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An optically pumped iodine laser amplifier Billing, Martyn Kenneth 1980

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AN OPTICALLY PUMPED IODINE LASER AMPLIFIER by MARTYN KENNETH BILLING B.Sc, The University of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OF MASTER OP SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept t h i s thesis as conforming to the required, standard THE UNIVERSITY OF BRITISH COLUMBIA January 19 80 © Martyn Kenneth B i l l i n g , 1980 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e 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 o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r 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 Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 D a t e z f ^ ^ *s / ? 7 9 D E - 6 B P 7 5 - 5 I 1 E A B S T R A C T The design process of an o p t i c a l l y pumped a m p l i f i e r for a CF^I photodissoelation l a s e r i s described. In p a r t i c u l a r , a preamplifier i s designed to amplify a 1 0 0 mJ l a s e r pulse of 1 ns. duration which, by natural divergence, i s contained i n a beam of 2 . 5 cms diameter. Experimental studies of the sub-system of th i s preamplifier and the associated diagnostics are described. The operation of the preamplifier as part of the t o t a l l a s e r system i s discussed and suggestions are offered for the ongoing development of the device at the University of B r i t i s h Columbia. i i i TABLE OP CONTENTS Page ABSTRACT l i TABLE OP CONTENTS i i i LIST OF FIGURES v LIST OF TABLES v i i i CHAPTER I INTRODUCTION 1 CHAPTER I I THE MAJOR COMPONENTS OF A GAS LASER AMPLIFIER 5 CHAPTER I I I THE SYSTEM DESIGN PROCESS 7 CHAPTER IV SYSTEMS ANALYSIS 1 1 1 . The Photolysis of C F 3 I 1 1 2 . The Laser Transition . 1 2 2 . 1 The Spectrum of the Transition ....... * 3 14 2 . 2 Pressure Broadening 2 . 3 The Effe c t i v e Cross-Section 15 3 . Stored Energy 21 3 . 1 Chemical Deactivation • 2 1 3 . 2 Radiative Deactivation 28 3 . 3 The Temporal Behaviour of the Stored Energy due to the Onset of P a r a s i t i c O s c i l l a t i o n s 3 ^ 3.34'' I n e r t i a l Delay 3 6 4. Gain ^ 2 5. Extraction Ratio 47 6 . Saturation Energy Density 47 7. Beam Quality 48 i v Page 8 . Pulse Shape Modification ^9 9 . E f f i c i e n c y 5 0 1 0 . Buffer Gas Pressure 5 1 1 1 . The Flash Tube C i r c u i t 5 2 CHAPTER V THE SYSTEM DESIGN PROCESS 5 5 1 . The Given Variables 5 5 2 . The Gas Pressures 5 8 3 . Stored Energy, Gain and Extraction Ratio 5 9 4. Stored E l e c t r i c Energy 6 2 5 . The E l e c t r i c a l System and the Pump Light Pulse 6 4 6 . Mechanical Design , 6 9 CHAPTER VI DIAGNOSTICS 7^ CHAPTER VII THE EXPERIMENTS 73 CHAPTER VIII CONCLUSIONS 8 9 BIBLIOGRAPHY 9 5 V LIST OP FIGURES Figure Page 1 Schematic of the Asterisk I I Iodone Laser .... 2 2 Schematic diagram of an o p t i c a l l y pumped gas la s e r a m p l i f i e r . 5 3 The system design process 7 4 The systems analysis process 9 5 System design relationships 10 6 The energy l e v e l s and degeneracies g of the Elgenstates of t o t a l angular momentum of the nucleus plus the electrons (quantum number F) of atomic iodine 12 2 o 7 The spectrum of the 5P - 5P^ t r a n s i t i o n , showing the hyperfine s p l i t t i n g due to the angular momentum and. the quadrapole moment of the e l e c t r i c f i e l d of the nucleus 1 3 8 The depletion of the inversion of an homo-geneously broadened l i n e 18 9 The depletion of the inversion of an inhomo-geneously broadened l i n e 19 10 Guided wave mode confined within the l a s e r tube since the angle of incidence 0 i s large . 3 1 11 Guided wave; modes t y p i c a l of small incident angles, the wavefront being confined by the flas h tube r e f l e c t o r • 3 1 1 2 The transient behaviour of the inversion and the r e s u l t i n g l a s e r energy due to a pump l i g h t pulse I n i t i a t e d at t = 0 3 6 1 3 The i n e r t i a l delay of a l a s e r pulse generated i n a resonant cavity 3 7 14 The i n i t i a l conditions and domain of integ -r a t i o n of the d i f f e r e n t i a l equation character-i z i n g the amp l i f i c a t i o n of a l a s e r pulse ..... 44 v l Figure Page 15 System design diagram i n d i c a t i n g the given variables 57 16 The section of the system design diagram which i s used to define the gas pressures .......... 59 17 The section of the system design diagram used to define the stored energy, gain and extrac-t i o n r a t i o s 6 1 18 The section of the system design diagram used to define the stored e l e c t r i c energy 6 3 19 The section of the system design diagram containing the remaining undefined variables . 64 20 Details of a c y l i n d r i c a l sub-assembly and an 0 ring sealed window assembly 73 21 Current pulse p r o f i l e s . The current pulses dr i v i n g the a s o c i l l a t o r (upper) and the amp l i f i e r (lower) flash tubes are shown • 74 22 The incident and amplified l a s e r pulses. The output from the two photoconductive detectors i s shown,tthe f i r s t (second) being generated by the amplified (incident) l a s e r pulse 75 2 3 Schematic diagram of the ampl i f i e r and associated diagnostics 77 2 4 The current flow i n the secondary winding of the S.C.R. tr i g g e r transformer. Noise i s seen to occur each time the current passes through zero 31 2 5 The current flow i n the secondary winding of the S.C.R. tr i g g e r transformer shown when a long cable to the oscilloscope i s used • • 82 26 The amplified l a s e r pulse and the o s c i l l a t o r and a m p l i f i e r current pulses are shown. The additional pump energy delivered to the active medium i s seen not to increase the system gain 86 v i l Figure Page 2 7 The temporal behaviour of the pump current and the subsequent system gain for a zero buffer gas pressure i s shown for the ampl i f i e r i n i t s present state of construction 8? 28 The temporal p r o f i l e of the i n t e n s i t y of the incident (broken l i n e ) and amplified ( s o l i d l i n e ) l a s e r pulse i s shown ••• 9 0 2 9 A long duration l a s e r pulse generated by a gain switched o s c i l l a t o r stage, without a mode locking system 9 2 v l i i LIST OF TABLES Table Page 1 Current pulse ch a r a c t e r i s t i c s f o r capacitor bank 6 8 CHAPTER I INTRODUCTION In 1938 Porret and Goodeve published a theoret i c a l paper i n which they demonstrated that the photolysis of alkyllodes should produce iodine atoms mainly i n the excited 2 P| state ( 1 ) . Stimulated emission to the 2 P ^ y 2 ground state was f i r s t observed and reported by Kasper and Pimentel i n 1964 ( 2 ) . In 1 9 6 6 the f i r s t attempts to model the kinematic processes occurring during the photolysis and subsequent l a s i n g were made, ( 3 ) and i n 196? scaling laws were derived which predicted that the iodine l a s e r could be used to produce large output power pulses ( 4 ) . The f i r s t systematic study of the iodine l a s e r began at the I n s t i t u t e of Plasma Physics (IPP), Garching, F.R.G., i n 1970 and by 1972 , motivated by the need for high power l a s e r pulses f or fusion experiments, the decision was made to develop an IKJ-lns device. This l a s e r , c a l l e d Asterlx I I I ( 5 ) i s now operational and a schematic diagram of the major components i s shown i n Figure 1. Puis* Shop* Monitor F i g . 1. Schematic of the Asterisk I I I Iodine Laser. The acousto-optically mode locked o s c i l l a t o r has an active volume 1 cm. i n diameter and 1 m; long and i s operated i n the gain switched mode. A pulse cutting system t-separates out a IKJ-lns pulse for ampli f i c a t i o n by the four subsequent stages. The energy i n the output pulse of the 3 entire system i s derived mainly from the f i n a l a m p l i f i e r which has an active volume 2 0 cms. i n diameter and 1 0 m. long. The a l k y l l o d i d e ( C 3 F 7 I ) i s o p t i c a l l y pumped using 64 Xenon fl a s h tubes, each 1 m. long. Three pre-amplifier stages with diameters chosen to accomodate the natural divergence of the beam are used to raise the energy density to a l e v e l s u f f i c i e n t to release the stored energy i n the f i n a l a m p l i f i e r . Faraday rotators and a saturable absorber are included to improve the o p t i c a l i s o l a t i o n of the i n d i v i d u a l stages. The r e p e t i t i o n rate of the Asterisk I I I i s l i m i t e d to one shot each eight minutes by the gas recycling system which "cleans" the used gas and automatically delivers a new charge. A terawatt Iodine l a s e r i s also being developed at the Sandia Laboratories, Albuquerque, New Mexico (6). These gas l a s e r systems have certain advantages over high power s o l i d state devices: 1 . Large geometric dimension of the active medium can be achieved more e a s i l y and cheaply. 2 . Unlike s o l i d state devices, the f i n a l a m p l i f i e r of a gas l a s e r system may be operated In saturation. The broad l i n e width of the l a s e r t r a n s i t i o n i n s o l i d state materials results i n the saturation energy density of an a m p l i f i e r exceeding the damage threshold for the medium. 