t i o n a l  disturbance  densities,  thereby  front  (see F i g u r e  II-3).  The basic  behaviour  causing  faster  root  in regions  the density  between  region  2  .  7  This  of the ablation front. pressure,  of higher  perturbation  II-3(a). c,  a  from that  velocity  Hence  Initially,  However, yfp.  densities  to steepen  essen-  is s u p e r s o n i c  will b e f o r m e d .  of the density,  o f a c o m p r e s s e d s o l i d is d i s t i n c t  distinguishing feature  ablation  b y the ablation a n d a shock  a b l a t e d is d e t e r m i n e d  as depicted i n Figure  to the square  will propagate  lower  temperature  in the cold region ahead  inward  sound  of the material  into  with  a  com-  the local  Therefore,  than  the  the  i n those  a sharp  of  shock  of a compressed gas. T h e  t h e c o n d e n s e d a n d g a s e o u s s t a t e is t h e f o r m o f inter-  CHAPTER  F i g u r e II-3  Developement of  a  Shock  Front  II:  CHAPTER action  between  the  atoms.  In  a  gas  the  interaction  takes  place  mainly  through  collisions.  T h e r e s u l t i n g p r e s s u r e , b e i n g r e l a t e d t o m o m e n t u m t r a n s f e r , is o f t h e r m a l o r i g i n , P O n  the  other h a n d ,  atoms  n o n t h e r m a l (or elastic)  of solids can  Specifically,  quires pressures in excess of 100 M b a r  pressure  is o n l y  , which  9 6  strongly  through  atomic  forces.  =  p o s s i b l e if t h e  9  a compression ratio  o f e /a*  =  2  300 M b a r  T h e extreme range of pressure a n d temperature  this  features re-  that strong compression of  a p p l i e d p r e s s u r e is c o m p a r a b l e w i t h t h e  is m e a s u r e d i n u n i t s  is  of four in solid a l u m i n u m  . T h i s reflects the fact  6  nkT.  It  p r e s s u r e , w h i c h is a b s e n t i n g a s e s , t h a t d e t e r m i n e s t h e b a s i c  of shock-compressed solids.  solid materials  interact  II:  (at  Bohr  inner  radius)  atomic  .  achieved in laser-matter  interactions  i m p o s e s severe r e q u i r e m e n t s o n the e q u a t i o n of s t a t e . A suitable e q u a t i o n of state m u s t  take  into  well  account  the  as, q u a n t u m  A with  its  difference  effects  c o m m o n own  equation  ions  interaction energy  as  and  A n  tive interaction and  Kirzhnits  e  7  0  be  of electrons  In  particular,  ignored.  r{  the  included.  electrons  ions  However,  is t h e  e  and  electron gas.  with parallel  as t h e  incorporates  In in  the  like  an  comparable  possible solution to  this  gas  the to  problem  as t h e s u m o f k i n e t i c  and  In  or antiparallel  Thomas-Fermi-Dirac  quantum  corrections  to  spins t h r o u g h the  is t o  model. this  A  further  basic  model  Pauli  forces  Fermi use  a  Coulomb effec-  exclusion  improvement (referred  the  coulomb  the  and  each  and  Coulomb  compressed solid, be  systems  ideal  approach the  electron-ion can  A  as s e p e r a t e  behave this  target.  to  made as  the  model).  tabulated  interactions.  programs.  ions  i n t h e c o r o n a , as  i m p r o v e d v e r s i o n o f t h i s m o d e l i n c l u d e s e x c h a n g e effects ( t h a t is, t h e  Currently,  experimental  consider the  present  shock-compressed  which treats the electron energy  is k n o w n 3  in the  where  2  Thomas-Fermi-Kirzhnits  target  are  Ze /r i,  7  important  degenerate  should therefore  components.  by  of state.  a Fermi  Thomas-Fermi m o d e l  principle)  is t o  electrons  energy  and  which become  approach  electrons behave between  in ion and electron temperatures  equations  particular,  computed  of state  the  results  is  Sesame finding  represent 6 9  data  the  library  extensive  use  most which in  accurate is t h e  data  for  laser-  accumulation  hydrodynamic  of  simulation  CHAPTER  II-2  and  Medusa  Numerical Formulation in  Medusa  is p r i m a r i l y  thermodynamic  intense  laser b e a m .  velocity,  designed to model in one spatial  behaviour In this  of a single  model,  discussed  d u e to weak energy  are incorporated  into  fluid,  electrons  implying no charge separation.  istic t e m p e r a t u r e  II:  two temperature  a n d ions  However,  hydrodynamic  plasma irradiated  are a s s u m e d to have  by  the same  an  fluid  e a c h species m a i n t a i n s its o w n c h a r a c t e r -  coupling between  Medusa  dimension the  through  the two. T h e processes  the three  conservation  previously  equations.  T h e  f o r m t h e s e e q u a t i o n s t a k e is n o w p r e s e n t e d .  II-2-A E q u a t i o n s o f M o t i o n  The  m o t i o n o f t h e p l a s m a is g o v e r n e d b y t h e N a v i e r - S t o k e s  equation,  du p  which  is a  plasma  consequence  which  Tt  ~  =  of the conservation  j  a  defines the m o t i o n of the L a g r a n g i a n  t  the hydrodynamic  pressure  P  '  [ 2  of momentum.  j =u(r,t)  and  v  Here  coordinates  u  is t h e v e l o c i t y  according to  [2.28]  t  is d e f i n e d a s  e  ion pressure,  hand,  P,-,  the electron  behave  is c a l c u l a t e d  pressure,  as a n o n - d e g e n e r a t e  P  e  [2.29]  are a s s u m e d to behave  equation  of state  model  3  7  3 6  , can have  several  gas equation o f state.  forms.  gas equation  as a degenerate  o r a piecewise  f  assuming a n ideal  gas, a n ideal  electrons  2 7 ]  of the  P = F. + P + P.  The  -  analytical  If t h e e l e c t r o n s  of state  is u s e d .  gas o n e c a n select either  fit t o t h e q u a n t u m  O n the  other  are assumed If,  however,  to the  a  Thomas-Fermi  corrected  Thomas-Fermi  . S i n c e t h e i d e a l gas e q u a t i o n o f state is o n l y v a l i d for t e m p e r a t u r e s  less t h a n  lOev  CHAPTER and  densities  appropriate density  less  than  for solids.  1 g m / c m The  associated w i t h the  3  ,  the  quantum  pondermotive  corrected  Thomas-Fermi  ( r a d i a t i o n ) p r e s s u r e , Pf,  l a s e r b e a m , is g i v e n  ° *  b y  3  due  model  to the  is  it  can  adversely  produce  affects  laser  more  momentum  6  "crtt  T h i s p r e s s u r e c a n h a v e significant effects o n the d e n s i t y profile i n the c o r o n a r e g i o n . ically,  II:  local profile steepening  which  7  by  reducing the  p l a s m a scale  Speciflength  absorption.  II-2-B E n e r g y E q u a t i o n  A n  energy  e q u a t i o n of the  form  „  is u s e d f o r b o t h t h e  source  term  S  „  ions a n d electrons.  C v  T h e  dT  =  (  is g i v e n f o r t h e  ^  In  a  n  dp  n  terms  d  dV  „  of the  B  =  T  (  ions a n d electrons  Si = H i -  internal  ^  )  U = U(p,T)  energy  ,  [2.32]  r  respectively  as  K + Yi + Q [2.33]  S  where H of energy  represents between  the the  flow ions  and  is t h e  rate  of bremsstrahlung  Q  is t h e  rate  of viscous below  modifications  3 3  to  in  shock  M K S  + K + Y  e  of heat  J  summarized  = H  e  + J +  due to t h e r m a l  electrons;  Y  emission; X  heating.  units.  e  In  The  conduction ; K  is t h e r a t e o f  is t h e  rate  of thermonuclear  is  rate  of  the  Medusa  the  .  these  expressions for  H  e  exchange  energy  absorption of laser  expressions u s e d for  particular,  the original version of  X  various and  X  release;  light; terms  and are  represent  CHAPTER T h e heat  flow  term  is given b y the conventional  Fourier  relation  [2.34]  H = - V K V T  w h e r e K is the t h e r m a l conductivity.  Kf whereas  K  E  is m o r e  = 4.3 x l ( r  accurately n  e  r.-  given  1.955  =  T h e e x p r e s s i o n f o r K,- i s a d a p t e d f r o m S p i t z e r  1 2  5 / 2  b y  x 10~ r 9  4  e  (log A ) "  Z  and  M  the heat  = 1.24  / ^ -  1  (I )2  2  5  / (log A ) ~ 2  x 10  b y  7  T  3  3  ( Z  1  + I ) "  flux  t o the free s t r e a m i n g  to be  [2.35]  1  [2.36]  2  9  /  2  n7  1  /  2  Z-  ,  1  [2.37]  are the effective charge state a n d ion m a s s respectively.  Moreover,  Medusa  limits  limit  ( « ) m a »  = fn v kT  F  by  * * -  3 9  0  w h e r e l o g A is the C o u l o m b l o g a r i t h m g i v e n  A  1  II:  e  using a modified electron thermal  = «  e  m  a  x  V T ,  [2.38]  conductivity  <-^{ ir-)' l+  \  —( This harmonic mean  T h e energy  important  in high density  1  +  [2.39]  -1  7i£lf  | v r |  )  a p p r o a c h is c o m m o n t o m o s t s i m u l a t i o n c o d e s .  exchange term  K  The  "-mas /  =  0.59 x 10- n (T,- - T  thing t o note here regions.  is g i v e n b y  8  e  is the density  e  ) T ~ * M -  l  Z  2  scaling which  log A.  inevitably  [2.40]  l e a d s t o T,- =  T  e  CHAPTER Absorption critical by  density.  the  of laser  The  light  is  rate of laser  a s s u m e d to light  occur via  a b s o r p t i o n is r e l a t e d  Moreover,  is  $L  related to  the  laser intensity  9 {r,t)  =  L  at  J.R.  i  A £ ( l - B ) / t¥ 2  G  account  is  it is c l e a r  Stallcop  the  Gaunt  factor,  B  — t o  1 2  and  n /n , .  =  e  cr  The  t  K.W.  _  }  Zy/Z  the  results  of  Karzas  and  Latter  4  .  6  that for h i g h temperature  plasmas  Medusa  K  Gaunt  k  Billman  a p p r o a c h is a d e q u a t e  generated  plasmas  achieve  in the  continuum radiation emitted by by  the  C o u l o m b  field  Energy  factor,  which  [2.43] is  is  introduced  expressions an  - 3  ''  2  J  is a d a p t e d  from  D.J.  J  Rose  of several  =  -8.5  x  Clarke  inverse  first  dumping  overdense  we  zone.  consider.  h u n d r e d electron-volts.  In  e l e c t r o n s , as a result  Medusa  the  In  4  8  to  de-  Maxwellian  be  [2.44]  x  a  expression neglects other forms of radiation energy  of  bremsstrahlung  V0r n T$~Z*M- . lA  a  loss o c c u r s i n t h e f o r m of b r e m s s t r a h l u n g  charged particles.  and M .  over  scaling of  the classical  r a d i a t i o n e m i t t e d b y t h e e l e c t r o n s is a s s u m e d t o e s c a p e f r o m t h e p l a s m a . F o r a plasma,  obtained  improvement  the T,.  to  ineffective.  charged particles, mainly  of other  by  R  regime of laser intensities  temperatures  this range m a t t e r c a n b e completely ionized.  flections  ,is g i v e n  6  2.43  (for h i g h laser intensity), quite  4  models the anomalous absorption processes discussed previously by  crude  Laser  by  Ro  k  a fraction of the laser p o w e r reaching the critical density layer into the rather  r =  ,  ZGf  Expression  bremsstrahlung absorption mechanism can become  This  t)  [2.42]  classical a b s o r p t i o n coefficent p r e s e n t e d in s e c t i o n II-l-A. F r o m  , i.e.  the  $i,(r,  L  f o r q u a n t u m : m e c h a n i c a l e f f e c t s , is c a l c u l a t e d f r o m a n a l y t i c a l  fitting  This  intensity  r)]9 {Ro,t).  2  the  laser  the p l a s m a b o u n d a r y  13.510 JT  a =  by  the  to  or  exp[-a(i2o -  a b s o r p t i o n coefficient, a d a p t e d f r o m  where  to  bremsstrahlung up  expression  p  T h e  inverse  II:  s u c h as t h a t  generated by  bound-  CHAPTER bound loss  and by  4 9  free-bound  as m u c h as  transitions.  a factor  In  some  cases  this  can  underestimate  the  II:  radiation  of 10.  V i s c o u s s h o c k h e a t i n g is i n c l u d e d i n t h e  form  dV Q  w h e r e q is t h e V  is t h e  The  the energy  simulations of planar  ,  ^ r ,  v i s c o u s p r e s s u r e , as d e n n e d b y  specific v o l u m e .  Finally,  =  R.D.  Richtmeyer  reason for this t e r m  and  K.W.  M o r t o n  is d e s c r i b e d i n t h e f o l l o w i n g  released t h r o u g h thermonuclear reactions  aluminum  ,  [2.45]  Y  was  6  0  ,  and  section.  neglected in  our  targets.  II-2-C M e t h o d of Solution In t h e n u m e r i c a l s o l u t i o n o f e q u a t i o n s [2.19] a n d [2.25], t h e m e t h o d o f employed. the  e q u a t i o n is s o l v e d  order  to  a shock to a few  avoid  the  stability  surrounding  relations across the shock.  problems  finite  The  inherent  in  the  methods.  Furthermore,  variable.  They  (minimum  that  the  limit are  (which  fractional  than  travel  the  effectively  density  10%)  .  the  be larger  computuational  (typically  Medusa  to insure n u m e r i c a l by  at  time  second order  can be f o u n d in the  most  0  whereas  the  step.  sound  The  the  space  time  speed)  time  step  can  an  aspect  and  time.  to note A  condition  5  0  the  that  propagate  through  less t h a n  complete #  the  implies  by  are  that  one  cell  demanding  some  numerical  listing of this 99.  