4 However, gas l a s e r s , having narrow l i n e widths, may be operated i n saturation, thereby achieving a much improved extraction r a t i o . The l i n e p r o f i l e may be controlled by pressure broadening and the effect to optimize the operation of the device. 3 . An improved beam qu a l i t y i s possible since l o c a l perturbations i n the o p t i c a l properties of the medium, t y p i c a l of glasses, do not occur. An iodine l a s e r i s under construction at the University of B r i t i s h Columbia, primarily for the use i n laser-plasma i n t e r a c t i o n experiments. During the construction phase careful studies of the various subsections are being under-taken i n order to generate a technical' expertise within the department and contribute to the technical development of the device. At present, a fog c e l l o p t i c a l I s o l a t e r i s being evaluated. To t h i s time an o s c i l l a t o r stage has been b u i l t and a preamplifier with an active volume 1 cm. i n diameter and 1 m. long i s under construction. This paper describes the design procedure for a gas l a s e r a m p l i f i e r stage, and i n p a r t i c u l a r the design of a preamplifier for a 100 mJ-Ins l a s e r pulse contained i n a beam of diameter approximately 2.5 cms. i s presented. CHAPTER I I THE MAJOR COMPONENTS OF A GAS LASER AMPLIFIER A schematic diagram of the major components of an o p t i c a l l y pumped gas l a s e r a m p l i f i e r i s shown below. MIXING CHAMBER F i g . 2. Schematic Diagram of an Op t i c a l l y Pumped Gas Laser Amplifier. 6 The active medium Is contained In a doped quartz tube and o p t i c a l pumping Is achieved using high i n t e n s i t y short pulse xenon ;flash tubes which are driven by a low inductance capacitor bank, the current being switched with a spark gap triggered by an S.C.R. un i t . An active and a buffer gas are mixed i n the mani-f o l d chamber before being passed to the l a s e r tube. The gas system i s evacuated by a mechanical and a d i f f u s i o n pump. 7 CHAPTER I I I  THE SYSTEM DESIGN PROCESS The objective of the system design process i s to define the choice of component parts and t h e i r assembly Into the complete device, together with the operating conditions, to achieve a specified system performance (Fig. 3 ) . F i g . 3 . The System Design Process 8 The system performance of an iodine a m p l i f i e r can be spe c i f i e d i n terms of seven parameters. 1. Gain: the t o t a l Increase i n energy of an incident pulse on passing through the am p l i f i e r . 2. Bandwidth: characterizing the frequency dependence of the system gain. 3. Extraction Ratio: the r a t i o of the stored energy to the energy extracted by the incident l a s e r pulse. 4. Beam Quality: the s p a t i a l coherence and i n t e n s i t y p r o f i l e of the beam should not be disturbed by the amp l i f i e r . 5. E f f i c i e n c y : the r a t i o of the energy stored i n the capacitor to the energy extracted from the active medium by the incident l a s e r pulse. 6. Lifetime: the l i f e t i m e of the fla s h tubes. ?. Si m p l i c i t y of Maintenance: (see Chapter 5)» In practice the design process cannot proceed as i l l u s t r a t e d i n Figure 3» Rather, the device design and the operating conditions are chosen and the system perform-ance i s then evaluated. Changes are made i n the design or operating condition u n t i l the required system performance i s achieved (see Figure 4). 9 Pig. 4. The Systems Analysis Process. The i n t e r r e l a t i o n s between the system performance, device design and operating conditions can be represented schematically on a Polya-Fuller map (Figure 5)t where system variables are represented by e l l i p s e s and the relationship between the variables by squares. This diagram indicates c l e a r l y the complicated interdependence of the d i f f e r e n t design choices and performance c r i t e r i a . In order to be able to proceed with the design process, these relationships must be found e x p l i c i t l y . 1 0 Fig* 5» System Design Relationships CHAPTER IV SYSTEMS ANALYSIS A detailed analysis of the iodine l a s e r system Is presented i n t h i s chapter and the functional relationships as represented on the Polya-Fuller map are derived. CHAPTER IV SECTION 1 THE PHOTOLYSIS OF C F 3 I The absorption spectrum of CF^I, which i s both Doppler and pressure broadened, has a maximum at 4.6 eV (2660A0) associated with the processes CF 3I ^ CF 3 + I ( 5 P i ) , CF 3I ^ CF 3 + I ( 5 P 3 / 2 ) (1) The cross-section for producing ground state (5P 2 , ) 3/2 i s small ( 7) and hence t h i s process may be ignored. Breaking the C-I bond requires an energy of 2.46 eV and an additional 0.95 eV excites the iodine atom i n t o the 2P?j/ 2 state (8)..- The remaining 1.45 eV ultimately contributes to the heating of the entire gas. CHAPTER IV SECTION 2 THE LASER TRANSITION Lasing occurs between the 5PX excited state and the 2 5P4 ground state of atomic Iodine. The excited and the ground states have degeneracies of 2 and 4 respectively and the t r a n s i t i o n has a radiative l i f e t i m e of 170 ms. ( 9 ) . „ The iodine nucleus has a t o t a l angular momentum of J N =5/2 (natural occurrence 100$ ; (10) ) and hyperfine s p l i t t i n g i s observed. (See figures 6 and 7) F 9 7 F.NERRY 3 2 5 2 4 3 Z 7 5 3 Pig. 6 . The energy l e v e l s and degeneracies g of the Eigenstates of t o t a l angular momentum of the nucleus plus the electrons (quantum number F) of atomic iodine. 13 CHAPTER IV SECTION 2.1 THE SPECTRUM OF THE TRANSITION The spectrum of the energy l e v e l s at a pressure of 15 Torr has been measured by Jaccarlno ( 11 ) and Is shown In Figure 7» 1 INTENSITY F i g . ?• The spectrum of the 5P£ - 5P ^  t r a n s i t i o n , showing the hyperfine s p l i t t i n g due to ihe angular momentum and the quadrapole moment of the e l e c t r i c f i e l d of the nucleus. The rate of stimulated emission S(w) into the frequency i n t e r v a l w to w+dw may be expressed ei t h e r In terms of a frequency dependent inversion n(w) and a constant cross-section o* S(w) * o-(w) x f l u x x n(w) (2) or i n terms of a frequency dependent cross-section o-(w) and t o t a l inversion n S(w) = o*(w) x f l u x x n (3) 14 Under the assumption that the occupation of the lower energy l e v e l s i s small, the graphs of or(w) and n(w) take the same form as figure 7. CHAPTER IV SECTION 2.2 PRESSURE BROADENING Pressure broadening often r e s u l t s i n a Lorentzian l i n e shape such that a(w) for a single t r a n s i t i o n i s given by cr(w) = 2TT 2 Ac 2 f(w-wQ) (4) w2" A wD where wQ i s the resonant frequency of the t r a n s i t i o n &w 0 i s the h a l f width A i s the Einstein c o e f f i c i e n t for spontaneous emission between the upper and lower energy l e v e l s and f(w-wQ) = [ l + [2(w-wQ) ] 2 j* " 1 (5) Since the h a l f width varies d i r e c t l y with pressure the cross-section o-(w) of each t r a n s i t i o n can be plotted for d i f f e r e n t degrees of pressure broadening. C0 2 or Argon may be added to the active gas to achieve t h i s broadening, the broadening c o e f f i c i e n t s being 9MHz per Torr (12) and 4.5 MHz per Torr respectively (13, 12). Calculations by K. Hohla (5) show that at a buffer pressure of 400 Torr C0 2, the t o t a l cross-section o-(w) for a t r a n s i t i o n between the 15 upper and lower energy l e v e l s has merged into a single l i n e . At t h i s pressure the frequency r o l l o f f due to the l i m i t e d bandwidth w i l l not s i g n i f i c a n t l y broaden a l a s e r pulse of 1 ns. duration as i t passes through an a m p l i f i e r (14). S i m i l a r l y , a buffer pressure of 2000 Torr Argon Is s u f f i c i e n t for a 200 ps. pulse (6). CHAPTER IV SECTION 2.3 EFFECTIVE CROSS-SECTION In the analysis of Sections 2.3 and 2.4 of t h i s chapter, I t Is convenient to describe the rate of change of photon density within the radiation f i e l d due to stimu-l a t e d processes by the equation dq = cr £ c q(t) n(t) (6) dt where q i s the t o t a l number of photons per unit volume within the radiation f i e l d , o~E Is an effective cross-section for the processes, c i s the v e l o c i t y of l i g h t and n i s the t o t a l Inversion per unit volume. I f such a model i s to be used, then the l i n e shape of the rad i a t i o n f i e l d and. the gain p r o f i l e of the l a s e r medium must be accounted f o r within the e f f e c t i v e cross-section <rw. An expression for o*g. w i l l now be derived. The rate of change of the number of photons i n a u n i t volume within the radiation f i e l d i s given by d^ = B 1 2 q nj - B 2 1 q n 2 (7) where nj i s the t o t a l number of atoms i n a unit volume that could emit a photon into the radiation f i e l d , n 2 Is the t o t a l number of atoms i n a unit volume that could absorb a photon from the r a d i a t i o n f i e l d and B^ 2 and B 2^ are the Einstein c o e f f i c i e n t s f o r the t r a n s i t i o n s . Using the r e l a t i o n B12Si * B 2 l g 2 we can write equation (7) In the form §3. = B 