code  demands  this  restricted  reducing difference  Physically,  is t h a t  p l a s m a group internal lab report  finite  steps used by  zone be  in  Rankine-Hugoniot  by explicit  is f u r t h e r  change of any  important  in b o t h  stability,  local sound speed.  local  equation,  of the shock while  Courant-Friedrichs-Lewy  or temperature  The  momentum  difference zones while preserving the  T h i s preserves the essential features  restricted  c e l l she)/St  disturbance one  are  5  artificial viscous pressure dissipates energy  the gradients across the front to values that allow the treatment  within  5  explicitly.  a r t i f i c i a l v i s c o u s p r e s s u r e is i n t r o d u c e d .  no  differences '  T h e e n e r g y e q u a t i o n is s o l v e d i m p l i c i t l y b y a C r a n k - N i c h o l s o n s c h e m e  momentum  In  finite  specified schemes  version  of  CHAPTER II-3  Recent A d d i t i o n s  The  non-local  most  significant  thermodynamic  oped by D. Salzmann  modifications to  radiation  at t h e University  The a t w o level density  original version of  main  part  Medusa  a n d radiation transport calculations devel-  ofAlberta.  These routines, which  we n o w describe,  i n calculating theaverage ionization, internal  calculates  a n average  equilibrium  energy  8 4  level o f i o n i z a t i o n , ^ , b y u s i n g  . However,  with the wide variations  f o u n d i n l a s e r - p r o d u c e d p l a s m a s it is d o u b t f u l t h a t  in  such a model  It w a s f o r t h i s r e a s o n t h a t a t i m e i n d e p e n d e n t  of the n o n - L T E  a n d the total  Z, 2  densities o f 1 0 lations.  1  8  - 1 0  2  4  radiation c m  -  3  enough so that  easily  n o n - L T E  hasbeen  4 9  .  for electron  giving  temperatures  the mean  values  c a n adjust  In o u r long pulse  T h e non-LTE  physics  by Salzmann  themselves  (2 n s F W H M )  is i n c o r p o r a t e d  a n dK r u m b e i n  5  1  t o these  Medusa  for aluminum  interpo-  a n di o n densities changes  experiments  in  Z  of 15-1000 ev a n d i o n  if t h e rate o f c h a n g e o f t e m p e r a t u r e  t h e ionization states  calculated  is a s e t o f d a t a  . T h erest o f t h e r o u t i n e s i m p l y p e r f o r m s t h e r e q u i r e d  approximation).  satisfied  package  energy  T h i s p r o c e d u r e is v a l i d o n l y  independent  which  the code  was required in the simulations.  The  is s l o w  incorporating into  Equilibrium  approximation to a Saha  a n dtemperature  routine  is  1  involved  spectrum.  c a n b e valid over t h eentire d o m a i n .  and  5  Non-Loco/ Thermodynamic  II-3-A  Medusa  (non-LTE)  equilibrium  m a k e extensive use o f tabulated d a t a and  II:  this  through  (time-  condition the data  a n dcarbon. T h e  calculations were based o n the assumption that the p l a s m a w a s i n a quasi-steady-state a n d included the following  1.  electron-impact  2.  radiative  processes:  ionization - ionization t h r o u g h electron-ion collisions.  recombination - recombination  of a n electron  a n dan ionwith  associated  photon emission.  3.  dielectronic  recombination  -  dominant  at high  temperatures  a n d low densities  it  CHAPTER consists bound  4.  of radiationless  recombination of an  e l e c t r o n is e x c i t e d i n t o a h i g h e r  three b o d y another  recombination -  i o n (or  electron  and  an  ion, while  an  II:  atomic-  level.  recombination of an electron  and  an  ion in presence  of  electron).  T h e total radiation energy, besides bremsstrahlung radiation, n o w includes the released t h r o u g h f r e e - b o u n d a n d b o u n d - b o u n d (line)  energy  transitions.  II-S-B R a d i a t i o n T r a n s p o r t  Radiative laser-target  processes  interaction.  and  The  radiation  hot,  transport  dense  plasmas  play  an  important  produced emit  and  role  in  the  reabsorb  t h r o u g h v a r i o u s m e c h a n i s m s ( b o u n d - b o u n d , b o u n d - f r e e a n d free-free e l e c t r o n i c This  radiation  represents  hydrodynamics.  First  a significant  energy  transfer  of all, r a d i a t i o n transport  mechanism  In the case of h i g h Z  driven  ablation  to  driven  ablation.  '  5  3  as  opposed  Furthermore,  radiation  c o m p r e s s i o n p h a s e , t h a t is, p r e h e a t of  the  target  core.  W i t h  the  the  goal  more  of  c o u l d lead to target  investigating  W h e n r a d i a t i o n p r o p a g a t e s a d i s t a n c e ds, absorptions along the p a t h .  spectral intensity  I  v  in Eulerian  c  j„  and  k  v  are  electron  thermal  energy  radiation  conduction  heating preceeding the  various  a d d e d to  radiative  Medusa  main  compression  processes  the  .  the intensity will be increased b y  emissions the  the  =ju  -  [2.46]  K h  form, 1  where  the  is  as  alternatively  to  affect  T h u s the equation of radiative transfer for  ^ or  these  was  transitions).  strongly  . T h i s c o u l d a d v e r s e l y affect the u l t i m a t e  5 4  radiation  targets, this c o u l d lead to  conventional  following simplified m o d e l of radiation transport  and reduced by  can  can contribute significantly  transfered to the ablation surface. 5 2  and  overall  volume  dl„ „.  at  •  dl, „  emission  as  = j u - k  and  v  I  v  [2.47]  ,  absorption coefficients  respectively  5 5  '  5  6  .  CHAPTER Although,  in principle  this  equation  can  be  solved numerically  p u t e r time m a k e s several simplifications necessary. emission or  scattering.  r e g i o n s as i l l u s t r a t e d as  in Figure  a consequence only  sorbs.  J „  ablation  differs b y  we  II-4. O n  that  Region  the  other  a factor  of  1000.  we  can  seperate  space  finding  the  adjacent  most  cases  this  into  thin to  h a n d , r e g i o n 2 is o p t i c a l l y  In  increase  F i r s t , we neglect a n y f o r m of  1 is c o n s i d e r e d o p t i c a l l y  is c a l c u l a t e d b y  one d i m e n s i o n the intensity element  '1'  I (r\)  is g i v e n  v  com-  stimulated  two  distinct  radiation  thick  and  cells in w h i c h  boundary  in  only  the  coincides  and ab-  emitted with  the  /„(r ; r ) 2  at p l a s m a element  t  '2' d u e to radiation  from  by  4(»"2;ri) which  assume  large  front.  In plasma  emits.  ro(i/)  The boundary  intensity,  Secondly,  the  II:  =  J „ ( r i ) e x p ( -  =  /  k„dr),  /  becomes  t  /  (r  1  I  )exp(-  k„dr),  [2.48]  Jr  0  since  region  radiation  at  1 does not  absorb.  a frequency  in  v  The  corresponding energy  a p e r i o d of time  v  2  r i  ) =  —  total  absorbed energy  E OT{r )= T  where the equation  assumption that [2.50] c o n t i n u u m  is g i v e n  the  n o n - L T E  20  strongest  results  lines  was  tabulated by  dr \ •/()  also  [2.49]  v  dvE {r \r ),  x  ^0  v  2  from  15 t o  included.  Salzmann  and  '  x  is i n c l u d e d .  is a c c o u n t e d f o r b y  20 segments e x t e n d i n g in p h o t o n energy from  k dr).  /  by  region 1 radiates  radiation  to  Jr,  2  only  '2' due  [Ti+br A r / „ ( r , . ) e x p ( -  c  Therefore, the  element  is  At  At E (r ;  absorbed by  The  the numerical solution  dividing the  10000 ev values  K r u m b e i n  In  5  1  .  frequency  . Furthermore, for  [2.50]  I {r{) v  are  line  taken  space  to  into  radiation from  the  CHAPTER  TT  -7-  CORONA  / / / /  / / / / /  TARGET  r (v) G  ELEMENT  Figure  II-4  Important  1  ELEMENT  regions in radiation transport  calculations.  2  II:  27  CHAPTER  II:  II-2-C Post-Processor In this c o n t e x t t h e t e r m p o s t - p r o c e s s o r refers to a p r o g r a m d e s i g n e d s p e c i f i c a l l y to cess a n d m a n i p u l a t e many  quantities  of interest  plasma parameters computer  time  the results p r o d u c e d b y  s u c h as e m i t t e d r a d i a t i o n s p e c t r u m  o b t a i n e d f r o m simulation results.  is n o t  needlessly  interactive post-processor was  The specified bilities.  post-processor now  time These  3-dimensional  as  a simulation program.  well  range  as  the  from  increased  with  The  Using a post-processor  can be calculated from  advantage  o f t h i s m e t h o d is  optioned calculations.  For  this  the that  reason  an  developed.  available total  is c a p a b l e  radiation  generating  simple  plots, a n e x a m p l e of w h i c h  of evaluating  energy. one  It  also has  the  extensive  dimensional plots  is g i v e n i n F i g u r e  II-5.  X-ray  to  spectrum graphics  more  incorporating other features  relatively  Appendix A  straightforward.  this post-processor c a n b e f o u n d in the p l a s m a g r o u p internal  lab  A  #  a  capa-  summarizes  complete  report  at  sophisticated  the c o m m a n d language recognized by the post-processor. T h e m o d u l a r f o r m of the should make  ac-  101.  program listing  of  CHAPTER  F i g u r e II-5  Target  density  as f u n c t i o n of t i m e  and  space.  II:  29  CHAPTER  III:  C H A P T E R III  MASS ABLATION RATE AND ABLATION PRESSURE  A  knowledge  w i t h laser-driven fusion. the a  of themass  ablation  Specifically,  and  is essential  rate,  and  m,  for evaluating  ablation  efficient  are i m p o r t a n t  pressure,  t h efeasibility  a c c u r a t e m e a s u r e m e n t s o fthe laser intensity  ablation parameters  stable  ablation  fuel  pellet.  Moreover,  these  u s e d t o v e r i f y s o m e o ft h e m o r e f u n d a m e n t a l a s p e c t s o f l a s e r - t a r g e t the existence o fstrong heat pressure  with  shorter  flux  a  o f inertial  and wavelength  i n determining a nirradiance  implosion o f the  P bi,  associated confinement scalings o f  regime consistent measurements  These  twoconsiderations  can be  interaction, for e x a m p l e ,  i n h i b i t i o n a n d theoretical predictions o fincreased  wavelengths.  with  have  stimulated  ablation  numerous  t h e o r e t i c a l a n d e x p e r i m e n t a l i n v e s t i g a t i o n s i n recent years, i n c l u d i n g a series of e x p e r i m e n t s performed at theUniversity  In t h e  first  ofBritish  scaling o f the  0.53/xm is p r e s e n t e d . two  laser  intensities  scaling laws, the  III-l  7  .  ablation  interactions using  pressure  and  mass  A l s o g i v e n is t h e w a v e l e n g t h 5.0 x 1 0  previously  1  2  and  2.6x 1 0  1  3  Medusa ablation  m .  and  P hi a  obtained  In particular, the  rate  at a laser  through  calculated  wavelength of  scaling o fthe ablation parameters  W / c m  2  .  In section  obtained using ion ablation measurements,  scaling laws a r es u m m a r i z e d a n d  state analytical  5  p a r t of this chapter we present the values of  detailed simulations of laser-target intensity  C o l u m b i a  at the  III-2 t h e e x p e r i m e n t a l a r ep r e s e n t e d .  c o m p a r e d w i t h t h eresults p r e d i c t e d t h r o u g h  Finally, steady  models.  N u m e r i c a l S i m u l a t i o n s using  Medusa  T h e n u m e r i c a l simulations described in this section were p e r f o r m e d w i t h the  Medusa  CHAPTER hydrocode now  as described i n chapter  II.  T h eimportant  S i m u l a t i o n  In trated  P a r a m e t e r s  o r d e r t o best d u p l i c a t e t h e e x p e r i m e n t a l c o n d i t i o n s , a trianglular pulse, as illus-  in Figure  III-l, w a s u s e d .  T h ea b s o r b e d laser intensity,  *a  where  is t h e a b s o r b e d laser e n e r g y  E  a  $  50/im  aluminum  foil  t o t a l o f 4/xm w e r e o f u n i f o r m w i d t h . width  ratio of 0.977 between  p e runit  [3.1]  area  a n d TL  o f 200 variable-size cells.  is t h e F W H M  First  i n section  of the pulse  III-2.  F o rnumerical T h e first  purposes, the  7 0 cells o c c u p y i n g a  adjacent  cells (see F i g u r e  III-2).  In this way,t h e thinnest  o f all, it m a i n t a i n e d h i g h r e s o l u t i o n i n t h e a b l a t i o n r e g i o n . S e c o n d l y ,  The  fluctuations  quantum  gives rise t o a v e r y than  in thehydrodynamic  corrected  ( w l x 1 0  _  3  having  could  lead  quantities.  T h o m a s - F e r m i equation o f state  lowpressure  cell  T h i s specific configuration w a schosen f o r t w o  a g r a d u a l increase i n cell size r e d u c e d a n y artificial i m p e d a n c e m i s m a t c h w h i c h to substantial  (2  T h e r e m a i n i n g 130 cells were o f v a r i a b l e size w i t h a cell  m a t c h e d t o t h e cell size o f the first z o n e .  