1 2 q(nj - g a/g 2 n 2) = B 1 2 q n* (8 ) dt Res t r i c t attention to the photons In the radiation f i e l d within one h a l f width at f u l l maximum of the spectral l i n e ( f(w) ) then q = J f(w) dw (9) w_ and n' may be written as n f ( t ) « n(t) / G(w) dw (10) w Here, G(w) i s the l i n e shape factor of the l a s e r t r a n s i t i o n , Aw Q i s the h a l f width of the l a s e r t r a n s i t i o n , w0' I s the central frequency of the radiation f i e l d spectrum, ^ w 0 t i s the half width of the radiation f i e l d spectrum and n i s the t o t a l inversion per unit volume and w± = wQ 3 wQ. Substituting equation ( 1 0 ) into ( 9 ) we have w+ M = B 1 9 q n / G(w) dw ( 1 1 ) dt " J Aw 0 w_ Defining the e f f e c t i v e cross-section to be °E 2 B 1 2 / c / G ( w ) d w < 1 2 ) J wQ w_ we have as required dg. = <rE c q n (6) dt There are two cases to consider. The homogeneously broadened l i n e where G(w) i s not a function of time, and the inhomogeneously broadened l i n e where G(w) changes with time; 18 In a homogeneously broadened l i n e the t o t a l number of atoms i n energy Eigenstates which can emit a photon i n t o the radiative f i e l d i s maintained, by a process s u f f i c i e n t l y fast that the entire Inversion i s depleted by l a s i n g . (See Figure 8 ) G(-4 Fig. 8 The depletion of the inversion of an homogeneously broadened l i n e 0 An inhomogeneously broadened l i n e exhibits hole burning whereby the atoms able to emit a photon into the radiation f i e l d are consumed fa s t e r than they can be replenished from other spectral regions of the t r a n s i t i o n , i«e., G(w) changes with time. (See Figure 9) 1 9 1 t« o ,/ "*' / Pig. 9« The depletion of the inversion of an inhomogeneously broadened l i n e . whether a t r a n s i t i o n i s homogeneously or inhomogeneously broadened depends on the pulse duration of the radiation f i e l d . In the CP-jI l a s e r the t r a n s i t i o n i s Doppler and pressure broadened, andin both cases c o l l i s i o n s between p a r t i c l e s are responsible f or the " d i f f u s i o n " between spectral regions. The c h a r a c t e r i s t i c time, t c , between c o l l i s i o n s can be written *o = 1 (^3) n o v °k where n 0 i s the t o t a l p a r t i c l e density, v i s the mean ther-mal v e l o c i t y and o^ i s the gas-kinetic c o l l i s i o n cross-section. 20 Using values for the CF^I l a s e r of ^ * 3 x 10 1 8 ( 100 Torr) v = 2 x 10^ cmVsec ( 400 K) o-k = 6 x l O " 1 ^ cm2 ( 7 ) we f i n d t c - 2 x 10*9 s The rad i a t i o n f i e l d i n an o s c i l l a t o r stage e x i s t s f or approximately l^ «.s., which Is one order of magnitude greater than t h i s c h a r a c t e r i s t i c time between c o l l i s i o n s * Therefore, the t r a n s i t i o n may be treated as homogeneously broadened with time independent o"£. In an a m p l i f i e r stage the bandwidth of the t r a n s i t i o n i s chosen to accomodate the incident s i g n a l . Consequently, a short duration incident energy pulse w i l l imply a large gas pressure and subsequently a short c h a r a c t e r i s t i c time between c o l l i s i o n s . The t r a n s i t i o n may, therefore, again be modelled as being homogeneously broadened. The r e l a t i o n between the ef f e c t i v e cross-section, the pressure of the active gas and the pressure of the buffer gas f o r a 1 ns. l a s e r pulse has been measured and presented graphically by K. Hohla et a l (10). 21 CHAPTER IV SECTION 3 STORED ENERGY The population Inversion, created by the photolysis of C F 3 I , i s depleted by chemical and radiative processes. Excited iodine may react with the various by-products of the photolysis process or may decay spontaneously, or by stimulated emission, to the ground state. CHAPTER IV SECTION 3.1 CHEMICAL DEACTIVATION 3.1.1. The Chemical and Photolytlc Processes The processes occurring i n a gas mix, i n i t i a l l y con-s i s t i n g of C F 3 I and Og, which i s o p t i c a l l y pumped, are: 1. Photolysis: CF^I * fcw K l » CF^ + I(5P|) CF 3I + fcw J j L ^ CF 3 + K 5 P 2 / 2 ) K 2 i s small and consequently t h i s process i s ignored ( 7 ) 2. Recombination Processes: I * + CFj K 3 » CF^I K 4 I + CF q „ CF-,1 Deactivation Processes! a. Reactions of the form I * + M v I + M i ) I * + £F3I I + CF 3I i l ) I * + CF 3 Z+. I + CF 3 K ^ i i l ) I * • C2F6 Z*_ I + C 2F 6 i v ) I * + 0 2 I*. I + 0 2 v) I * + I 2 I + I 2 These two p a r t i c l e encounters behave as f i r s t order reactions such that dn c/dt = K n A ns for A + B >. C + D b. Reactions of the form I * + I + N * I 2 + N v i ) I * + I + CF 3I T I 2 + CF 3I v i i ) i * + i + i 2 K l l y 21, The reaction rates of these three p a r t i c l e encoun-ters are of second order and are characterized by dn l 2/dt = K(nj + n-j-*)2 n N 4 . Dimerizatlon of the CF^I Radical: 2CF 3 C 2F 6 This i s also a f i r s t order reaction. Estimated and measured c o e f f i c i e n t s are l i s t e d i n reference (.")• Notation: n C F 3 I - n o n I * 5 n l n I = n 2 n C F 3 = n 3 n c 2 F 6 = n 4 n I 2 = n 5 n w = n 6 n 0 2 = n ? 3.1.2 The Rate Equations The rate of change of the concentration of CF 3I depends on the following processes: K 1 1. CF 3I + t. w CF 3 + 1* = dn 3/dt = K ^ n g dno/dt = -K 1n 0n 6 2. I * + CF 3 3 V CF 3I = dno/dt = K3XI3ZI1 3 . I + CF 3 ^- CF 3I = dno/dt = K^n 3n 2 Thus we have dn G/dt = -Kjn Qn^ + K 3n 3n^ = K^n 3n 2 2k S i m i l a r l y dnj/dt = K 1n Q n 5 - K^OqYI^ - K^n^xij - K y^n-j - K^n^n^ - Kgn^r, - K ^ n ^ - + n 2 ) 2 n Q - K 1 1 ( n 1 + n 2 ) 2 n 5 dn 2/dt = K^nQni + K 6 n l n 3 " K4n 2 n 3 + K^n^n^ + Kg^n-p + K^njn^ - K 1 0 ( n i + n 2 ) 2 n o - K ^ f n j + n ^ 2 ^ dn^/dt = K^nQn^ - K 3 n 1 n 2 - Kj^n-j - K 1 2 n 3 dn/j/dt = K 1 2 n 3 dn^/dt = K^(n1+n2)Zn0 + ^ ( 1 1 ^ 2 ) ^ dn 6/dt = P(t) - K.jn 0n 6 where P(t) i s the rate of change of photon density due to op t i c a l pumping dn^/dt = * - Kg^n^ 3.1«3, Dominant Deactivation Process In order to achieve a complete understanding of the temporal behaviour of the population of I * , these rate equations must be solved numerically. However, some in s i g h t into the r e l a t i v e importance of the di f f e r e n t deactivating processes may be gained by evaluating the h a l f l i f e of I * for each, using an estimate for the number density of the c o l l i s i o n partner. In general, f o r the blmolecular reaction KM A + B C + D the h a l f l i f e i s T | A = - (In | ) / K M n B and for the second order three body encounters considered A + B + C i C + D the h a l f l i f e i s T|A - l / 2 K M n B n c  K 5 1 . I * + CF 3I i _ I + CF 3I For 1 0 0 Torr CF 3I we have T i j # cr 1 0 * 3 seconds 2. I * + CF 3 X- I + CF 3 K I * + CF 3 ^_ CF 3I By estimating the t o t a l energy emitted by the f l a s h -lamps within the absorption spectrum of CF 3I, an upper bound of 1 0 * ^ cms"-^  i s found for the concentration of the CF 3 r a d i c a l . This then gives T|j# c: 2 . 5 x 1 0 ~ ^ seconds where i ? 1 1c K 3 = 3 . 7 x 1 0 " 1 s" 1 K 5 = 3 x l O " 1 ^ " " 1 K 6 = 3 . 7 x 1 0 " 1 2 s ' 1 K 7 = 4 . 5 x l O " 1 ^ " 1 K 8 = 8 . 6 x 1 0 " 1 2 s " 1 K Q = 5 x 1 0 ~ 1 2 s " 1 26 K ? 3. I * + C 2F 6 U I + C 2F 6 has a value of 4 .5 x lO'^seconds" 1 (10) and therefore the corresponding h a l f - l i f e of I * Is long. C 2Fg may be used as a thermal buffer since even for 100 Torr C 2Fg we have T|j# ~ 10"3 seconds 4. I * + 0 2 X- I + o 2 For a pressure of residual oxygen of 3 x 10"3 Torr -.-3 T f l * - 1 0 seconds K Q 5 . I * + I 2 I — I + Ig I t i s d i f f i c u l t to estimate the number density of Ig. However, since the rate c o e f f i c i e n t f o r the reaction i s 5 x 10""12 s e conds~l (lOi I t i s clear that even small quantities w i l l r e s u l t i n s i g n i f i c a n t deactivation. 3.1.4. Concentration of Important Deactivating Species We have thus found that the CF-j r a d i c a l and molecular iodine are the species primarily responsible f o r the deactivation of the excited iodine. I t Is not i n s t r u c t i v e to study the reactions which govern t h e i r populations. The CFj r a d i c a l , produced by photolysis, Is eliminated In the following ways, with h a l f l i f e estimated as before. K 1 2 c 2 CP 3 — C F 3 I T i C F ^ ^ 3 x 10~ 6seconds I + CF 3 CF 3I The population of ground state iodine i s small ( 7 ) and thus the dimerization reaction governs the concentration of CF 3. S i m i l a r l y , f o r I g we have K h. I + I * + CF 3I 10> I 2 + CF 3I T i l 2 * 10- seconds I + !• + I 2 J ^ i - 2 I 2 T i l 2 * lO^seconds Thus only a small concentration of molecular iodine occurs during the duration of the pump pulse. 3 . 1 . 5 . Thermal Effects I t i s important to keep the gas mix cool since the rate c o e f f i c i e n t s and hence chemical deactivation increases with temperature. Also, thermal di s s o c i a t i o n of CF 3I, which p r e f e r e n t i a l l y produces atomic iodine i n the ground state ( 1 5 ) d i r e c t l y reduces the inversion. Heating i s primarily due to the dimerization of 2 CF 3 to C2F£ and the photolysis of CF 3I, y i e l d i n g 3.66 and 1 . 4 5 eV per reaction respectively ( 1 6 ) . A buffer gas, which w i l l not chemically i n t e r a c t with CF 3I or subsequent by-products of the photolysis, may be used as a thermal reservoir. 28 3.1 . 6 . Summary For a gas mix with l e s s than 3 x 10"^ Torr of residual oxygen, the dominant deactivating species are the CFj r a d i c a l and molecular iodine. Both r e s u l t i n a s i g n i f i c a n t loss of stored energy during a t y p i c a l pump pulse ( 6 - 2 0 ns.). CF-j rapidly dlmerlzes to CgFg and consequently i s eliminated soon a f t e r the pump pulse has terminated. A buffer gas may be added to absorb thermal energy, thereby keeping the chemical deactivation rate and the rate of thermal d i s s o c i a t i o n of CF-jI producing ground state iodine to a minimum. CHAPTER IV SECTION 3 .2 RADIATIVE DEACTIVATION 3.2.1. P a r a s i t i c O s c i l l a t i o n s Since the small signal gain of the la s e r medium i s large the threshold conditions for o s c i l l a t i o n i n a cavity with low Q, t y p i c a l of an ampl i f i e r , may be achieved. The energy loss due to these p a r a s i t i c modes i s so large that the threshold inversion turns out to be the upper l i m i t of the stored energy ( 1 0 ) . 1. Resonant Cavity Modes Reflecting surfaces such as the laboratory walls and o p t i c a l components together with dust p a r t i c l e s which act as scattering centres may give r i s e to the l a s i n g of cavity modes. The threshold inversion i s defined by the condition that the energy input into the mode due to stimulated and spontaneous emission i s i d e n t i c a l to the energy loss due to imperfect r e f l e c t i o n s and absorptions. I f q 0 i s the energy density at the f i r s t mirror with r e f l e c t i v i t y R^, then a f t e r one complete cycle through the cavity the energy density w i l l be changed to q = (q 0Ri T exp. ofa n L)(R 2 T exp. ofa n L) (14) where R 2 i s the r e f l e c t i v i t y of the second mirror, T i s the transmittance of the medium i n the cavity and i s the eff e c t i v e cross-section f or stimulated emission into the mode. For a mode which grows i n time we have (15) From t h i s we see that the threshold Inversion N m = nL THRESHOLD In (l/R^R 2T 2) 2 crM (16) This condition may also be expressed i n terms of the qual i t y factor Q of the cavity defined by the d i f f e r e n t i a l equation dq/dt =(-W Q/Q; q (17) where l/w Q i s the time taken for the energy pulse to make a round t r i p to the cavity. Rearranging equation 17 and integrating over one cycle denoted 0£ t 6T, we have Ln q(T) - In q(o) = (~wQ/Q ) T = - l / Q = > Q = 1 . (18) ln(q(6)/q(T) ') Evaluating t h i s i n terms of the cavity parameters we fi n d Q = 1 (19) lnd/fyRgT 2) Thus, using t h i s i n equation 17 the threshold inversion, or maximum stored energy, Is given by N T = 1/2QOJJ (20) 2. Guided Wave Modes Os c i l l a t i o n s which grow i n time also occur due to re^ fl e c t i o n s from the l a s e r tube wall or the fl a s h tube r e f l e c t o r s . For large angles of Incidence 0 the wave i s predomin-antly r e f l e c t e d at the surface of the quartz l a s e r tube and therefore travels exclusively i n the activated l a s e r medium (see Figure 10). This results i n a large Q value and consequently a low threshold Inversion. F i g . 10. Guided wave mode confined within the l a s e r tube since the angle of incidence 8 i s large. Although rays incident at small angles are transmitted i n t o the non-activated region, the increased number of bounces before the wave leaves the am p l i f i e r can also r e s u l t i n a s i g n i f i c a n t amount of energy being extracted. (See Figure 11) Fig . 11. Guided wave modes t y p i c a l of small incident angles, the wavefront being confined by the flash tube r e f l e c t o r . Rays at large angles of incidence may be suppressed by i n s e r t i n g an aluminum c o i l against the inner surface of the l a s e r tube such that they are r e f l e c t e d and coupled into more lossy modes (17). P a r a s i t i c modes with frequency near the l a s e r l i n e centre have the lowest threshold and are therefore the most troublesome. The cross-section at the l i n e centre may be lowered by pressure broadening and hence the maxi-mum stored energy increased. Ruby and Nd-glass have a maximum cross-section of approximately 10""2®cms2 (16) and thus can achieve a stored energy density an order of magnitude greater than iodine, which has a value i n the range 2 - 5 x 10~*9 cms2. An energy density of 6 J/cms 2 i s possible i n iodine with OMAX reduced to 2 x 10'^^cms2 by pressure broadening. D. Gregg et a l suggest that a d d i t i o n a l broadening may be achieved by using the Zeeman effect (18). 3 . 2 . 2 . Optical Coupling Losses Prepulses generated by super radiance r e s u l t i n a serious energy loss as they pass through the a m p l i f i e r chain. A saturable absorber, as developed at the IPP, Garching, may be used to Isolate each a m p l i f i e r stage. However, the device i s elaborate and s t i l l i n the early stages of i t s development (19„•). The super radiant f i e l d i s l e s s d i r e c t i o n a l than the l a s e r beam and hence a reasonable degree of i s o l a t i o n may be achieved by separating the stages by a large distance. This does not require any compromise i n the design of a f i n a l a m p l i f i e r since the large beam diameter and energy density define a distance between the stages which i s s u f f i c i e n t to provide good I s o l a t i o n . However, i n i t i a l l y the natural divergence of the narrow l a s e r beam results i n an energy density below that required to saturate an am p l i f i e r , even for a separation distance required for a minimum i s o l a t i o n . I f t h i s method of o p t i c a l i s o l a t i o n i s used then one of two design compromises must be made. 1. The buffer gas pressure may be lowered, thereby reducing the saturation energy and improving the extraction r a t i o . The reduced bandwidth w i l l r e s u l t In some broaden-ing of the l a s e r pulse and lower buffer pressure results i n a smaller maximum stored energy. 3k 2. The buffer gas pressure may be chosen to provide adequate bandwidth and maximize the stored energy. The res u l t i n g poor extraction r a t i o must be accepted. CHAPTER IV SECTION 3 .3„ THE TEMPORAL BEHAVIOUR OF THE STORED ENERGY DUE TO THE ONSET OF PARASITIC OSCILLATIONS The time evolution of the energy i n an a x i a l mode of a resonant cavity containing an activated medium i s studied. The rate of change of the t o t a l number of photons per unit area % i n the mode i s given by dU M/dt = fAN^ + ofe ( C U M / L ) 4 N - cUM/2QL (21) where N^ i s the t o t a l number of p a r t i c l e s which could emit a photon i n t o the mode, N i s the t o t a l inversion, f i s the f r a c t i o n of the spontaneously emitted photons which are emitted i n the d i r e c t i o n of the cavity a x i s , A i s the Einstein c o e f f i c i e n t f or the spontaneous emission process, c i s the v e l o c i t y of l i g h t , og i s the ef f e c t i v e cross-section for the mode, Q i s the qu a l i t y factor of the cavity and L i s the distance between the mirrors i n centimeters. The f i r s t term on the left-hand side of equation (21) describes the energy change due to spontaneous emission. 35 The second term characterizes the stimulated radiative processes and the t h i r d describes the power loss due to imperfections i n the cavity. The population of :the upper l e v e l (N.^ ) i s decreased by chemical deactivation, spontaneous and stimulated emission and increased by pumping such that dNj/dt = P 1 ( t ) - cr M(c/L)U MAN - AN^ (22) S i m i l a r l y dN 2/dt = P 2 ( t ) + o M(c/L)u MAN + ANi (23) where P^(t) denotes the rate of change of the population of the i - t h energy l e v e l due to both pumping and chemical deactivation. The system of equations 21 , 22 and 23 have been solved numerically by K. Hohla et a l d£) for the conditions t y p i c a l of the Iodine l a s e r o s c i l l a t o r (Figure 1 2 ) . I.e. ^wQ = 5 x 1 0 9 Hz RiRgT 2 = 0 . 3 P 2 ( t ) was taken to be zero. The form of t h i s solution Is also appropriate for the transient behaviour of the p a r a s i t i c modes of an a m p l i f i e r stage. F i g . 12. The transient behaviour of the inversion and the re s u l t i n g l a s e r energy due to a pump l i g h t pulse i n i t i a t e d at t = 0. CHAPTER IV SECTION 3 . 4 INERTIAL DELAY The i n t e r v a l between the inversion reaching threshold and the f u l l development of the l a s e r pulse i s referred to as the i n e r t ! a l delay of the system and may sometimes be used to advantage. (See Figure 12) 37 This delay can be understood q u a n t i t a t i v e l y by examining the dominant terms i n the rate equations for the i n t e r v a l near the threshold. Equation 21 reduces to dU M/dt = crM (c/L)U M AlJ(t) (24) For / I N constant, t h i s has solution % U ) = U Q exp. cfo (c/L) /hl(t) (25) However, / I N i s increasing due to pumping and hence the rate of change of U M ( t ) w i l l increase with time. (See figure 13) t F i g . 