reasons.  , is g i v e n b y  TL  w a s c o n s i d e r e d as t h e target.  50/xm foil w a s d i v i d e d into a total  a  = ^  T h e r e a s o n e x p r e s s i o n [3.1] w a s u s e d w i l l b e c o m e e v i d e n t  A  was  c o m m o n t o all runs are  summarized.  III-l-A  ns).  parameters  III:  M b a r )  was used throughout.  near solid density  at temperatures  It less  5 e V.  H e a t t r a n s p o r t w a s i n h i b i t e d b y a flux l i m i t o f 0 . 0 4 . arbitrarily  to agree  with  the standard  Moreover,  f o r t h e intensities  /  a n d pulse  w  T h i s value for / was chosen rather  0.03 — 0.06 u s e d i n n u m e r i c a l  lengths  we considered, increasing  simulations /  6 1  .  to 0.06 h a d  negligible effects o n t h e results.  E l e c t r o n a n d i o n t e m p e r a t u r e s were setinitially t o 5 x 1 0 high temperature  4  K ( w  5eV).  This  abnormally  is r e q u i r e d t o m a i n t a i n a sufficient i n i t i a l e l e c t r o n d e n s i t y t o e n a b l e  laser  CHAPTER  4.0ns tm ie  2.0 ns F i g u r e  III-l  Laser  absorption.  T h e n e e d for this  processes by in  excess  the 5  e V  which  of  actual  1 0  1  W / c m  2  temperature  5eV  implies  In mental  the  at  tion  process  initial  ionization can  involved. the  than  to  conditions, a  purely  2  onset  the  internal  addition  This  " p r i m i n g " ionization stems from the current uncertainty in  of irradiation  ad hoc  inverse 5%  Fermi  energy  at  considered  and pressure  of the  higher  a  level  is s t a n d a r d  temperature  energy  prescription provided  occurring  be  is k n o w n , h o w e v e r ,  that  instantaneous  in most  for a l u m i n u m  are  weakly  a means  intensities.  at  at  intensities  regardless  inverse  with 3  a 5  .  This  then  temperature.  dominates  critical  of  hydrodynamics  solid densities.  density  of a p p r o x i m a t i n g the  W h e n  the  simulation programs  dependent on  absorption, which remaining  at  of ionization consistent  introduces no significant error in the  bremsstrahlung  d u m p  It  Therefore, having  this initial temperature  is l o w e r  that  simulations.  initial laser ionization occurs.  mechanism  Furthermore, since  pulse used in  III:  for was  our  employed.  resonant  bremsstrahlung  is  experi-  absorp-  dominant,  CHAPTER  38  III:  -JS-  LASER  •• •  ••• -Ir-  70 eel Is _ J  1 3 0 cells  f c  4  46  F i g u r e IH-2  energy  was  when  further  electrons, imental  zoning used in the  s o u r c e is i n s i g n i f i c a n t b e c a u s e  However, It  Numerical  as  resonant assumed  o p p o s e d to  evidence  parameters,  which  5%  absorption that  the  suggests pertain  very  few  mainly  simulations.  of the energy  is d o m i n a n t ,  energy  generating  computer  a  electrons.  fast  electrons  to numerical  r e a c h i n g c r i t i c a l is a s m a l l  3 0 %  d e p o s i t i e d at  fast  Aim  n  c r i t  This arc  d u m p  may  went  choice  be  more  into heating was  generated.  considerations, are  made  The  quantity.  realistic the  because  remaining  discussed in  6 -  .  thermal exper-  Medusa  Appendix  A.  III-4-B C a l c u l a t e d Intensity S c a l i n g of  T h e  functional dependence of  m  m and  and  Pabi  P*u  o n laser intensity  was  investigated  at  a  CHAPTER laser wavelength  o f \L  = 0 . 5 3 / i m . T h e results are s u m m a r i z e d i n F i g u r e IH-3.  The  III:  ablation  pressure was c a l c u l a t e d b y a v e r a g i n g the pressure i n the cell adjacent t o the s t a g n a t i o n p o i n t over was by  a time  period,  r jj a  chosen t o agree calculating  = 2.7ns,  centered  at t h e laser peak.  with theexperimental value.  t h e total  mass  ablated  and  T h e  7.2 x 1 0  =  ( ^ 3 ) ° '  4  5  scaling  gm/cm -sec  4  value of r  a  n  mass ablation rate was determined  dividing b y thesame  b e s t fit t o t h e s i m u l a t i o n r e s u l t s y i e l d e d t h e i n t e n s i t y  m  This particular  time. T h e  lawu:  ( A  2  characteristic  L  = 0.53jim)  [3.2]  and  Pabi =  ni-l-C  l-47(-j3)  was  also u s e d t o investigate  laser intensities o f 5 x 1 0  1  and  2  2.6x 1 0  III-5 y i e l d t h e e m p i r i c a l s c a l i n g  3.81  1  3  the  2  .  The  x 10 A£ -  3  9  g/cm -s  for  $  m  = 7.19 x 1 0 A £ -  4  9  g/cm -s  for  $  4  0  dependence of  m  and  Pu  results presented i n Figures  a  at  III-4  laws:  =  0  [3.3]  0  wavelength  W / c m  0.53/im).  P J,J  m  4  =  L  C a l c u l a t e d wavelength S c a l i n g o f m a n d  Medusa  and  {X  M b a r  2  2  a  a  = 5.0x 1 0  1  2  W / c m  2  [3.4a]  = 2.6x 1 0  1  3  W / c m  2  [3.46]  and  Pau  = 0.67A£ -  Pau  =  0  2 . 6 4 A £  0  1 8  2  9  M b a r  for  $  M b a r  for  $  a  a  = 5.0 x 1 0  1  2  W / c m  2  [3.5a]  = 2.6x 1 0  1  3  W / c m  2  [3.56]  CHAPTER  SIMULATION RESULTS \ = 0 . 5 5 in  in in < 0.1  *  ABSORBED  F i g u r e  III-S  Calculated intensity  INTENSITY  scalings of  10  m  and  13  < W/cm ) 2  P bi a  III:  CHAPTER  • *. • *.  =  2.6 x  1 0 "  =  5.0 x  1 0  1  2  W / c m  2  W / c m  2  cj ID  o £ *>  <  •  o  < m <  to in <  0.2  0.3 WAVELENGTH  F i g u r e  HI-4  OA  0.5  (jjm)  Calculated wavelength scaling of mass  ablation  rate.  III:  36  CHAPTER  K •  *  •  * .  a  =  2.6 x  1 0  1  3  W / c m  2  =  5.0 x  1 0  1  2  W / c m  2  -•  Ul  z> in UJ  z  o  0.6-1  Q2  0.3 WAVELENGTH  F i g u r e  III-5  Calculated wavelength  OA  0.5  (jjm)  scaling of ablation pressure.  III:  37  CHAPTER  III-2  Experimental Results In  a  III:  this section the experimental m e a s u r e m e n t s  brief description of the  laser  facility  and  the  detailed discussion c a n be f o u n d i n reference  of  m  and  experimental  are p r e s e n t e d .  Pu a  techniques  u s e d is  First,  given.  A  [55].  III-2-A Ion Expansion Measurements The iments  experiments  Group*  laser,  when  fim),  third  ergies  using  used  Quantel  in conjunction  (0.35  of 6  a  described here  and  fim)  , 2 and  1.0  performed  neodymium-glass with various  fourth  Joules  were  harmonic  respectively.  laser  harmonic  (0.27 In  fim)  order  by  the  sub-micron  system,  NG-34  crystals,  can  light  with  Laser  (figure  deliver  maximum  to suppress u n c o n v e r t e d  III-6).The  second  to the  target  x  showed  time-integrated on  target  was  introduce  A n ion  spatial  by  fluctuation  array  energy  irradiated and  a  modulations  (4  fim  showed  modulations  of  <  changing  in the  velocity  target.  the  E(0),  the  measured  mass  laser  focal spot  6 9  respectively  From  T i m e resolved (30 psec  intensity  of 7 ion c a l o r i m e t e r s  and  energy,  at a n i n c i d e n t a n g l e o f 1 0 ° .  measurements varied  a  required  chamber.  50 /im (thickness),  measurements  en-  laser light,  T h e laser b e a m was f o c u s s e d w i t h f/10 optics onto a l u m i n u m foils, typically 15 m m  (0.53  on-target  m i n i m u m o f 3 d i e l e c t r i c m i r r o r s w i t h r e j e c t i o n r a t i o s o f 10:1 w e r e u s e d t o d i r e c t t h e laser b e a m  Exper-  area, the  the  angular  10%.  p u m p i n g energy.  The  of  <  Although  this  cups  6  0  distributions  of the  from  the  mean  ablation rate a n d ablation pressure can be  J[2E{0)/(v{9)) ]2xsm$d9  whereas  irradiance  method  can  negligible.  were u s e d to r e m o t e l y  expanding plasma  x  resolution)  3 0 %  incident  effects were f o u n d to b e  and 7 Faraday of  resolution)  15 m m  front  monitor  side  ion velocity,  of  the  (v(6)),  calculated,  2  [3.6]  TO = Pabl =  *  A .  N g  D.  Pasini,  P.  J[2E(9)/{v{0))]2wcos0sm$d9  Celliers, D.  Parfeniuk  a n d L.  [3.7]  D a  Silva  CHAPTER  F i g u r e  III-6  NG-34  Laser  System.  divisions 500 ps).  T h e photograph shows  a typical  laser pulse  III:  (horizontal  where  is t h e  AM  m e a n ion velocity we  took  cups.  ablation is b e s t equal  (v(6)).to  This  was  area  and  r tj a  is  a  was  incident  ablation  given by determining the ion velocity the  velocity  at  peak  ion  as  p  obtained  T . Goldsack  D  2  2  The  Although  the  2  from  , v  2  p  f(v),  Faraday  w  0.9(v(6))  w h e n a c o n s t a n t s t a t e o f i o n i z a t i o n is a s s u m e d .  a p p r o x i m a t e d b y the area of the laser focal spot, r ( * ~ " " ) , energy.  time.  III:  distribution function,  current,v ,  c o n s i d e r e d sufficient s i n c e , as c o n c l u d e d b y  i n d e p e n d e n t of intensity or laser wavelength  A f,i  a characteristic  CHAPTER  corresponding value of Z?,  p o t  =  was  SOfim  containing 9 0 % of  determined from  the  spatially  a n d t e m p o r a l l y r e s o l v e d m e a s u r e m e n t s o f t h e i n t e n s i t y d i s t r i b u t i o n at t h e f o c a l s p o t u s i n g a streak by was  the  camera. full  A  width  t y p i c a l i n t e n s i t y d i s t r i b u t i o n is s h o w n i n F i g u r e  IH-7.  1/e  (7/9)  2.7 n s e c i n o u r  amplitude  of the  laser p o w e r  taken  to  a  was  power  ik  estimated 2  4  .  This  experiments.  IH-2-B M e a s u r e d Intensity and Wavelength Scaling of  Ablation  the  r bi  m e a s u r e m e n t s p e r f o r m e d at  the following empirical scaling  the  three  m and  available  Pu a  laser wavelengths  yielded  laws:  [3.8a]  [3.86]  [3.8c]  and M b a r  for  M b a r  for  X  L  = 0.265 tim.  [3.9a]  [3.96]  CHAPTER  X - C O O R D  F i g u r e III-7 Focal spot image at best focus  m i c r o n  III:  CHAPTER  ( The  a b s o r b e d intensity,  $  $  \0.78 M b a r  the  a  cr  absorption fraction  equations  P bi a  energy,  (> 85%).  [3.8] a n d [3.9].  More  is f o u n d t o b e a f u n c t i o n  theories  ~  2 4  illustrate against and  is t h e i n c i d e n t  Ei ,  2  8  in which  at absorbed  X  L  III-9 r e s p e c t i v e l y .  whereas  Ill-3  Pu a  varied  flux  from  L  = 0.532 i i m  [3.9c]  accurately, o f laser and  however,  intensity.  2  34  to  A^  0 5 7  (2.0  nsec)  values 1  2  a n d n b, is a  scaling laws c a n b e derived dependence of  t o steady-state  scalings arecompletely  , 6.6x 1 0  observed wavelength 0  pulse length  is c o n t r a r y  experimental 1  3.10  thewavelength  This  wavelength  o f 2.6 x 1 0  A^ '  nab.,  is t h e effective  dependences,  The  \  In general, wavelength  intensity  the wavelength  for  , w a staken as  a  $ a = ~.  where  III:  of  a n d1 0  m 1  3  m a n d  ablation  independent. T o  a n d  W / c m  from  2  scaling o f m varied from  Pn a  are plotted  i n Figures  A£  1 1 5  to  III-8  A^ ' 1  37  .  Comparison of Scalings Obtained from Simulations, Experiments, and Analytical Models.  T h e scaling laws for laser-driven ablation c a n b eclosely a p p r o x i m a t e d b y the  general  form :  m = AQZXl"  [3.11]  and  P  T h e  values  of  A,a,8,B,i,  and  6  = B*Z\i  [3.12]  6  abl  we o b t a i n e d are  presented i n Table  III-l a l o n g w i t h t h e  CHAPTER  2  1 2  ~ in  o 2.6x10W/cnrT,  41  •I  1  o  x-137 X " L  • 6.6 x 1 L ? W / c m . X * ^ 2  5  o 1 x 10W/W, A " L  Ixl r— <  i, K \  o CD <  CO to  <  .8  .6  A  .15  1  I .6  WAVELENGTH (pm)  F i g u r e  III-8  Measured wavelength  scaling of mass  ablation  rate.  I  1 l  8  1.0  III:  43  CHAPTER  8  °2£x10 W/W, • £6x10 W/cm . A' °' 2  4  0  L  <6  1 x 10 W/cm , A* 3  2  L  a52  1  .8 .15  •  i .6  WAVELENGTH (Mm)  F i g u r e  IH-9  M e a s u r e d wavelength scaling of ablation pressure.  i  i .8  i 1.0  III:  44  CHAPTER values  predicted through steady  state  analytical  models  2  4  III:  .  Table III-l  General  Scaling  L a w  a  A  Parameters  B  /?  7  6  (Mbar)  g/cm-s)  (10* Simulation  3.4  0.54  0.39-0.49  1.3  0.80  0.18-0.29  Experimental  5.5  0.55-0.72  1.15-1.37  2.0  0.78-0.92  0.34-0.57  Analytical  3.2  5/9  4/9  0.6  7/9  2/9  the various  intensity  where $  is i n 1 0  a  From scalings  W / c m  a n d Ax, is i n  2  III-1,  i t is e v i d e n t  are all in reasonable  Pn a  exists  in the wavelength  s c a l i n g is s i g n i f i c a n t l y  Interestingly,  fim.  summarized in Table  a n d  m  discrepancy  wavelength  agreement.  scalings.  stronger than  that  O n the other  In particular,  the  scalings  scaled more  of mass  weakly  ablation  w i t h laser  hand,  either the simulation o r analytical  rate  a n d ablation pressure.  wavelength  at lower  irradiances.  fore  A t l o w laser intensities, total  reaching  simulations. as  would  the  where  pressure  hypothesis. sure  Thus  peak  shorter  A  f o r r» ,t. c r  long scale  n n, CT  T h e ablation p a This was a  This  independent  o f t h e laser  wavelength  pulse)  laser  region.  effect  is t h a t  This  was clearly  energy  absorption  is p a r t i c u l a r l y  length plasmas  we observe  direct  wavelength  absorption occured in the underdense plasma be-  at m a x i m u m  as a f u n c t i o n o f t i m e  W h a t  is e f f e t i v e l y  density,  the density  b e t h e case  experiments ablation  the critical  results.  dependance  consequence of t h e strong inverse b r e m s s t r a h l u n g absorption f o rt h es u b - m i c r o n laser light.  con-  experimental  b o t h t h e s i m u l a t i o n a n de x p e r i m e n t a l r e s u l t s s h o w e d a n i n t e n s i t y  in the wavelength rameters  3  the results  of both  siderable  1  c a n develop.  demonstrated n o longer  important Figure  scaled  in long  HI-10w h i c h  Medusa  in  as A ^  laser  pulse  shows the  f o r Ax, = 0 . 5 3 / x m a n d Ax, = 0 . 2 7 f i m , s u p p o r t s during  of wavelength.  a significant  low intensity However,  increase  irradiation  at h i g h  the ablation  intensities  in ablation pressure  2  this pres-  (specifically  at  is o b s e r v e d f o r t h e  pulse.  considerable discrepancy i n the magnitudes of  E x p e r i m e n t s p e r f o r m e d at t h e University  of Rochester  m (A)  a n d  P ti  (B)  a  using a different  as d o o u r s i m u l a t i o n results, t h a t t h e m e a s u r e d m a g n i t u d e o f m a n d P  0  is also  m e t h o d  6  4  evident. suggest,  n are a factor of two  CHAPTER  III:  F i g u r e III-10 Ablation pressure as function of time for a) Ax, = 0.53ttm and b) Xj, = 0.27/zm and laser intensity of 2.6 x 1 0  13  .  CHAPTER too high.  This  calculation to  Several lowing  result over  estimate  effects  chapter.  is r a t h e r  which  surprising.  Intuitively, we  would expect  t h e m a g n i t u d e s i n c e it n e g l e c t s  may  account  for these  any  discrepancies  lateral  are  a  III:  one-dimensional  energy  transport.  considered in the  fol-  CHAPTER  CHAPTER  IV  PROCESSES AFFECTING T H E SCALING  In lation  chapter  and  III  was  that  results.  approximately  cal simulations.  Secondly,  two  First  significant  of all, the  a factor  differences  magnitude  of two higher t h a n  the m e a s u r e d wavelength  LAWS  existed  of the  between  the  experimental  simu-  ablation  that predicted through  numeri-  scaling was considerably stronger  than  calculated.  In They  this chapter  we  consider three  are t w o - d i m e n s i o n a l  IV-1  processes which  may  account  effects, i o n r e c o m b i n a t i o n , a n d x-ray  for these  differences.  radiation.  T w o D i m e n s i o n a l Effects  In two  noted  experimental  parameters  that  we  IV:  using  important  streamlines clearly  the  plasma  case will  near  the  takes  for  conduction  place  assuming zone.  which  is  seems  justified.  For  considerably  The  other  to  to  between planar  flow  assumption  than  of the  target  to  the the  describe  flow  and  focal  the  therfore  that  diameter  inherent  the  flow  be  conditions, the  D (pd spot  in  a  parallel  spherically.  spot  80/xm).  process  plasma  driven  absorption surface is  ablation  ablated  However,  diverge  experimental  smaller  to  surface.  begin  equal  our  the  the  ablation  eventually  model  First,  perpendicular  approximately  interaction criterion  one-dimensional  assumptions.  are  flow  distance  a  by  and  ,D the  is p l a n a r , to  each  that  is,  other.  a  transition  occurs  t p o t  .  Since  ablation  the  model  front,  planar  planar  is  the  that  is the  at  a  important a  suitable  within  about flow  the  This  pressure  c o n d u c t i o n z o n e is  one-dimensional  making  thermal  predominantly  Hence,  are  the  Such 6 4  we  7  8  1  the tim  hypothesis  lateral  energy  CHAPTER transport area  is negligible.  o f t h e laser  experimental  focal  evidence  It  then  spot.  allows  u s to take  Recently,  which  suggests  however, that  w h e n t h e f o c a l s p o t d i a m e t e r is less t h a n by  considering the F W H M  target the  plasma.  effective  Their  ablation diameter  only  Pant,  fa 1 5 0 > m . intensity  showed  that  varied from  area  Sharna  i n long pulse  of thespatial  measurements  ablation  A j,j  and  laser  to b e equal  a  Shirsat  experiments,  An  I n t h e i r e x p e r i m e n t , A^i profiles  while  D  o f the  X-rays  varies f r o m  t p o t  to the  have  6 5  found  ^  a  A  emitted  b y the  150>m to 30/im,  150/zm t o 120/im.  H o t e l e c t r o n a s s i s t e d t r a n s p o r t h a s b e e n p r o p o s e d a so n e s u c h m e c h a n i s m  possible m e c h a n i s m is a r a p i d t h e r m a l as d e s c r i b e d b y G r u n , D e c o s t e , R i p i n in our experiment, the latter the lack  A s a result,  tal  focal  region.  plasma.  The  flow  periphery. the  and Gartner  will effectively  equals  The  In the early  could quickly  region.  phase,  inhibits lateral  area.  A t later  generate  This  is s u p p o r t e d b y s o m e incidental  energy  recent  X-ray  heating  numerical  goes into X - r a y  calculations  and  [3.7]  that  m and  is the  total  in corona temperature  absorbed energy.  P ti  are  a  (v(6)) A  peripheral boundary.  Lateral  given  which  suggest as  a r e a is e v i d e n t  if we recall  by  [4.1] all  [4.2] abl  energy  transport  a n d a c o r r e s p o n d i n g d e c r e a s e i n {v(0)).  [4.2], t h i s t h e n l e a d s t o a n a p p a r e n t l y  spot  surrounding  2  (v(0))A  from  generation.  i m p o r t a n c e o fc o n s i d e r i n g this increase i n interaction [3.6]  area  a  experimen-  a cooler  o f the  con-  times,  flow  F o r our  spot  observed  ablation  p l a s m a across the focal spot  is i n t e n s e  •Pall a  tot  spot  Another  of a small focal  . Since no hot electrons were  t h einteraction  t h e flow o f h o t , t h e r m a l  m <x  E  .  6  o fthe focal spot enabling rapid heat  increase  second possible process  ofthe  from equations  and  3  6  trans-  c o u l d b e driven b y the radial pressure gradient w h i c h results across the focal  m u c h as 2 0 %  where  2  t h elaser focal  aret w o proccesses which  first involves  focal spot.  The  area  around the perimeter  This  conditions, there  This  across the b o u n d a r y  mechanism seems more plausible.  theablation  cooler p l a s m a evolves the  transport  o f a p e r i p h e r a l p l a s m a ( t h a t is p l a s m a o u t s i d e t h e f o c a l s p o t )  duction.  t p o t  is c a l c u l a t e d  T h e r e are several suggested m e c h a n i s m s t oe x p l a i n the o b s e r v e d lateral e n e r g y port.  IV:  higher mass  w o u l d lead to a decrease  According toequations  ablation rate and ablation  [4.1]  pressure  CHAPTER if t h e  i n c r e a s e i n An  is i g n o r e d .  a  Incorporating modify  the  this  magnitude.  effect Since  into the  and experimental measurements weakly with intensity from  the  measured  numerical  IV:  (if at all). total  the  analysis  intensity  of  the  scalings  are in reasonable  experimental  obtained from  agreement, we  data  will  numerical  simulations  c a n infer that  M hi  mass  and  a  the  ablation  du  depth  scales  An a  T h e effective increase in the a b l a t i o n area c a n b e  ablated  primarily  estimated  derived  a  from  simulations  [4.3]  Mali = pdablAaU  w h e r e p is t h e m a s s d e n s i t y o f t h e t a r g e t . ablation  area  Although  this  could be increase  1 3 0 ftm in  the  calculated experimentally intensity  by  a reduction  area  measured  would  laser  reduce  focal  the  spot  results  This  in the  modification  from  the  of  by  different  magnitude  simulation and experimental  m  results.  of  TO  Yet  1.4  and  intensity and  P i ab  it d o e s n o t  by  Pu a  scalings  diameter  magnitude  a f a c t o r o f 2.5, it c o u l d b e a r g u e d t h a t  in magnitude  correction factors  of  a decrease  1.22. of the  The  The  the  agreement  affect  wavelength  fim.  and  Pu a  in the  overall  difference  ablation  improves the  m  80  the  laser effect  in  the  parameters. between  the  scalings.  Ion Recombination in an Expanding Plasma  In c a l c u l a t i n g  TO  and  inferred from the Faraday on the  ablation  of the  a s s o c i a t e d w i t h t h e l a r g e r e f f e c t i v e l a s e r s p o t is a l s o w a r r a n t e d .  would be  IV-2  instead  S u c h estimates indicated that the d i a m e t e r of  charge  estimate  of  state of the  the  error  P bi a  from the experimental ion data, an average ion velocity  c u p traces.  T h e validity  ions effectively  introduced  recombination process in the  by  this  o f this a s s u m p t i o n is s t r o n g l y  "freezing" out approach  expanding plasma.  can  before reaching the be  obtained  by  is  dependent  detector.  A n  considering  the  PV: 5 1  CHAPTER  IV-2-A Theory I n a t i m e v a r y i n g p l a s m a , t h e f r a c t i o n a l d e n s i t y , fz,  o f t h e charge state  satisfies  Z  4 9  df  z  = n (-S fz e  where nation  n  e  is t h e e l e c t r o n d e n s i t y  rate which  - <*zfz + Sz-ifz-i  z  , Sz  is t h e i o n i z a t i o n rate,  c a n be expressed in terms  [44]  +<*z+ifz+i)  a n d az  o f the radiative,  is t h e t o t a l  OLRZ,  a n d three  recombi-  body,  a^z,  recombination rate through the relation  [4.5]  az = <*nz + n azze  A l t h o u g h these rate coefficients have b e e n numerically evaluated b y Bates, and  McWhirter  7  9  , approximate  analytic  expressions have  been found.  Kingston  F o r instance, the  ionization rate f r o m t h e i o ng r o u n d state, averaged over a M a x w e l l i a n electron distribution, can b e expressed  as  8  0  SZ =  where  E^  {ET^^TE^)  is t h e i o n i z a t i o n e n e r g y a n d T  three b o d y  e  agrees  with  temperatures  those  proposed by Bates  forwhich  c o e f f i c i e n t is g i v e n  a  R Z  which  = 5.2 x 1 0 -  = 8.75x 1 0 -  3 Z  b y  1  4  , i n the range  8  x  P ( - ^ / ^ )  c  m  is t h e e l e c t r o n t e m p e r t u r e  recombination rate, the analytical  a  e  2  7  3  / s e c ,  [4.6]  (both in e V ) . For the  expression p u t forth b y Veselovskii  Z  3  to within  r  -  9  /  I n VZ  2  2  a factor  r e c o m b i n a t i o n is i m p o r t a n t .  + 1  as  [4.7]  o f 2-3 f o r p l a s m a  F o r radiative  8 1  densities a n d  recombination, the rate  0  Z y £ £ / r  e  10 k e v <  [ 0 . 4 3 + (1/2)  T /Z e  a  R Z  2  <  \n(E^/T )  + 0.47(E| /r )- / ]cm /sec )  e  e  1  3  3  [4.8a]  1 5 0 k e v , is a p p r o x i m a t e l y  = 2.7 x  IQ- Z T-^ . 13  2  2  [4.86]  CHAPTER  IV:  It i s i m p o r t a n t t o n o t e t h a t t h e a b o v e e x p r e s s i o n s a r e s t r i c t l y v a l i d o n l y f o r h y d r o g e n like  atoms  when  Fortunately,  the  temperature,  is m u c h  T, e  lower  than  the  ionization potential,  m o s t o f t h e r e c o m b i n a t i o n t a k e s p l a c e w h i l e t h i s c o n d i t i o n is s a t i s f i e d  8 2  E^. .  A s p r e s e n t e d , e q u a t i o n [4.4] d e s c r i b e s t h e e v o l u t i o n o f t h e i o n p o p u l a t i o n s i n a p l a s m a element whose temperature most  of the  energy  of  the  effectively the  internal  energy  expansion,  constant  of the  to w i t h i n a few  after  an  Under  ion  flow  expansion time =  r /t , 0  is l a r g e l y  percent  of their  the  laser-heated p l a s m a has  the  results  Medusa  laser pulse,  of the  then  time-of-flight relation v  accuracy  a n d d e n s i t y as a f u n c t i o n o f t i m e is k n o w n .  velocity to-  of  This  a  dependent  o n the  to fa  assumption of constant  velocity  at  the  i s t h e d e n s i t y a t t h e t i m e to.  this density  the  element  is a p p r o x i m a t e l y p o s i t i o n at  time  to-  In  the  given  by  t.  The  0  converged  expansion velocity,  conservation of mass  ns  requires  o f t h e p l a s m a e l e m e n t , V.  n.-(0)(£)  =  For  [4.9]  8  Experimental data acquired by R u m s b y  8  3  supports  scaling.  