13. The I n e r t i a l delay of a l a s e r pulse generated i n a resonant cavity. The amount of energy delivered i n the f i r s t pulse w i l l depend upon the t o t a l number of atoms which can be pumped to the upper state before the rapid growth of the l a s e r pulse occurs. I f pumping i s terminated at t g , as shown i n figure 12, then a l l of the energy i s contained within the f i r s t l a s e r pulse. Rapid pumping can therefore be used to eliminate the need for Q switching a l a s e r o s c i l l a t o r (20) and i n an am p l i f i e r stage i t i s possible to exceed the threshold for p a r a s i t i c o s c i l l a t i o n s and therefore increase the maximum stored energy. I n e r t i a ! Delay i n an Amplifier Stage The i n e r t i a l delay of an a m p l i f i e r stage could be used to advantage i f an inversion s i g n i f i c a n t l y greater than the threshold f o r p a r a s i t i c o s c i l l a t i o n s could be achieved. The small signal gain and consequently the extraction r a t i o as well as the o v e r a l l gain of the am p l i f i e r would be improved. In order to evaluate the r a t i o of the maximum stored energy to the threshold inversion i n an am p l i f i e r , approxi-mate expressions f or the i n e r t i a l delay and the maximum inversion are derived from solutions of the rate equations. The following simplifying assumptions are made: 1. The pump rate P i s constant. 2. Chemical deactivation can be ignored. 3 . Spontaneous emission can be ignored. Then equations 21, 22 and 23 become dU n/dt = o* M(c/L)U M AN -(c/2QL)U M dNj/dt = P - c r M ( c A ) U M A N dN 2/dt = o-M (c/L)U M ZlN From equations 2? and 28 we f i n d d / d t ( N 1 ^ g 1 / g 2 ) N 2 ) « P - (l+gi/g2)°M i . e . d A N / d t = P - b or M(c/L)U M A N when b = (1 + gj/gg ) I n i t i a l l y , when the inversion i s small P » b c r M ( c / L ) u M A N and equation 30 s i m p l i f i e s to d ^ N/dt ? P. This has solution A N ( t ) = Pt + A N T , where we have defined A N(t=0) = A N T = A N THRESHOLD Substituting equation 33 into 26 dU M/dt = <rM (cfL)U M(Pt +AN T) -(c/2QL)u M (34) Now, at threshold d.UN/dt = G, and using 26, equation 34 reduces to dU N/dt = O- M(C/L)U m Pt (35) which has solution % = UM 0 e x P (o- McPt 2/2L) (36) where U M i s the t o t a l number of photons per unit area In llo the cavity when, the inversion reaches the threshold value. This solution i s v a l i d for P^bofa (c/L)U M A N. However, i t may be used to estimate the i n e r t i a l delay. Afte r the i n e r t i a l delay the rate of stimulated emission has become equal to the pump rate such that equation 30 becomes P = b crM (c/L)U M AN(T) (37) Using equations 33 and 36 i n 37 P = b K, (c/L)U M exp (orM CPT2) (pT +ANm) (38) o 2L from which we f i n d r2 = __2L_ In ( LP ) ( 3 9 ) crMcP ( o M c U M o ( P r + A N T ) j 41 Using equation 33 we may now write down an expression for the r a t i o of the maximum stored energy to the threshold inversion A N(r) = 1 + P r A N T A N T 1 + P ( 2L In [ LP ^j) * A N T ( o-McP [ O M C U M q (Pr + A N T)J) (40) Using equation 20, t h i s becomes A N(r) = 1 + 2PQorr A N T n ( 2L In f LP ] } (. °M c P I cr McU M o(P + l/2QcrM)j ) (41) The fundamental difference between an o s c i l l a t o r and an a m p l i f i e r stage i s characterized by the q u a l i t y factor Q of the resonant cavity. Typical values for an o s c i l l a t o r and an a m p l i f i e r are O.83 and 0.0? respectively ( 5 ) , and hence from equation 41 we expect the &N(7")/&NT r a t i o f o r the a m p l i f i e r to be at l e a s t one order of magnitude less than for the o s c i l l a t o r and therefore the phenomenon of i n e r t i a l delay cannot be used to advantage i n an a m p l i f i e r stage• 42 CHAPTER IV SECTION 3 GAIN The l a s e r pulse may be described i n terms of the density of photons q x,t) cm~3. This photon density i s changed by stimulated and spontaneous emission and stimulated absorption. Since the l i f e t i m e for the excited state i s 170 msec. ( 9 ) , the spontaneous emission process may be ignored and the photon density i n an elementary volume which sweeps through the am p l i f i e r with v e l o c i t y c w i l l s a t i s f y dq/dt = Zq/bt + c d.q/ox = c c~E q(t) n(t) (42) where c i s the v e l o c i t y of l i g h t , n i s the t o t a l inversion and o"g i s the eff e c t i v e cross-section defined by equation (12). We consider the case where the Inversion i s changed only by stimulated radiative processes. That i s , the pump pulse i s considered to have terminated and both chemical deactivation and spontaneous emission are ignored. Then dn/dt = dnt/dt -(g1/g2)dn2/dt = -dq/dt ~(gi/g2)dq/dt = - (1 + Si/&2^ d < l / d t = - b c q cr E n (43) where i s the population of the i - t h energy l e v e l , g^ the degeneracy of the l e v e l and b = (1 + g!/g2) (44) That i s dn/dt = -bcqcTgn (45) Substituting t h i s into equation 42 we f i n d * q/at + c dq/ar = - l/b dn/dt (46) This may be integrated with respect to t , 0 < t i t f t f t f , + d/dx / cq(x,t)dt = (-l/b)n We recognize cq = fl u x of photons and thus i d e n t i f y cq(x,t)dt = Total number of photons s E(x) Unit area (48) Then (47) becomes ( t f q(x,t) + d/dx E(x) = - l / b n(x,t) (49) We choose I n i t i a l conditions and t f such that q(x,0) = q ( x , t f ) = o, 0 < x $ L as shown i n figure 14. Pig, 1 4 . The i n i t i a l conditions and. domain of integration of the d i f f e r e n t i a l equation characterizing the a m p l i f i -cation of a l a s e r pulse. Then 49 becomes d/dx E(x) = - l / b n(x,t) 0 <x<L (50) Rearranging equation 4-3 and integrating with respect to t n( x , t f ) t f /dn/n = o-gb / cq dt = -OgbE(x) (51) n(x , 0 ) 0 which has solution n ( x , t f ) = n(x , 0 ) exp, - OgbE(x) (52) Using t h i s i n equation 50 we have d/dx E(x) = - ( l / b ) n ( x , 0 ) [exp. [-o EbE(x)] - l j ; 0 <x*L (53) F i n a l l y , we integrate with respect to x, O i x J L , and divide by E(0) such that V = EO) = 1 i n ( l +(e b o fEE ( 0 ) . 1 } ^ ( t ^ L ? " ETxT bo-EE(0)^ I J (5*0 Small Signal Regime Vs = U« V B{o) — > 0 In t h i s regime the Incident energy per unit area i s small such that the inversion i s not s i g n i f i c a n t l y depleted by stimulated emission. For small bo-EE(0) we may expand the exponential ebOEE(0) anji a i s c a r d terms 0(bcr EE) 2. Then ( ebo- EE(0) _ l ) e o - E n ( 0 ) L _ ^ b c r ^ O j e 0 ^ (55) S i m i l a r l y , for bo EE ( 0)e o r E n^°^ L the logarithm may be expanded according to l n ( l + x) = x - x 2 <*• i? and again terms 0 ( x 2 ) are discarded. Equation (54) then becomes V s ^ l / b o E E ( 0 ) (bo-E E(0)e°Mn(°)L) _ eo~ En(t=0)L Using equation 20 and 56 we f i n d that the maximum small signal gain V g M i s completely defined by the qu a l i t y factor Q of the cavity VSM = E (57) Typical values of = 10-^  are achieved for amplifiers by careful mechanical design and the avoidance of re f l e c t o r y surfaces ( 5 ) . Large Signal Regime The Incident signal i s large such that the inversion i s t o t a l l y depleted. For E(0) large, equation 54 reduces to V L ^ ( l / b a E E ( 0 ) ) In exp. bor EE(0) exp. : OgnfO)L = 1 + n(t=0) bE(0) (58) Vg i s t y p i c a l l y two orders of magnitude greater than Vj_, r e s u l t i n g i n a change i n the temporal p r o f i l e of an energy pulse as i t passes through the am p l i f i e r . (See Chapter 4 . 8 ) 47 CHAPTER IV SECTION 5 EXTRACTION RATIO The extraction r a t i o of an am p l i f i e r i s defined as = ^OUT " (59) ESTORED EOUT ^ Eo^ i s t h e t o t a l output (input) energy per unit i n the l a s e r medium. The maximum extraction r a t i o occurs when the incident pulse has energy density i n the large signal regime through-out the amp l i f i e r . This y i e l d s an extraction r a t i o of 0.66 due to the degeneracy of the energy l e v e l s . Choosing the condition ebo*EE(°) 5 to define the large signal regime, the incident energy density to achieve the area and E STORED i s the t o t a l energy per unit area stored. CHAPTER IV SECTION 6 SATURATION ENERGY DENSITY maximum extraction r a t i o E g, may be evaluated. (60) CHAPTER IV SECTION 7 BEAM QUALITY In order to preserve the beam p r o f i l e and minimize i t s divergence i t i s important to generate an homogeneous inversion. An empirical formula r e l a t i n g the l a s e r tube diameter and pressure of the active medium has been determined by K. Hohla et a l (21 ) P = 170 x D"1 Torr (6l) where P i s the pressure of the active gas and D i s the diameter of the l a s e r tube i n centimeters. This homogeneous inversion can be disturbed by a shock wave generated by the vaporization by the pump l i g h t , of deposits condensed on the tube wall (18, 22 )• Pumping must be terminated and the stored energy released before the shock wave has propogated a s i g n i f i c a n t distance, thereby destroying the homogeneity. An estimate of the shock v e l o c i t y of 3 x 10^ cm/sec or 0.3 mm/per sec (6) may be used to evaluate the loss of active volume as a function of ellapsed time a f t e r the i n i t i a t i o n of the pump pulse. The f i r s t and second amplifiers of the IPP, Garching, system use a high capacitor changing voltage and con-sequently a short duration pumping pulse (17). During the 4 9 r e s u l t i n g pulse the shock wave propogates only 1,8 mm and the major portion of the activated medium i s undisturbed. However, the lower charging voltage used at the Sandia Laboratories (6) results i n a 20 pis current pulse and therefore a s i g n i f i c a n t l o s s i n the unperturbed active region. (See Chapter 4.11) Experiments conducted at the Sandia Laboratories demonstrated that the shock wave i s driven by heat absorbed i n carbon deposited on the tube surface. This carbon results from the photolysis of iodine compounds at wave-lengths le s s than 200 nm and can therefore be avoided by f i l t e r i n g out these wavelength components from the pump l i g h t . I t was found that using l a s e r tubes made from Germlsil, a Titanium doped quartz which i s opaque at wave-lengths l e s s than 200 nm not only eliminated the shock wave but also the brown-black surface deposits which a f t e r 20 shots absorb approximately 20$ of the UV pumplight (6). CHAPTER IV SECTION 8 PULSE SHAPE MODIFICATION As an energy pulse passes through the am p l i f i e r , two processes operate simultaneously to modify i t s temporal p r o f i l e . 1. The f i n i t e bandwidth of the a m p l i f i e r has the effect of attenuating the higher order Fourier components and therefore broadening the pulse. 2. A pulse passing through a section of the ampl i f i e r depletes the inversion and therefore the i n i t i a l part of the pulse i s amplified more than the l a t e r part. Thus the pulse p r o f i l e becomes skewed and the h a l f width i s reduced. For a rigorous theor e t i c a l treatment of t h i s phenomenon the reader i s referred to a paper by J . N. Olsen ( 2 3 ) • CHAPTER IV SECTION 9 EFFICIENCY The e f f i c i e n c y of an amp l i f i e r i s defined as the r a t i o of the energy extracted from the active medium by the l a s e r pulse, to the energy stored i n the capacitor. I t has a maximum value of approximately 1% l i m i t e d primarily by the difference between the broad, spectrum of l i g h t produced by the Xenon fl a s h tubes and the narrow absorption l i n e of CF^I at 2660A°. Pressure broadening t h i s l i n e and a careful choice of Xenon gas f i l l pressure i n the fl a s h tubes to maximize the l i g h t output i n t h i s spectral region, improves the e f f i c i e n c y . Imperfect o p t i c a l coupling between the fl a s h tubes and the active medium also reduces the system e f f i c i e n c y . The 51 f l a s h tubes must be positioned such that the angle sub£ tended between the arc and the active volume i s maximized. Light which i s not emitted into t h i s angle must suffer a r e f l e c t i o n at the surrounding mirror before entering the active medium. Research i s i n progress to define the optimum choice of material f o r these mirrors since much of the l i g h t undergoes multiple r e f l e c t i o n s (6). Aluminum f o i l i s being used at present i n the l a s e r at the University of B r i t i s h Columbia. Pumping the l a s e r medium above the threshold f or p a r a s i t i c o s c i l l a t i o n , chemical deactivation during long pumping pulses and o p t i c a l coupling losses also r e s u l t s i n a s i g n i f i c a n t reduction i n the system e f f i c i e n c y . Typical e f f i c i e n c i e s of 0.1 and 0.3# f o r preamplifier and f i n a l a m p l i f i e r stages respectively are being measured (17, 24). CHAPTER IV SECTION 10 THE BUFFER GAS PRESSURE Typical buffer gasses are COg and Argon. Increasing the pressure of the buffer gas i n the mix has the following advantages. 52 1. The bandwidth of the amp l i f i e r i s increased ( page 14), 2. The maximum stored energy i s increased ( page 28). 3 . The temperature r i s e of the gas mix during photolysis i s reduced, thereby keeping the rate c o e f f i c i e n t s f o r the chemical deactivation process to a minimum ( page 28). 4 . The coupling e f f i c i e n c y of the pump pulse l i g h t to the active medium i s improved by pressure broadening. There are two disadvantages; 1. The extraction r a t i o i s reduced (page 4 7 ) . 2. Chemical deactivation by the buffer gas i s increased. For subnanosecond l a s e r pulses the buffer gas pressure i s defined by the bandwidth necessary to ensure an acceptable amount of pulse broadening (page 15). CHAPTER IV SECTION 11 THE FLASH TUBE CIRCUIT The design of the fla s h tube c i r c u i t system may be separated into two d i s t i n c t forms which we c a l l the high voltage and low voltage schemes. In the high voltage scheme a high Intensity short duration pumping pulse ( t y p i c a l l y 6 p*s.) i s produced, whereas the 53 low voltage system results i n a much longer ( t y p i c a l l y 2 0 J* s.) and l e s s intense pulse. We examine the design compromises inherent i n each scheme. The High Voltage Scheme  Advantages 1. The effect of chemical deactivation i s small i f the energy i s stored and released within a time short compared with the h a l f l i f e of I * due to these processes. 2 . A shock wave w i l l only propagate a smalL distance i n -wards from the wall of the l a s e r tube disturbing the o p t i c a l homogeneity of the medium. 3 . I f the pumping pulse i s short enough to d e l i v e r a s i g n i f i c a n t amount of energy during the i n e r t i a l delay of the system, then the stored energy density can exceed the threshold for p a r a s i t i c o s c i l l a t i o n . Dlsadvantages 1. A higher voltage, and. consequently more expensive, power supply i s required to charge the capacitor. 2 . The e l e c t r i c i n s u l a t i o n must be designed for the high working voltage. 3 . More f l a s h tubes are required to d e l i v e r the same energy. The Low Voltage Scheme  Advantages 1. A less expensive lower voltage power supply i s required. 2. The e l e c t r i c i n s u l a t i o n suitable f o r the lower working voltage i s s u f f i c i e n t . 3. More energy can be delivered by fewer f l a s h tubes than i n the high voltage scheme. Dlsadvantages 1 . S i g n i f i c a n t chemical deactivation occurs during the long pump pulse. 2. A shock wave w i l l disturb a large volume of active medium. 3. Very l i t t l e energy i s delivered during the i n e r t i a l delay of the system. CHAPTER V THE SYSTEM DESIGN PROCESS Having derived the relationship between the system design, operating conditions and performance, the design process may proceed. This involves finding a route through the Polya-Fuller map u n t i l a l l of the variables are defined. CHAPTER V SECTION 1 THE GIVEN VARIABLES The f i r s t stage i n the design process i s to l i s t the system variables which are given (see Figure 15)• 1. Incident Energy e 0. The incident energy i s expected to be approximately 100 mJ i n a pulse of duration 1 ns. (24) 56 2. Beam Quality; The Inversion density must be uniform and no o p t i c a l lnhomogeneltles due to turbulance should be present In the active volume of the l a s e r medium. 3 . E f f i c i e n c y ; Minimum value 0 .1#. 4. Lifetlme; The l i f e t i m e of the flash tubes should exceed 1500 shots ( 5 ) . 5 . Q for P a r a s i t i c Modes; Typically t h i s has a value which leads, v i a equation 5 2 , to a maximum small signal gain of 103 i . e . Vgpj = 1G 3. 6 . Laser Tube Diameter; 2 .5 cms. Defined by the divergence of the beam and separation required for o p t i c a l i s o l a t i o n . 7. Reflection M a t e r i a l ; Aluminum f o i l . 57 Fig* 15* System design diagram i n d i c a t i n g variables. the given 58 CHAPTER V SECTION 2 THE GAS PRESSURES Refer to Figure 16. Having chosen the l a s e r tube diameter to be 2 . 5 cms., the pressure of the active gas required to produce an homogeneous inversion i s defined by equation ( 6 1 ) . i . e . P = ~ 70 Torr 2 . 5 The minimum buffer gas pressure to provide the required bandwidth i s 400 Torr C0 2 (Chapter 4 . 2 ) . Increasing t h i s pressure raises the threshold for p a r a s i t i c o s c i l l a t i o n s and consequently the maximum stored energy. I t i s important to pump the medium to t h i s energy density such that the maximum small signal gain i s attained. This ensures that the l a s e r pulse i s amplified to the l o c a l saturation energy density within a short distance and hence a good extraction r a t i o i s achieved. I t turns out to be d i f f i c u l t to arrange a s u f f i c i e n t number of fl a s h tubes to achieve a large stored energy around the small diameter l a s e r tubes. Hence, for a short duration l a s e r pulse, the buffer gas pressure I s completely defined by the bandwidth requirement. The e f f e c t i v e cross-section f o r a gas mix of 400 Torr C0 2 and 70 Torr CF3I i s found to be Fig. 16. The Section of the System Design Diagram which i s used to define the gas pressures. CHAPTER V SECTION 3 THE STORED ENERGY, GAIN AND EXTRACTION RATIO Refer to Figure 17. Using a t y p i c a l value maximum small signal gain (Chapter 4 , Section 3) the maximum stored energy i s calculated using equation ( 5 6 ) . V s M = 103 = e°E 4N T =p> A N T = 2 . 