temperature  s c a l i n g is p o s s i b l e . T h e e l e c t r o n t e m p e r a t u r e b e h a v i o u r , w h i c h w e c o n s i d e r t o b e to the ion t e m p e r a t u r e ,  c a n be d e t e r m i n e d f r o m the energy  Z,  charge state  gas pressure the  is P  =  n,-(l  relation  is +  E =  Z)kT  |(1 .  +  Z)kT  These  .  equivalent  equation  If w e u s e a n i d e a l g a s e q u a t i o n o f s t a t e , t h e n t h e t h e r m a l e n e r g y p e r h e a v y p a r t i c l e  law, yield  be  case of a 4  A s a result of the energy released in the r e c o m b i n a t i o n process, n o simple  in average  will  time  having  kinetic  8 4  M«)  w h e r e n,(0)  plasma  to  that  10 n s .  t h a t t h e n u m b e r d e n s i t y , n,-, b e p r o p o r t i o n a l t o t h e v o l u m e implies  given  expansion velocities  asymptotic velocities  simulations imply  spherical expansion, this  been converted  w h e r e r o is p l a s m a e l e m e n t  0  If w e c o n s i d e r  T h e specific v o l u m e  is  expressed  V = 1/n,-,  expressions, combined with the  density  and  the  scaling  8 4  [4.11]  52  CHAPTER where  E  r c  In tron  i  is t h e p o r t i o n o f r e c o m b i n a t i o n e n e r g y  the recombination of a n electron  is first  captured  energy  E  bound  electron  the  electrons  process,  into  other  the energy  the potential  forms  collision, the elec-  levels o f t h e a t o m  radiation.  levels o f t h e a t o m  energy  of energy.  b y the electron-electron  of line  a n ion in a three b o d y  one of the upper  A  I  part  collisions.  a n d ions as a result o f energy  the form  to the plasma.  with  a  binding  the action of electron collisions a n d radiative transitions, the  descends down  deexcitation  free electrons  in  T h e n under  FS kT.  transformed  b y the i o n into  with  returned  IV:  transfer.  from  the recombination  o f it, E,  is  is t r a n s f e r r e d  z  This  to the g r o u n d level.  energy  is t h e n  T h r o u g h t h e c o m b i n e d effects  immediately  directly  distributed  T h e remaning energy, I  —  During  z  of re-absorption  between  is  E,  to the  released  a n d electron  collisions, s o m e p o r t i o n o f this radiation energy will, i n time, also b e t r a n s f o r m e d into In t h e regime o f p l a s m a densities to radiation.  Hence, for simplicity  with the energy tends  we expect  the temperature,  the results  of the recombination energy,  E'  z  This then  we c a n justifiably  assume that the energy  released b y radiative r e c o m b i n a t i o n s , leaves t h e p l a s m a .  to underestimate  Therefore,  w e a r e c o n s i d e r i n g , t h e p l a s m a is e f f e c t i v e l y  transparent along  — E,  This  z  assumption  a n d as a consequence, t h e degree  of ionization.  to be a lower b o u n d to the true solutions.  F o r the value  we use the expression p u t forth b y Z'eldovich  =  I  heat.  1.1 x  10~ Z 3  i/e  z  2/3  n  i/e i/i2 r  e  and Raizer  8  4  ,  [4.12]  V  implies  [4.13]  In d e r i v i n g  equation  [4.9], a n y p r o c e s s e s i n v o l v i n g  energy  redistribution  a m o n g the  p l a s m a elements, such as t h e r m a l c o n d u c t i o n or reabsorption of radiated p h o t o n s , have neglected. become and  While  ineffectual  these  processes  m a y be important  as t h e e x p a n s i o n p r o c e e d s .  [4.9] f o r m t h e b a s i s o f o u r a n a l y s i s .  early  Equation  in the expansion, they  [4.11],  been  rapidly  along with equations  [4.4]  CHAPTER  IV-2-B  M e t h o d of Solution  The tion. [4.4]  For and  system  this  of equations, being strongly non-linear, have no simple analytical  reason  [4.11]  a  computer  program  was  written  being in Lagrangian varies  form, describe the  as a f u n c t i o n of t i m e  according  r{t)  Since  we  f r o m the [4.14])  are  primarily  target,  must  be  described by was  to  the  interested  C.W.  in  time  G e a r  0.1%  8  5  This  is  evolution of a p l a s m a element  =  r(t ) 0  the  +  conditions  to  and charge  expansion was  whose  [4.9],  position  [4.14]  0  Faraday  cup  a corresponding time  accomplished by  , to solve the  density j  previously,  representing  temperature  [4.4] a n d  two  using  a  current  at  (calculated  ti  The  distance  using  modified Gear  differential equations.  a  equation  algorithm,  overall  ri  as  integration  .  ion current  alluded  equations  v{t-t ).  predicted  can be  easily  j =  As  differential  to  i o n p o p u l a t i o n s at  evaluated.  below  the  the  plasma elements Equations  O n c e the ion populations a n d the associated average known,  solve  solu-  numerically.  T h e i n i t i a l p l a s m a p r o f i l e is d i v i d e d i n t o N  error  IV:  a  the  accuracy  freely  of  calculated through the  expanding  results  plasma.  state profiles were taken f r o m  followed for a total  of w  8 ns  IV-2-C Simulation of the Ion Current  after  the  are  relation  .  riiZev.  the  c h a r g e s t a t e at the d e t e c t o r  [4.15]  is For  largely this  Medusa  dependent  reason,  the  on  the  initial  s i m u l a t i o n results  4 ns laser pulse was  initial density,  in  initiated.  which  CHAPTER  Figure r V - 1  Initial density.temperature and charge state profiles  IV: 5 5  CHAPTER  F i g u r e  rV-2  Calculated Faraday  cup trace.  Detector positioned 20 c m f r o m  target.  TV:  56  CHAPTER  F i g u r e  IV-3  Measured  Faraday  C u p  trace.  IV:  Detector positioned approximately 30 c m  from  a n d c h a r g e state profiles as d e p i c t e d in F i g u r e IV-l  were  target.  r V - 2 - C  S i m u l a t i o n  of  the  Ion  C u r r e n t  Initial density, t e m p e r a t u r e taken  from  Medusa  calculations.  The  profiles represent  the state  of the e x p a n d i n g p l a s m a  at a t i m e 4 n s a f t e r t h e e n d o f t h e l a s e r p u l s e . T h e e f f e c t i v e i r r a d i a n c e w a s  5.0 x 1 0  at  a position 20  a  laser  wavelength  f r o m the target ion current The  the  /im.  The  predicted  is i l l u s t r a t e d i n F i g u r e I V - 2  i f o n e a s s u m e s a c o n s t a n t Z,  characteristic  traces  of 0.53  IV-3)  are  calculated  value  of  also v  p  is  evident almost  cup  trace  at  . A l s o i n c l u d e d i n F i g u r e IV-2  is t h e  i n d e p e n d e n t o f t i m e , t h a t is w i t h o u t  ion ablation features  (Figure  Faraday  (narrow peak) in  a  the  factor  2  2  traces.  higher  than  We that  note,  discussed in section IV-l.  a one-dimensional model. Secondly,  the  constant  cm  recombiation.  however,  measured.  T h e possibility of this was  velocity  2  calculated  e x p l a n a t i o n s are possible. F i r s t , d u e to lateral energy t r a n s p o r t the a b l a t e d ions are than would be predicted by  W / c m  f o u n d in experimental Faraday  calculated of  1  model used could  cup that  Several slower  previously  overestimate  57  CHAPTER the  velocity.  Since  we  are  primarily  comparing calculated current  traces  interested  that  the  ion velocity is,  t;  p  is t h e  >  charge  where  calculated  to  this  result.  to  recombine.  in  Figure  is t h e  v  p  peak  First The  IV-4.  out  time  state  within  since  ening of the  net  effect  current  the  peak  of  Z  peak.  The  for  statistical  average  the  individual  hence  It  assump-  is c l e a r  that  after  is a s h i f t  recombination  T w o  processes  detector plasma  rate coefficient density.  s h a r p e n i n g of the  velocity,  state.  reaching  an  processes  increased recombination in the higher density  The  .  2 2  including ion  charge  for increasing  two  and  neglected.  centimeters  velocity  as a f u n c t i o n of d e n s i t y  of these  effects  is f a s t e r i f r e c o m b i n a t i o n is c o n s i d e r e d .  recombination  lower  recombination  show the error inherent in the  a few  plasma elements  dependence  will be  IV-2  assuming constant  of all, the  the value of Z  The  calculated  velocity  Secondly,  charge  which shows seconds.  "freezes"  associated with the current peak  Vf,  effective  state  the  this d i s c r e p a n c y c a n b e  T h e two calculations presented in Figure tion  in  IV:  This  first  scales  is  is v e r i f i e d b y  current  peak  peak  and  less  time  presented  current  is a d i r e c t  found  material  to  which  contributes very of  the  (v{6)}  be  ablation  =  is i n f a c t  0.4  v.  A  p  IV-5  of 4 x  and  a  1 0  ablated near  This  by  the  relation  (v($))  from  the  Another w i t h the  targets.  ion current  aspect  detector  obtained by  of  Gupta,Naik,  A l t h o u g h we  carbon  is t h e  slow,  the e n d of the laser pulse.  high  targets.  indicated  the  validity  of the ablatively  of taking  recombination  This study  and Pant  For this reason  v, p  the  it  calculation velocity  at  driven ions instead of deriving  8  6  was  which  that  we  motivated  have by  considered  some recent  was  how  v  p  experimental  IV-6) we  is i n q u a l i t a t i v e observed  is  varied results  m e a s u r e d this d e p e n d e n c e for c a r b o n a n d  considered a l u m i n u m targets, the functional dependence of v  W h a t  density  trace.  ion  positon.  detector position (Figure for  (v(0))  contribution to  (v(6))  p e a k i o n c u r r e n t , as t h e m e a n v e l o c i t y  of  [4-15]  or after  also  7  sharp-  consequence  little to the driving pressure a n d s h o u l d not b e i n c l u d e d in the parameters.  -  plasma.  as c a l c u l a t e d  major  the  Figure  <»(')> =  was  vj  with density,  a recombination time in the  That  contribute  have  element  the  that  agreement initially  with their v  p  m  v/  p  experimental  but  gold  on  the  results  that" g r a d u a l l y  v  p  CHAPTER  F i g u r e  r V - 4  Average  charge state vs time for two  different initial  temperatures.  IV:  59  CHAPTER  10  F i g u r e  r V - 5  Average  charge state vs density for two  different  initial  temperatures.  IV:  60  CHAPTER increased while effects target  remained constant.  vj  previously  discussed.  in our experiments  It  Since  T h e  the  the variation  Faraday of v  ion expansion velocity  the  effects  when m a k i n g multiple detector  IV-3  equal  distances  transfer  radiation  energy  all  Energy  loss,  or  scaling measurements  ion  energies.  energy. At  is n e g l i g i b l e .  low  m  In  and  fact,  intensities  However,  incident laser energy  to  with detector position can be  p  However,  25  cm  from  ignored.  if o n e r e q u i r e s a n a c c u r a t e v a l u e f o r  measurements far  be  considered.  care must be taken  away  f r o m the  by  the  can  be  hot,  the  Furthermore,  to place the detectors  at  target.  either  contribute is n o w  coronal plasma  to  radiated  the  represents  away  ablation  from  the  process.  an  important  target,  How  energy  representing  these  a  considerations  discussed.  P {,j 0  the  one assumes that the energy m e a s u r e d by the  calorimeters  measure  the  a n d long laser wavelengths  a photon energy  radiated  away  sum  of  ion  at h i g h intensities a n d short laser wavelengths  can be converted into X-ray radiation.  range  f r o m the  o f 15 e V  target.  to  10 K e v .  T h e  and  the p l a s m a X-ray  obtained using the post-processor discussed in C h a p t e r over  15  C o n t r i b u t i o n of X - r a y E n e r g y to the Ion C a l o r i m e t e r M e a s u r e m e n t s  In calculating is  positioned  of ion recombination must  a n d sufficiently  emitted  mechanism.  substantial  IV-S-A  were  Effects of X - r a y R a d i a t i o n on the S c a l i n g M e a s u r e m e n t s  The  affect  cups  recombination  is c l e a r f r o m t h e n u m e r i c a l c a l c u l a t i o n s j u s t d e s c r i b e d t h a t t h e e f f e c t s o f i o n r e c o m -  b i n a t i o n o n t h e s c a l i n g l a w s is n e g l i g i b l e .  nearly  r e a s o n f o r t h i s , o f c o u r s e , is t h e  IV:  II.  quantity  X-ray n  x  X-ray  radiation  radiation  energy  as m u c h as 4 0 % of  T a b l e IV-1 The  calorimeters  summarizes energy  is t h e  is  the  results  integrated  fractional  energy  CHAPTER  12  F i g u r e  IV-6  v  p  vs  distance between  detector and  target.  IV:  62  CHAPTER Table  Radiated  X-ray energy  W / c m 5 . 0 x l 0  2 . 6 x l 0  For  Percentage  fim  2  1  1  2  3  isotropic  target IV-1.  Actually  thin.  From  the  this  KeV,  »7x  0.07  0.35  14%  0.07  0.27  16%  0.08  0.53  2 2 %  0.11  0.35  3 5 %  0.18  0.27  4 2 %  0.21  approximately  calorimeters.  is t h e  case  X-ray  if w e  spectra,  it a p p e a r s  that  half  of  the  X-ray  T h i s a s s u m p t i o n was  only  can  which  this  energy  scaling of the  most  coronal p l a s m a to of  a s s u m p t i o n is i n d e e d  introduced  by  energy data  we  is a s g i v e n b y know  calorimeters. back We  radiation  that T h e  scattered  recall  that  can  Table  be  established  IV-1  the  X-ray  9 0 % of the  remaining energy (due  to  as  follows.  the  measured quantities  m  o  c  are  ^  ,  A  limit  10  1  3  .  incident laser energy target  instabilities  given  in  z  be  the  Table  optically  radiation  a n artificially  consider  o f 2.6 x  is a c c o u n t e d f o r b y parametric  We  from  has  an  valid.  can be inferred.  for a laser intensity  approximately  energy the  ablation parameters  away  used in determining n  consider the suggest  radiates  Since the X - r a y e m i s s i o n increases for shorter laser wavelengths, wavelength  wavelength  Energy  14%  calculated  o f 1.5  X-ray  and  0.53  radiation,  a n d reaches  energy  IV-1  as a f u n c t i o n o f laser i n t e n s i t y  Intensity  IV:  stronger  on the scaling that  From  the the  total  error X-ray  experimental  is a c c o u n t e d f o r b y  kinetic  energy  discussed in  (fa  chapter  the  5%)  and  Ufa  5%).  by  [4.17]  and  Put  oc  [4.18]  CHAPTER However,  they  should be  given  IV:  by  Ei -r-ry  Etot m n 7-^(0.9  OTl  m  a  a  \ -  IA m l  f? )  [4.19]  x  and  P .. rr ^ (  Pabi*  Since the  wavelength  s c a l i n g o f (0.9  0 . 9 - n , ) .  -  is g i v e n  (0.9-^)0:  the  modified experimental scaling laws  [4.20]  by  A  ;  0  1  7  ,  [4.21]  become  m  oc A j T  [4.22]  0 - 9 8  and F.6I  at  an  the  itensity  of  calculated  this  effect  2.6  1 0  wavelength  cannot  fully  i n t e n s i t y s c a l i n g o f r\ wavelengths.  x  In  x  1  3  W / c m  explain the  particular,  for  of  -0.10] $~ a J  a  [scales as  r) ) x  P bi a  ^  0  3  [4.23]  .  6  scaling oc A £  discrepancy  0  "  for  2  in  9  .  the  is w i t h i n  Pu a  O n  the  other  wavelength  the  uncertainty  h a n d , it  is c l e a r  dependence  of m .  c a n also account for the stronger intensity scaling observed for  Pn  —  This  dependence  s c a l i n g is r e d u c e d f r o m (0.9  .  2  «  0 . 2 7 fim  oc $  0  -  9  2  to  laser Pu a  a  irradiation $ ° -  8  2  by  the  measured  including the  ablation  intensity  of  that The  shorter pressure  dependence  1  IV-3-B Radiation Driven Ablation The process  7 7  '  radiation 8  7  .  electron thermal The  increase  lead to  emitted  Energy  transport  transport  in X-ray  towards by  the X-ray  target  could  radiation  is  itself  contribute  considerably  to  more  the  ablation  efficient  than  a n d leads to increased mass ablation rate a n d ablation pressure.  emission associated with shorter  a stronger wavelength  scaling.  Since radiation  laser wavelengths transport  was  could,  therefore,  neglected in  the  nu-  CHAPTER merical  s i m u l a t i o n s , it  m  P bi  and  is p o s s i b l e t h a t  were underestimated.  a  b o t h the  magnitude  Medusa  Although  now  and wavelength  nary  runs which have  b e e n p e r f o r m e d verify  i r r a d i a t e d w i t h 0 . 5 3 fim increased of the  by  m  5%  laser pulse  at  (4.0  In s e c t i o n I V - l larger  than  the  (for with laws.  ns)  The  it  due to the  exact  effect AM.  The  into  the  1  3  W / c m  the effective  Au a  wavelengths).  data  analysis to  ,  radiation greater  would  assess since  prelimi-  is X - r a y  weaken little  the  the  transport at  the  heating of  increase  of the  the  radiation  experimental  is k n o w n  end  considerably  with increasing X-ray  Incorporating  targets  emission.  ablation area can be  gets larger  laser  is d i f i c u l t  the few  dependence of X-ray  one possible process for this that  2  difference s h o u l d be even  strong intensity  Since  with shorter  of this  ns.  discussed how  is c o n c e i v a b l e  wavelengths  d e p e n d e n c e of  e n d o f 1.2  we have  target-irradiation shorter  the  However,  of  transport,  For example, for a l u m i n u m  l a s e r l i g h t a t a n i n t e n s i t y o f 1.0 x 1 0  laser focal spot.  focal spot periphery  this effect.  dependence  incorporates radiation  the h i g h cost of simulation p r o h i b i t e d any detailed c o m p a r i s o n s .  IV:  of  Au a  scaling  wavelength  CHAPTER  CHAPTER  SHOCK WAVE  A n suring  Hugoniot of  the  from  equation driven  pressure.  speed.  these in  been  ablation pressure involves  used  conjunction  computer  since pressure  a high pressure  the  at  several  intensity  in  and  internal  provide  regime.  This  accurate  a  energy  valuable  laboratories  and  with  simulations, yields  can  '  1  3  with  of the shock parameters p e r f o r m e d b y S E S A M E  measure  be  deduced regarding  second application of  1 1  moderate  library  Parfeniuk  laser-  success.  ablation  Medusa  mea-  Itankine-  direct  wavelength scaling of the  t a b u l a t e d e q u a t i o n of state f r o m the  the  information  q u a n t u m - c o r r e c t e d T h o m a s - F e r m i equation of state u s e d in  Recent numerical calculations more  effective  measurements  studied  of c a l c u l a t i n g  when  with  Furthermore,  velocity,  waves has  This,  alternatively  of state parameters  purposes  the  shock or  3 6  shock  shock  our  sure,  relations  driving  directly  For  associated  V  MEASUREMENTS  alternative m e t h o d for determining the  the  V:  pres-  is  sufficient.  7 4  using  support this  the  hypoth-  esis.  In velocity  the and  first  ablation  procedure used to results the  are  then  ablative  section  used  this  pressure  determin  pressure  measurements  of  the  chapter  we  determined  by  asymptotic  in section V-3 in  aluminum.  discussed  previously.  to  present  Medusa  .  shock velocity  determine  The  the  primary  the  relationship In  section  between  V-2  is d e s c r i b e d .  intensity  objective  is  and to  the  the  experimental  T h e  experimental  wavelength  verify  shock  the  ion  scaling  of  ablation  CHAPTER  V-l  S c a l i n g of S h o c k V e l o c i t y w i t h A b l a t i o n P r e s s u r e  Figure V-l at  V:  intensities  First result  of  all,  shows the trajectories  of 4 x the  1 0  shock  1  3  and  is  1.0 x  10  observed  of the shock front calculated for 0.53/im 1  to  4  W / c m  2  .  Several  "accelerate"  interesting features  initially.  Such  an  irradiation  are  evident.  acceleration  of a sequence of progressively stronger shocks overtaking each other.  is  the  This  sequence  o f s h o c k s is g e n e r a t e d d u r i n g t h e r i s i n g p o r t i o n o f t h e l a s e r p u l s e w h e r e t h e l a s e r  intensity  increases linearly w i t h time. will p r o p a g a t e  at  the  b e h i n d the shock. front  continues  to  W h e n the laser intensity starts to decrease, a rarefaction  local s o u n d speed f r o m the  ablation surface a n d reduce the  pressure  B e c a u s e of the finite p r o p a g a t i o n t i m e of this r a r e f a c t i o n wave, the accelerate  past  the  peak  of the  laser  pulse.  Once  the  shock  rarefaction  r e a c h e s t h e s h o c k f r o n t a g r a d u a l d e c e l e r a t i o n o f t h e f r o n t is o b s e r v e d . S o o n a f t e r t h e is l a u n c h e d  and  at  s p e e d v,h  a steady  before  d e p e n d e n c e o f vh t  attenuation  driven by  on  P n a  the  h  rarefaction  ablation pressure The  = 9.4 x 1 0  wave occurs, the P u  . In  a  Figure  shock V-2  wave shock  propagates  the  calculated  calculated scaling of  5  P^f  c m / s ,  1  [5.1]  i n M b a r ) , is i n e x c e l l e n t a g r e e m e n t w i t h t h e a n a l y t i c a l s i n g l e s h o c k m o d e l p r e d i c t i o n  a  v.h  the  is p r e s e n t e d .  v.  ( PM  by  wave  «P i  V-2  4  .  Experimental Measurements  T h e of various  shock s p e e d was thicknesses.  luminescence of the  beam  7 4  If  target  the  determined from temperature  rear  transit  of the  time  shock heated  surface c a n be readily  e x p e r i m e n t a l s e t u p is p r e s e n t e d s c h e m a t i c a l l y  was  focussed on  with f/10 optics.  The  target  through  in Figure V-3.  region of the  targets  is h i g h e n o u g h ,  recorded o n a streak  The  target  measurements  target  the  camera.  T h e incident rear  surface  laser cor-  of  V: 6 8  CHAPTER  SHOCK TRANSIT  TIME A S A FUNCTION O F TARGFT THICKNESS  H  X= 0.53 L  UJ  00  MEDUSA-M (d) -AXIO -^) 13  <  •L cm* MEDUSA-M ((|) ~1X10 " }  DC  U  L  _  1  10  F i g u r e  1  20  1  30  40  TARGET THICKNESS Cum)  V - l Trajectories of shock propagation in aluminum from Medusa  simulation. Time  zero corresponds to the peak of the 2 ns ( F W H M ) laser pulse.  so  CHAPTER  CHAPTER  F i g u r e  V-2  Pressure scaling of the  shock velocity  from  Medusa  simulations  V:  V:  CHAPTER  F i g u r e  V-S  E x p e r i m e n t a l setup for measuring shock  velocity  V:  70  CHAPTER first  image  used the  to  best  was  a  overall  thick the  onto  streak  fiducial  the  that  system  aluminum  laser  stray  laser  signal to noise ratio  however,  typical  Furthermore,  minimize  focussed  noted, the  plane.  has  and  plasma  camera  the  finite  a temporal  slit  width  V-4  foil.  shock transit  Streak {X  Transit  L  =  the  on-set  time  record of target 0.53/xm, *  (100  filter  filtered  capable  of  time of the  ps  rear  selected of the  is g i v e n target  by  rear  the  the  taken .  rear  interval  surface  target  are  100 ps  5700 A  because  resolution.  a n d foil r o u g h n e s s  at  at  it  rear It  surface  between  gave  surface  should  into  Figure  was  account  V-4  shows  of a 30 the  be  peak  fim of  luminescence.  ! LASER FIDUCIAL  surface  =  2.0 x  10  measurements  have  been  A  was  2  centered  A)  image  shock-induced luminescence  t SHOCK LUMINESCENCE Figure  This  The is  filter  resolution of a p p r o x i m a t e l y  the  signal and  light.  which  record of T h e  b a n d pass  characteristics.  streak  when  a narrow  V:  1  3  luminescence  W / c m  2  and  the  laser pulse  fiducial  )  obtained for a l u m i n u m  foils of thickness  be  CHAPTER Transit tween  time  1 8 fim  teristics  and  of the  e n d of the  measurements 5 0 fim.  streak  The  lower  camera.  laser pulse.  radiation.  The  have  For  been  bound  thinner  T h e p l a s m a on the  resulting plasma  light  decay  in  the  shock  amplitude  lead to this shock a t t e n u a t i o n . propagating  from  the  propagating radially 2-dimensional effect  The trated  target  caused  The  asymptotic  data  points  Figure  side c a n  weaken  the  m a x i m u m target  between  velocity  1 8 fim  is  and  Meduta  A  power  law  simulations  In  the  next  wavelength  laser  energy  shock front  of  for  scaling law  ablation  luminosity  of  the  o f 0 . 2 7 fim  currently  10  1  a  2.5 <  1.7xl0  is i n  7  at  available  the  at  rear  laser \L  =  apparent  irradiation.  at this  this  0.27fim.  Since  first the  laser  camera  rear  34  surface  point back  to  and  fim  edge  may  the  fit  The  shock  front. <  This  50  fim.  t h i c k n e s s e s is i l l u s -  to  the  of 0.53  fim.  experimental  corresponding  [5.1]  wave  rarefactions  and wavelength  2  to b e  8.4  ablation  Mbar.  In  laser  form  [5.2]  agreement  is t h a t  radiates  results  measurements 1  W / c m  2  prevented  thick  the  from  both  made  at  III.  velocity  Figure  with  V-7  2  the  shows  aluminum  .  rear like  side a  were  The  limited  evaluation a streak foil.  recording optics.)  l u m i n o s i t y f o r 0 . 5 3 fim  note  surface  at  fim  processes  c a n consider to  equation  of 5 . 6 x l 0  wavelength.  we  cm/s.  6  by  wavelength  of a  the  Mbar,  excellent  an irradiance  surface  in the  T h e  the  m e a s u r e d s h o c k s p e e d s at different  8  shock  Secondly,  least-squares  dependence of the  experiment,  and  pressure  principle  region  W / c m  3  is a c o n s e q u e n c e o f h i g h e r m a g n i f i c a t i o n i n t h e  differences are fim  part  streak  for foils of various  and ion measurements presented in chapter  laser  scaling  This  charac-  underdense before  of the  T w o  front.  