3 x 1 0 i y photons-19 -2 cms - 3 . 5 J cms - 2 Using equation 54 the gain may bow be evaluated. V 1 i n f l • ( . ^ 8 0 - 1) . bcr EE 0 <- > We f i r s t evaluate the incident energy density i n units _p of photons cms EQ = Incident Energy (Joules) x (eV - Joule"*) Cross-sectional Area of Medium x (eV - photon - 1) =£>EQ ^  1 .3 x 10 1 7photons - cm"2 Substituting into equation 54 we find. V - 62 The extraction r a t i o may now be found using equation 59 V x E n - E n 7 = 0 0 - 0 . 3 4 (EST0RED = A NT> ^ = 0 . 3 4 6 1 F i g . 17. The section of the system design diagram used to define the stored energy, gain and extraction r a t i o . 62 CHAPTER V SECTION 4 THE STORED ELECTRIC ENERGY Figure 18 shows the system design for the stored e l e c t r i c a l energy. For a preamplifier stage the e f f i c i e n c y i s t y p i c a l l y 0.1# (Chapter 4.9). The energy extracted from the l a s e r medium, evaluated from the extraction r a t i o and the stored energy, together with the value f o r the ef f i c i e n c y may be used to estimate the t o t a l energy to be stored i n the capacitor. This value, being derived from an estimate of the e f f i c i e n c y , i s only approximate. The Q for p a r a s i t i c modes may also be somewhat le s s than the value chosen, thereby allowing for a higher stored energy density. Thus the system response to an increase i n the stored energy i n the capacitor should be studied experimentally. The gain would be expected to increase with stored e l e c t r i c energy u n t i l the threshold f o r p a r a s i t i c modes i s reached. Stored E l e c t r i c Energy - 77 x Stored Energy x ^ 6 K J F i g . 18. The section of the system design diagram used to define the stored e l e c t r i c energy. 64 CHAPTER V SECTION 5 THE ELECTRICAL SYSTEM AND PUMP LIGHT PULSE Figure 19 shows the relevant section of the system design diagram. In order to proceed with the design of the remainder of the system, a choice between the high and low voltage schemes for the f l a s h tube c i r c u i t , as discussed i n Chapter 4 . 1 1 , must be made. Before the work of R. E. Palmer et a l (6) showing that shock waves no longer occur when Germisil l a s e r tubes are used, the choice was not obvious. However, the low voltage system Is c l e a r l y superior i f t h i s problem i s eliminated. F i g . 1 9 . The section of the System Design Diagram containing the remaining undefined variables. 65 The Low Voltage Scheme Xenon f l a s h tubes with an arc length of 6 l cms,, and an explosion energy of 2500 Joules were selected. The recommended energy and current are 2000 Joules and 6 KA respectively. The flash tube c i r c u i t consists of a capacitor, the p a r a s i t i c Impedance of the c i r c u i t , and the f l a s h tube connected i n ser i e s . I t Is important to choose the mechanical design of the c i r c u i t to minimize the p a r a s i t i c impedance and thereby produce a short c r i t i c a l l y damped current pulse. The voltage-current c h a r a c t e r i s t i c of the f l a s h tubes has the form ( 9 ) , V = K D I * (62) where K Q i s given by K 6 = k 1 (63) d and 1 i s the length of the lamp i n cms., d i s the bore diameter i n cms., and k i s a function of the type of gas and i t s pressure ( t y p i c a l l y 1.2); ( 9 ) , ) . We f i n d K 0 ~ 104 -n. A^ for t h i s flash tube. Solution to the non-linear d i f f e r e n t i a l equation f or the series c i r c u i t are presented i n a paper by Ho l z r l c h t e r and Schawlow (25) . 66 The duration of the current pulse should be t a i l o r e d to d e l i v e r the energy i n as short a time as possible, to minimize the losses due to chemical deactivation, without exceeding the maximum recommended operating current. An upper bound of 20^0 for the pulse duration i s suggested by an examination of the chemical deactivation rates. In order to derive an approximate r e l a t i o n between the maximum current, the stored energy and the pulse duration, the c r i t i c a l l y damped current pulse may be trated as a sine function ( O ^ t S i T ) . Using the model we f i n d (64) where I M = maximum current i n amps. E = stored e l e c t r i c energy i n Joules = pulse duration i n seconds I f eight f l a s h tubes are used then 6K Joules of energy delivered i n a 2Cy.s pulse y i e l d s a maximum current of 7«5 KA i n each flash tube. This exceeds the maximum operating current and there-fore more fl a s h tubes must be used or the t o t a l energy or the tube l i f e t i m e s a c r i f i c e d . We choose to use eight flash tubes for the following reasons: 1. Two are required to Illuminate the f u l l length of the a m p l i f i e r and thus the t o t a l number must be raised to ten, thereby increasing the cost and the complexity of the mechanical design considerably. 2. The function of a preamplifier i s to raise the energy of the beam to the saturation density of the f i n a l a m p l i f i e r . This may be possible with a reduced stored energy density. 3 . The stored energy required i s based on an estimate of the system e f f i c i e n c y and may therefore be l e s s than the calculated value. 4 . The operating energy i s well below the maximum suggested by the manufacturer, and the design l i f e t i m e of 1500 shots may be attainable even with a maximum current 23% above the recommended value. Using a Rogowski c o i l we measured the current pulses with both 10 and 20^1 of capacitance i n the c i r c u i t . They were c r i t i c a l l y damped and had a duration of approximately 9 and 12M.5 respectively. The pulse duration i s proportional to J LC (9) and i n s e r t i n g the experimentally measured values Into t h i s r e l a t i o n we deduce that the p a r a s i t i c impedance i s not changed appreciably by adding capacitors. Thus we calcu-l a t e that 40 and 50/*f w i l l result i n pulses of approxi-mately 18 and 21^ .$ duration respectively. The following table l i s t s the calculated values of the pulse duration, stored energy and maximum current f o r a 40 and a 50^--f capacitor bank. STORED ENERGY = 6 K J MAX. CURRENT = 6KA C A P A C I T A N C E PULSE DURATION KA CHARGING VOLTAGE STORED ENERGY CHARGING VOLTAGE 40 18 8 1 1 7 KV 3<?KJ 14 KV 50 2 1 7-3 15 KV 4-5 K J 1 3 KV Table 1. Current pulse c h a r a c t e r i s t i c s f o r capacitor bank, A capacitance of 40j*-f and a charging voltage of 14 KV i s chosen to d e l i v e r 3.9KJ within a pulse of duration 18 5 • Having s p e c i f i e d the current pulse, the optimum Xenon gas f i l l f o r the f l a s h tubes may now be found from the manufacturer's s p e c i f i c a t i o n s . Reducing the stored e l e c t r i c energy from the optimum value of 6KJT to 3 , 9 KJ w i l l lower the inversion and consequently the system gain. Assuming the inversion i s reduced by one t h i r d to 2.3 J/cm.2 we f i n d that the system gain and extraction r a t i o are reduced to V''Or 33 , ^ Of 0.28 The buffer gas pressure could be reduced to improve the extraction r a t i o at the expense of the a m p l i f i e r bandwidth i f t h i s design compromise was more acceptable. Summary "Germisil" l a s e r tubes must be used to contain the active gas mix of 70 Torr CP^I and 400 Torr COg. Eight Xenon fla s h tubes connected i n p a r a l l e l and driven by a 4 0 c a p a c i t o r bank charged to 14 KV w i l l r e s u l t i n ' a gain of 33 and an extraction r a t i o of 0.28. I f necessary, the charging voltage may be increased to 17 KV to overdrive the flash tubes, a f t e r the effect on the l i f e t i m e has been measured experimentally. CHAPTER V SECTION 6 MECHANICAL DESIGN Summary of Mechanical Design Requirements 1. Simple routine replacement of defective Xenon fla s h tubes. 2. Laser tubes to be e a s i l y removable for cleaning or replacement. 3. Minimum p a r a s i t i c Inductance of the e l e c t r i c c i r c u i t . 70 4. Flash tubes located as close as possible to the l a s e r tube. 5 . Inner surface of l a s e r tube to be etched to improve homogeneity of inversion. 6. Aluminum f o i l used as r e f l e c t o r . 7. Germisll l a s e r tubes to eliminate shock waves and absorption by wall deposits. 8 . E l e c t r i c i n s u l a t i o n suitable f o r a working voltage up to 20 KV. 9 . Vacuum system able to achive a pressure les s than 10~ 2 Torr. The Apparatus The inversion i s created within two i d e n t i c a l c y l i n -d r i c a l sub-assemblies 75 cms. long and 11.5 cms. i n diameter each containing four Xenon fl a s h tubes and a l a s e r tube 8 5 . cms. long. The l a s e r tube i s located on the subassembly axis by holes i n two a c r y l i c end plates. The tube ends, protruding from these sub-assemblies, are Joined by a "Y" shaped 0 ring sealed coupling, the centre l e g of which i s connected v i a a cold trap to both mechanical and d i f f u s i o n vacuum pumps. 