thickness  from  to be  =  abl  evident.  of 4.0 x  calculated  5 0 fim  shock  time  calculated f r o m the  a  are presented.  observed.  s i m u l a t i o n s , is g i v e n  P f,i  of  fly-back  strongly heated by  saturation  high pressure  of shock transit  V-5 for a laser intensity  V-6 the values  clearly  the  the  limits  P  is  already  reduce  shock  became  the  be-  O n the o t h e r h a n d , for a l u m i n u m foils of 50  can  7 5  target  severe  foils of t h i c k n e s s  is i m p o s e d b y  rear side was  inward  a c c o r d i n g to  intensities  was  aluminum  F i r s t , as d i s c u s s e d in s e c t i o n V - l , a n axial r a r e f a c t i o n  experimental values  in Figure  pressure,  front  of 18 / i m  foils, the  rendered shock measurements impractical. thick,  obtained for  V:  (Figure  b o d y  7  6  the  shock  interesting  V-4) much the  of  wider  Several  of  intensity  record  (The  e m i s s i o n is  black  of  range  a  and  0.27  stronger  increase  in  CHAPTER  1 10  A  0  1 20  1 30  TARGET THICKNESS Gum)  F i g u r e  V-5  Shock  transit time  {Xi  =  0.53ttm)  1 *0  1 50  V:  73  CHAPTER  1  1  1  1  1 I I I I I  0.1  V - 6  Ablation Pressure  I  I  I  INTENSITY  vs  Laser  Intensity  (AL  =  74  I I I II  10.0  1.0  ABSORBED  F i g u r e  1  V:  10  0.53/im)  1 3  ( W/cm ) 2  CHAPTER emission must necessary I <x T for  to  to  an increase  the  observed  for a black b o d y )  4  rear  hot  would  is i f t h e r e  corona and  experiments  , it  1 2  in the  A l t h o u g h the  rear  surface  it is, n e v e r t h e l e s s , u n e x p e c t e d .  be  shock  shock parameters  insensitive  exists  is  in temperature.  increase  ablation pressures the  surface)  breakdown the  due  explain  identical  the  be  any  form  to  the  laser  compressed target.  known  that  hot  For  electrons  luminosity  (and  consequently  dependent  instance,  can  The  our  experiments  presented incident  in  chapter  energy  100 ps)  IV  goes  some f o r m of X-ray (fa  eliminates we  into  this  known  X-ray  heating.  w o u l d suggest that  in  a  radiation  temperatures. an  wave  7  A l t h o u g h this  associated increase  Figure  7  V-8  show  a  that  fact  there  the  penetrate  of  The  lack  t  Mbar.  V-3  =  1-35 x  10  6  what  way  we  risetime of the  the  However, as  this  could be  would  the  shock  lead to the  an  front  (10.6  shock  from as  Alternatively,  the  change w o u l d b e difficult to  measured shock transit  time  fim) wave-  electrons  the  results  4 0 %  observing  of may  due to the  of 6 x  be  change  to  could higher  shock  and  measure.  i n a l u m i n u m foils of v a r i o u s  an absorbed intensity  the  short  This  material  in pressure b e h i n d the  of  could  r e a r s u r f a c e l i g h t u p is  and heating  increase  that  between  of hot  much  to  luminosity  the shock-compressed material might increase.  following  (due  transport  ahead  wavelengths  is n e g l i g i b l e p r e h e a t .  n e s s e s i r r a d i a t e d w i t h 0.27fim l a s e r l i g h t a t value of vh  shorter  Therefore,  that  in shock velocity  the  at  the  in long wavelength  possible explanation.  energy.  The  of state, X - r a y a b s o r p t i o n w i t h i n result  as  temperature  is s m a l l  only  energy  ablation region, causing preheating of the u n c o m p r e s s e d target. in  in  Intuitively, one w o u l d expect  wavelength.  of wavelength  change  V:  10  1  2  W / c m  o b t a i n e d f r o m these results i m p l i e s a d r i v i n g p r e s s u r e Pu a  2  thick.  The  =  5.32  (Eq.[5.1])  Wavelength S c a l i n g of A b l a t i o n P r e s s u r e  At  an  absorbed irradiance  a b l a t i o n p r e s s u r e is g i v e n b y with the  of 6 x l 0  equation  ablation pressure derived  1  [5.2]  above,  W / c m  2  to be  P f,i = a  2  and  laser wavelength  4.59 M b a r . 5.32Mbar  T h i s result,  for  a laser  o f 0 . 5 3 fim when  the  combined  wavelength  of  0.27  CHAPTER  t  t  SHOCK LUMINESCENCE F i g u r e  V - 7  Streak (A  fim,  yields  L  =  record 0.27/im,  the scaling  D i s c u s s i o n  of  target  <I>  A  =  rear 6.0 x  LASER FIDUCIAL  surface, 10  1  2  shock  W / c m  2  luminescence  and  laser  fiducial  )  law:  P  V-4  of  V:  a  l  i  =  2.94A2;  0  2  3  M b a r  (Ax, i n m i c r o n s ) .  [5.3]  R e s u l t s  Calculation of the  ablation pressure from shock speed measurements has  eliminated  CHAPTER  X = 0.27 L  V:  77  y  ym  A T  ^  /  A  r  6 xi  r—  10  0  F i g u r e  V - 8  Shock  transit  1  1  ••  °  20 30 TARGET THICKNESS (^m)  time in aluminum (At  =  0.27/xm)  12  w / c m 2  1  40  " 1  50  CHAPTER many It  of the p r o b l e m s inherent  should enable  us to better  a n d simulation results.  (i)  from ion  in the ion m e a s u r e m e n t  understand the  discrepancies between  S u m m a r i z i n g , we h a v e the  three  wavelength  the  ion  scaling  III.  measurements relations:  measurements,  P  (ii)  technique described in chapter  V:  from shock  ~ x-0.47  [5.4]  measurements, [5.5]  (iii)  from  Medusa  measurements,  P ~ \-0.20 a6(,*imu L  at a laser i n t e n s i t y  w 6 x  1 0  1  2  W / c m  2  .  F r o m these results we c a n see t h a t t h e s h o c k a n d  u l a t i o n scalings are i n r e a s o n a b l e  agreement  the  however,  ion  measurement  discussed in chapter  scaling. IV,  the  If,  with each other but we  incorporate  modified wavelength  These dence  of  the  dimensional  the  considerably weaker X-ray  radiation  simthan  correction  scaling  Pabl,ion « K  is i n r e a s o n a b l e  [5.6]  A  1  0 Z  °  [5.7]  agreement.  results  suggest  ablation nature  inadequecies in the  of  the  pressure. the  ion As  ablative  theories.  measurements noted flow  in  could  over-estimated  chapter account  IV, for  X-ray this  the  wavelength  radiation discrepancy,  and  depen-  the  two-  rather  than  CHAPTER  CHAPTER  VI:  VI  SUMMARY AND CONCLUSIONS  VI-1  Summary  T h e  numerical  clarified several  The  ever,  a  scalings of the  showed excellent  strong  discrepancy  measurements) wavelength  and  experimental  aspects of laser-matter  intensity  simulations  simulations  wavelength  dependence  mass  of the  ablation  mass  of  rate and  with that  observed  scalings  presented  in  this  work  have  ablation pressure derived  from  interactions.  agreement was  results  obtained from  between  the  the  ablation  ablation  rate  ion measurements.  simulated  and  parameters.  and  The  How-  experimental apparent,  ablation pressure  (ion  stronger  inferred from  ion  m e a s u r e m e n t s was a t t r i b u t e d to the effect of X - r a y r a d i a t i o n e m i t t e d b y t h e c o r o n a l p l a s m a . T h e emitted  X-rays can increase  fecting target  The factor  magnitudes  of two  greater  periphery  the  effective  ion  measurements.  of the  ablation  Simulations a  energy  recorded by  marginal  of  than laser area.  the  measured  that  mass  predicted by  focal spot has This  effect  ablation  P a n t  8  6  .  ion calorimeters  rate  simulations.  been  identified  should be  and  ablation  Lateral as  carefully  as well as  energy  pressure  af-  transport  a possible cause assessed in the  for  final  was  change  in the  ion current  was  caused by  in qualitative  agreement  recombinations.  at p e a k  current  a  across  increasing analysis  of the ion r e c o m b i n a t i o n process in the e x p a n d i n g p l a s m a indicated  simulations predicted the change in the ion velocity This was  the  ablation.  the  only  the  However,  of  that these  with detector position.  w i t h experimental results reported b y  Gupta, Naik,  and  CHAPTER Finally, shock  speed  showed  a n d wavelength scaling of ablation pressure was  measurementsin  good  surements  the intensity  agreement  when  measurements  with  radiation  in the  aluminum  using  simulations  effects  are  0.53  and  taken  and  with  into  0.27  the  ttm  results  account.  The  determination of ablation pressure was  laser  obtained  light.  obtained  The  from  superiority  VI: from  results  ion  mea-  of shock  speed  demonstrated.  VI-2 New Contributions  A n tational  important  capability  new  in  the  contribution study  implementing a hydrodynamic thus  enhancing  through  the  our  theoretical  h y d r o c o d e , we  issues s u c h as r a d i a t i o n  The sure  anomalously  inferred  from  ion  enabled us to indentify  are  of  of  this  work  laser-matter  code.  transport  the  establishment  interactions  by  properly  T h i s will enable us to better  understanding in  is  the  of  the  position to  physics.  crucial  and equation of state in highly  and  our  compu-  upgrading  model our  interaction  address  of  experiments, In  particular,  interesting  compressed  physics  matter.  strong wavelength scaling of mass ablation rate a n d ablation measurements several  has  been  errors which  explained  through  the  arose in ion measurements.  and  pres-  simulations.  This  Furthermore,  suc-  cessful m e a s u r e m e n t of ablation pressure f r o m shock s p e e d was d e m o n s t r a t e d .  These  verified  predicted  both  the  intensity  and  wavelength  scalings  of the  ablation  pressure  calculation  of the  recombination  results by  simulations.  We with  have  also p e r f o r m e d  a hydrodynamic  fying the  code.  the  first  This has  clarified  the  ion charge state in an expanding plasma.  significance  process  of recombinations  coupled in  modi-  CHAPTER VI-S  Future Work  T h e  results  presented  in  this  b o t h in the numerical code a n d the  P r o d u c t i o n of X U V port  VI:  which  are  crucial  work  have  experimental  state.  T h e  improvements  techniques.  for  assessing the  effects  of radiation  driven  ablation  T h i s will simply involve using  radiation calculations incorporated into  could be verified by  need for  a n d X - r a y s i n l a s e r - m a t t e r i n t e r a c t i o n s as w e l l as r a d i a t i o n  preheat in targets should be evaluated in detail. current  d e m o n s t r a t e d the  experimental m e a s u r e m e n t s of the  Medusa  and  trans-  radiation  Medusa  in  its  and the post-processor  radiation energy  emitted  from  the  corona.  In  Medusa rently  terms  .  The  the  from the  At  of further  most important  best  s o l u t i o n is t o  S E S A M E  data  laser intensities  is e x c e e d e d .  code  >  new  features  should  1  a  tabular  equation  of Los A l a m o s National  4  W / c m  hopes  2  ,  to  of state  as  be  added  is c u r r e n t l y  the threshold for various p a r a m e t r i c model future  to  Cur-  available  Laboratory.  experiments  the  ability  instabilities to  simulate  important.  processes o c c u r i n g in laser-matter interactions are inherently  For instance, lateral Ultimately,  include  1 0  these instabilities will b e c o m e  several  modification involves i m p r o v i n g the equation of state.  library  T h e r e f o r e , if o n e  M a n y  developements,  energy transport has already  the need to consider magnetic  fields  been observed to play  two-dimensional.  an important  role.  will m a k e two-dimensional codes necessary.  A l t h o u g h work was started in this area, the current c o m p u t e r facilities p r o h i b i t any  detailed  calculations.  Finally,  an  additional experiment  l a t i o n p r e s s u r e at would enhance the thesis.  a laser  wavelength  reliability  of the  should be performed in order to evaluate  of 0.35 / i m u s i n g s h o c k v e l o c i t y ablation pressure wavelength  the  measurements.  scaling presented in  abThis this  82  Bibliography  1.  J . N u c k o l l s , L . W o o d , A . T h i e s s e n , a n d G . Z i m m e r m a n , N a t u r e 259,  2.  K. A . Brueckner  3.  R. C . M a l o n e , R. L . M c C r o r y a n d R. L . M o r s e ,  4.  D. .E.T . F. Ashby, Nuclear  5.  W . B. Fechner  6.  G.  P  Phys.  46,  3 2 5 (1974).  Phys.  Rev.  27,  Fluids  E. M . C a m p b e l l , W . L. Kruer,  F. L a s i n k i ,  K. Estabrook  R  .E. Turner,  8.  H . A . Baldis  9.  L. R. Veeser a n d J . C . S o l e m ,  a n dC .J . Walsh  R. J . T r a i n o r , J . W . 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Columbia Plasma  G r o u p i n t e r n a l l a br e p o r t # 7 5 ,  APPENDIX  APPENDIX  A:  A  MEDUSA POST-PROCESSOR  In  order to simplify  incorporated is  into  interactive.  an  answer  error  by  Only  command  W h a t  (or  terminated  the  t h e u s e o f t h e p o s t - p r o c e s s o r , as m u c h  this  language.  implies  message  issuing the  is  that  The the  if n e c e s s a r y )  program  and  STOP  c o m m a n d  program,  (or  END  of the  is  file c o n t a i n i n g  issued for  which  Medusa  the  data  results.  is n e c e s s a r y  and  This  the  a  in  as possible  Pascal  and  command,  instructions.  was  fortran,  replies This  with  loop  is  MTS) .  or  two questions are explicitly asked b y the p r o g r a m .  name  command  on  futher  u p o n b e g i n n i n g e x e c u t i o n , is t h e n u m b e r o f c e l l s u s e d i n t h e is t h e  written  acts  awaits  flexibility  The  Medusa  first,  asked  simulation.  q u e s t i o n is o n l y  data  file  immediately  has  not  The  asked  been  second when  a  previously  specified.  To each  aid  line  the  user,  the  program  (prefix) to indicate  ?  COMSD->  it's c u r r e n t  Indicates the  Indicates  the  c o m m a n d is  No  prefix  number  of  Angle brackets m a n d  status.  main program  three  Square  brackets  •  Braces  {}  at  the  beginning  of  are  i n f o r m a t i o n is r e q u i r e d .  is a w a i t i n g  dimensional  plot  a new  routines  indicates  the  program  is  For  instance,  when  command.  are  acting  active  "put  the n a m e  [ ] surround optional  surround things y o u  on  and  some  follows, the following syntax  surround c o m m a n d parameters.  description means  •  These  sequences  an  appropriate  requested.  string  < >  character  cells.  c o m m a n d description which  •  various  Indicates some form of additional asking for the  COM->  uses  may  of the  file  For  is  example,  command.In  the  used  <file  >  in a  com-  here".  parameters.  choose from, separated  by  vertical  bars  | .  For  APPENDIX example,  A-l  {one  | other  }  means  "type  either  'one' or  'other' "  .  Commands  T h e m a i n c o m m a n d s currently supported involve some form of plotting or of  X-ray  radiation.  function of  We  begin by  <variablename  T I O N  =  where  describing the  <coord  >  |  variablename  D E N S I T Y  Density  >  F U N C T I O N  plot  a quantity  as  a  c a n be  any  in K g / m  3  of the  Velocity  I O N T E M P  A V E R Z  Ion  in m/s  temperature  Specifies the  Specifies  that  in K  in K  charge state  other plot parameters  CELL  >  |  P O S I -  3  .  .  temperature  Average  <cell  .  V E L O C I T Y  Electron  T I M E A T {CELL =  following:  H y d r o d y n a m i c pressure in J / m  E L E C T E M P  O F  N C R I T }  P R E S S U R E  P O S I T I O N  c o m m a n d issued to  calculation  time.  P L O T  T h e  A:  .  .  .  specify the  area for which  L a g r a n g i a n cell w h i c h  the  value  of the  the quantity  is t o b e  quantity  at  is t o b e  plotted  plotted.  the  given  lab  coordinate  is  to  be  plotted.  N C R I T  Specifies that the value of the quantity  Initially  the  program  is  in  a  at  t h e c r i t i c a l d e n s i t y is  TELLAGRAF  mode.  to be  plotted.  What  this  means  is  that  p  APPENDIX are n o t actually commands  drawn  required  but rather  to create  user additional  flexibility  have the plots  generated  a  file  the plots.  is g e n e r a t e d This  then  contains  all the  TELL A  approach was selected because  in manipulating the layout immediately  which  of the graph.  the c o m m a n d N O  A:  GRAF  it allows  If t h e u s e r w o u l d  T E L L A G R A F  the  rather  should  be  issued.  The  P L O T  c o m m a n d issued to plot  variablename  a quantity  F U N C T I O N  O F  as a f u n c t i o n o f p o s i t i o n is  { P O S I T I O N  |  C E L L }  A T  T I M E  =  <time> .  The  P L O T  c o m m a n d issued to plot  variablename  a quantity  F U N C T I O N  O F  as a f u n c t i o n o f t i m e  { P O S I T I O N  | C E L L  a n d p o s i t i o n is  }  A N D  T I M E  .  T h e c o m m a n d i s s u e d to c a l c u l a t e a n d plot t h e X - r a y e m i s s i o n as a f u n c t i o n of p h o t o n energy  is  S P E C T R U M  where the  < t i m e l > [<time2> ]  timel  and  time2  X-ray  intensity  spectrum  calculates  the total  X-ray  A-2  at time  energy  timel  is c a l c u l a t e d .  (or intensity)  If  time2  is o m i t t e d  then  In b o t h cases t h e p r o g r a m  also  .  Three-Dimensional Plot Commands  After D  specifies the range of integration.  a three-dimensional plot has been generated the program remains in a  m o d e " a s indicated b y the prefix C O M S D - >  . T h i s permits the user a m o n g other  "threethings  APPENDIX to change box  the viewpoint.  as i l l u s t r a t e d i n F i g u r e  V I E W P O I N T  < x  where x, y, work  T h e  box  F i g u r e  (Figure  A - l  Data  S M O O T H  >  < y  t h r e e - d i m e n s i o n a l s u r f a c e is d e f i n e d w i t h i n  A - l . T h e viewpoint  >  <z  issuing the  z defines the viewpoint  in the  >  < n y  >  box  enabled by  < w  1 x  1  work  c o m m a n d  absolute coordinate system defined by  A-l).  smoothing can be  1 x  >  Three-Dimensional work  < n x  is set b y  a  A:  >  .  issuing the  c o m m a n d  the  APPENDIX T h i s t h e n d e f i n e s t h e v a l u e , Vij,  where  D^k  is t h e d i s t a n c e  modified parameters  A-S  at grid l o c a t i o n  between  simply  nodes  through the equation  and  issue t h e c o m m a n d  A:  (l,k).  PLOT  or  T o re-plot  the data  with  the  SURFACE.  Auxilary Commands  In this commands  section we summarize other  are n o t as i m p o r t a n t  commands  currently  available.  as those p r e v i o u s p r e s e n t e d t h e y  Although  are i n s o m e cases  these neces-  sary.  • {XAXIS This plot  | YAXIS  command  allows  | Z A X I S } L A B E L <"this is a label" > t h e user t o specify t h e axis labels t o b e used i n t h e plot.  T h e  title c a n b e set i n a s i m i l a r w a y .  •  OVERLAY W h e n  graph.  this  c o m m a n d is i s s u e d t h e s u b s e q u e n t  This permits  t h e user to plot several  curves  curve  will b e plotted o n the previous  o n a single  graph.  • D A T A F I L E <filename > T h i s c o m m a n d sets t h e several  data  file  to be  filename.  T h i s enables one to analyze  simulation results d u r i n g o n e r u n .  Normally, the  Medusa  data  position  file at  when  from various  a c o m m a n d  the beginning. times  this  is i s s u e d w h i c h W h e n  search  requires  o n e is i n t e r e s t e d  process  data, the post-processor in a  c a n represent  a  quantity significant  as  scans  a function of portion  of the  APPENDIX computation time.  •  [ N O ]  T h e  c o m m a n d  A U T O R E S E T  c a n be used to m o d i f y this procedure. then  If t h e u s e r i s s u e s t h e c o m m a n d N O  the p o s t - p r o c e s s o r w i l l b e g i n its s e a r c h w h e r e  return  •  to the original scheme b y  D E B U G  This issued  the  < f i l e n a m e  c o m m a n d  allows  p r o g r a m will,  A - 4  F i n a l  the  user  on subsequent  c o m m a n d simply  P L O T  C E L L  A T  P L O T  D E N S  all e q u i v a l e n t .  processor  to  check  program  execution.  c o m m a n d s , write out  various  W h e n  One  D E B U G  diagnostic that  the  T o disable this feature s i m p l y re-issue the  switches  for various  between  In  the  two  importantly,  additions straight  alternatives.  O F  appears For  can  is  messages program c o m m a n d  states).  rigid,  instance  C E L L  H Y D R O D Y N A M I C  A T  the parsing capabilities  the  of  commands  T I M E = 1 . 0 E - 9  D E N S I T Y  A S  A  F U N C T I O N  O F  1.0E-9  C E L L  the  presented  F U N C T I O N  T I M E  m i s t a k i n g this  More  search.  A U T O R E S E T .  U s i n g this feature one c a n easily verify  c o m m a n d syntax  D E N S I T Y  P L E A S E  are  the  post-processor allow  P L O T  previous  C o m m e n t s  Although the  A U T O R E S E T  >  is i n t e r p r e t i n g t h e c o m m a n d s c o r r e c t l y . (the  it e n d e d t h e  entering the c o m m a n d  i n d i c a t i n g e x a c t l y w h a t it is d o i n g .  D E B U G  A:  A T  above  T I M E  examples  as a r e q u e s t  however,  forward.  1.0E-9  the k e y w o r d  A T  is n e c e s s a r y  for a three-dimensional  the  modular  form  of the  to  avoid the  post-  plot.  program  should make  future  APPENDIX A P P E N D I X  M E D U S A  The 5 0 fim -  entire p a r a m e t e r  aluminum  target  I N P U T  B:  B  P A R A M E T E R S  list u s e d i n a m e d u s a s i m u l a t i o n t o m o d e l t h e i r r a d i a t i o n o f a  w i t h 0 . 5 3 fim  laser b e a m  at a n intensity  =  1 0  1  4  is p r e s e n t e d  below.  T a b l e  Medusa  LAMDAl  =  0.5327 -  GAUSS  =  -1.0  XZ  =  13.0  RINI  =  4.C27 -  CENTER  =  DRGLAS  B-l  Input  Parameters  PMAX  =  1.02717  ANPULS  =  1.0  PMULT  =  2.0  PLENTH  =  2.027-9  XMASS  =  26.98  NGEOM  =  1  RHOGAS  =  2700.00  FNE  =  1.0  0.0  TAMPED  =  F  DTAMP  =  25.027 -  =  0.0  ROGLAS  =  0.0000  DRPLAS  =  4 . 0 £-  ROPLAS  =  2700.0  HFRACT  =  -0.5  T1INI  =  5.0274  TOFF  =  4.027 -  ZGLAS  = 0.00  ZPLAS  = 70.0  NPRNT  =  200  NPZ  =  1  DELTAT  =  1.027 -  DTREGN  =  0.0  TEINI  =  MESH  =  6  5  6  5.0274 200  NRUN  =  100000  TSTOP  =  4.0027 -  AKO  = 20.0  AKl  = 0.10  AK2  = 0.10  AKZ  =  AK4  =  AKb  = 0.50  0.10  9  18  0.10  NITMAX  =  5  DTEMAX  = 0.20  DUMAX  =  NLPFE  =  F  STATE  =  SAHA  =  1.0  = T  ANABS  =  0.05  3.0  NLCRIl  =  T  FHOT  =  0.0  FTHOT  =  - 1 . 0  RHOT  =  0.0  =  0.04  PIQ{27)  -  0.0  P/Q(55)  =  2.0  MIT  NLBURN  =  F  NLFUSE  =  NLDEPO  =  F  NRADT  =  F  NLTE  = T  PONDF  =  1  CELRTl  =  0.99887  CELRTG  =  CELRTP  =  1.0000  A follows,  detailed we  description of each  briefly  discuss  parameter  the significance  F 1.0  c a n be found in Reference  of the parameters  AKO  - •• A K l ,  9  0.20  NLABS  F LI  5  [92].  In  what  D T E M A X ,  APPLNDIX DTIMAX, of  and  DUMAX,  which  affect  t i m e s t e p c o n t r o l a n d , as s u c h , affect  the  B:  accuracy  t h e results.  The  timestep  A t  n  +  1  /  is t a k e n  2  as t h em i n i m u m o f  »+i/2 <A K 0 t - ' n  A t  1  [B.l]  2  < AKlmin^-^^—'-j  [B.2]  (V  - V " 1  N+1  where  n refers  Expressions Relation discussed relation  t o t h e nth  similar [B.2],  which II,  [5.3]controls  a n d / refers  t o t h e cell w i t h b o u n d a r i e s  numerical  forT, and  a n dm  respectively.  AKS  relation  [B.Z]  _  m  ~  the value  e  and program execution  a n d T (AKA) e  criterion  i n specific v o l u m e  hand, to a  u  r—  n  +  1  < DUMAX  /  T  e  when  I  l  being coupled through T , and  2  after  [B.4]  the m t ha n dm -  to d T i ( D T I M A X )  w a sa d d e d at U . B . C . b y J o e K w a n  If r e l a t i o n  a n d Rj.  O n the other  Specifically, if  NITMAX  and  d T  (1982)  j  e  1 t h iterations  ( D T E M A X )  .  a n d represents a n u p -  iterations are  is n o t s a t i s f i e d , t h e n p r o g r a m e x e c u t i o n t e r m i n a t e s  ( S i m i l a r l y f o r T,- a n d T ).  T h e values  stability.  the change  a n de n e r g y  of u  du =  Medusa  b y limiting  of motion  per b o u n d o n the convergence criterion. and  t o T{(AK2)  Rj+i  e  T w os i m i l a r e x p r e s s i o n s a p p l y  The parameter  numerical  C o n v e r g e n c e is e s t a b l i s h e d  — 1 indicate  apply  V,  [B.2]  T ).  8u =  m  >  of the Courant-Friedrichs-Lewy  to ensure  accuracy  l m  where  volume,  a statement  is n e c e s s a r y  the equations  solved iteratively.  I -L_  f o r t h e specific  is s i m p l y  (similarly  Furthermore, are  to that  in chapter  specified fraction  timestep,  < AK2 min  performed  if  > AKS  [B.5]  [ B . 5 ] is n o t s a t i s f i e d , a n e r r o r m e s s a g e is g e n e r a t e d b y  continues.  o f these parmeters  a s u s e d i n all the  Medusa  runs  are  given i n table B - l .  APPENDIX We  arrived  with to  a  two  at t h e s e v a l u e s b y r e q u i r i n g t h a t t h e c h a n g e i n c o m p u t a t i o n a l r e s u l t s fold  evaluating  the  decrease timestep  p r o b l e m , it r e m a i n s  in  the  parameters  AK0---AK4  control parameters  the only practical  solution.  is c r u d e  be but,  negligible.  due  to  the  This  B:  associated approach  complexity  of  the  

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