71 Quartz windows at the Brewster angle are mounted i n assemblies which are Or ri n g sealed to the outer ends of the l a s e r tube. Evacuation of the tube draws these window assemblies firmly against the a c r y l i c end plates. The set of four f l a s h tubes are clamped between two aluminum c o l l a r s and aluminum f o i l i s wrapped around the outside to act as the r e f l e c t o r . This unit i s accurately located within the c y l i n d r i c a l sub-assembly by recesses i n the a c r y l i c end plates, which match the aluminum c o l l a r s (see figure 20). Simple removal of both the l a s e r tubes and the f l a s h tubes i s therefore achieved. A l a s e r tube may be pulled out a f t e r loosening the "Tw shaped 0 ring coupling. The u n i t , consisting of four flash tubes and r e f l e c t o r , s l i d e s out of the assembly a f t e r removing an a c r y l i c end plate. Each sub-assembly also contains a c y l i n d r i c a l copper return conductor which i s held i n po s i t i o n by a c r y l i c rings. E l e c t r i c a l connection to the fl a s h tubes i s made v i a holes d r i l l e d through the a c r y l i c end plates and i n t o the aluminum c o l l a r s . Two coaxial cables, one from each set of four f l a s h tubes, are brought i n p a r a l l e l to the spark gap. This coaxial spark gap i s located d i r e c t l y above the capacitor bank which i s positioned adjacent to the a m p l i f i e r i n order to minimize the p a r a s i t i c inductance of the c i r c u i t . CF^I was supplied i n 100 goi. cylinders by P.C.R. Research Chemicals, F l o r i d a , U.S.A., and research grade C0 2 (99.995#) supplied by Matheson Gas Products was used as the buffer. A small mixing chamber (4 . 5 cms. diameter x 10 cms. long) containing a steel rotor, coupled through the brass wall to a rotating magnet, i s provided to reduce the time required for these gasses to mix. Narrow bore copper tubing i s used throughout to transport the gasses. S i l i c o n controlled r e c t i f i e r (SCR) units are used to tr i g g e r the discharge of the capacitor banks of the o s c i l l a t o r and amp l i f i e r stages. These SCR units are themselves triggered v i a adjustable electronic delays from a pulse generator. The delay between the pulse from the generator and the triggering of each SCR unit i s used to set the a r r i v a l time of the la s e r pulse at the ampl i f i e r to coincide with the maximum stored energy. ALUMINUM COLLAR Pig. 20. Details of a c y l i n d r i c a l sub-assembly and an 0 ring sealed window assembly. CHAPTER VI DIAGNOSTICS Current Pulse P r o f i l e and Timing Rogowskl c o i l s are used to monitor both the o s c i l l a t o r and a m p l i f i e r f l a s h tube current pulses. The integrated pulses from these c o i l s are displayed on a dual beam Tektronix 531 oscilloscope and recorded photographically each time the l a s e r i s f i r e d . (See figure 21) 2ps/DIV. F i g . 2 1 . Current Pulse P r o f i l e s . The current pulses driving the o s c i l l a t o r (upper) and the a m p l i f i e r (lower) fl a s h tubes are shown. These photographs are used to measure the reproduc-i b i l i t y of the pump l i g h t pulses and also the time of a r r i v a l of the l a s e r pulse at the a m p l i f i e r . Noise, generated by the SCR pulse, also appears on these photo-graphs and therefore the spark gap timing j i t t e r may be measured. Amplifier Gain and Temporal P r o f i l e of the Laser Pulse Two Indium antimonide photoconductive detectors (Mullard ARPIO) and a Tektronix type 5 5 4 A oscilloscope are used to observe the incident and amplified l a s e r pulse. The signals from the detectors are delayed i n order that they do not coincide with the noise generated during the pump l i g h t pulse. The H y M amplifiers of the oscilloscope are used i n the A + B mode such that both signals can be displayed simultaneously by using a different delay i n the cables from the two photoconductive detectors. (See figure 22) 5mV/DIV. lp s / D I V . Pig. 22. The incident and amplified l a s e r pulses. The output from the two photoconductive detectors i s shown, the f i r s t (second) being generated by the amplified (incident) l a s e r pulse. The detectors begin to saturate at an output of 50 mV and therefore an oscilloscope s e n s i t i v i t y of 5 per d i v i s i o n i s appropriate. The amplified l a s e r pulse i s attenuated using calibrated, neutral density f i l t e r s to maintain the signal l e v e l within the l i n e a r region. This scheme c l e a r l y displays the modification of the pulse shape by the am p l i f i e r . Beam P r o f i l e Mechanical adjustments are provided to allow the measurement of the i n t e n s i t y p r o f i l e of the beam. A micrometer screw on the mirrow mounts located as shown i n Figure 5*5 provide for a v e r t i c a l sweep of the beam across the photoconductive detector. Horizontal adjustments are achieved by changing the pos i t i o n of the screw s l i d e s on which the detectors are mounted. OSCILLOSCOPE CAPACITOR BANK Fig, 23. Schematic diagram of the a m p l i f i e r and associated diagnostics. CHAPTER VII THE EXPERIMENT The Vacuum System Some d i f f i c u l t y was experienced i n achieving the 0 r i n g vacuum seals to the l a s e r tubes which were not round and had surface imperfections. After some experi-mentation i t was found that t h i n brass c o l l a r s , which would d i s t o r t to the non-round cross-section and provide a smooth surface, could be glued to the tubes. The 0 rings were able to accomodate the non-circular cross-section. A number of leaks were traced to blemishes on the 0 ring surfaces of the "Speedivalves" used i n the system. Since these valves were cast from aluminum they are e a s i l y scratched and care must be taken to avoid damaging them on i n s t a l l a t i o n . Residual paste f l u x , used when soldering the copper tubes to the speedivalve couplings was found to be very d i f f i c u l t to remove. These tubes were replaced by others on which acid f l u x was used. This i s e a s i l y removed by r i n s i n g i n hot water and a f t e r t h i s treatment outgassing i s complete within 24 hours. The o i l rotary and d i f f u s i o n pumps evacuated the completed system to 0.6 x 10"^ Torr and at t h i s pressure the leak rate was found to be 0.1 x 10*"^  Torr per minute. The Capacitor. Spark Gap. Flash Tube C i r c u i t The current pulse i n the c i r c u i t was found to be c r i t i c a l l y damped and the addition of more capacitors to the bank did not increase the inductance of the c i r c u i t appreciably. (Chapter 4.11) In order to minimize the timing J i t t e r of the current pulse i t was necessary to adjust the separation of the spark gap electrodes so that the discharge would occur spontaneously at approximately 200 volts above the working voltage. Rapid changes In the r e l a t i v e humidity of the atmosphere made i t d i f f i c u l t to maintain t h i s current gap set t i n g . With careful adjustment of the spark gap no difference i n the timing or p r o f i l e of the current pulse would be 80 observed from pulse to pulse. However, a f t e r approximately 250 shots a m i s f i r e occasionally occurred. A glass tube i n s u l a t o r i s included i n the spark gap so that the diameter of the outer conductor, and consequently the inductance of the switch, may be reduced. After replacing t h i s tube the m i s f i r e d id not occur, suggesting that metal deposits formed on the wall of the tube had provided an alternate path to ground for the discharge. Measurement of the P r o f i l e of the Incident and Amplified Laser Pulse  The use of delays to s h i f t the signal away from the noise produced by the f l a s h lamp c i r c u i t s was only p a r t i a l l y successful. A burst of noise l a s t i n g approxi-mately 200 ps. with p e r i o d i c i t y 2^*, persisted well i n t o the i n t e r v a l when the l a s e r pulse was displayed. This noise i s p a r t i c u l a r l y troublesome as i t completely obscures the leading edge of the l a s e r pulse. Experiments were conducted to minimize the capacitive and inductive coupling of the diagnostic c i r c u i t from the fl a s h tube c i r c u i t . A d i f f e r e n t ground c i r c u i t was used for these two systems and care was taken to shorten cables and eliminate loops. The most obvious improvement was made by repositioning the photoconductive detectors further away from the amp l i f i e r assembly, on an e l e c t r i c a l l y non-conducting table. However, the periodic noise was s t i l l troublesome and additional changes were required. The SCH u n i t discharges a I L C T" capacitor into a transformer, the secondary winding of which i s connected to the spark gap tr i g g e r electrodes. This secondary unit was found to be resonating (see Figure 23) and each time the current passes through zero and the arc was re-established, the noise burst appeared. The period of t h i s resonance was found to be very sensitive to the stray capacitance i n the c i r c u i t . Even the capacitance of the cable to the oscilloscope, used to observe the current flow, reduced the period of the o s c i l l a t i o n to 0.6^j . (See Figure 24) Locating the SCR unit only 25 cms. away from the spark gap, and keeping the two wires connecting the secondary of the transformer to the t r i g g e r electrodes physically separate, c r i t i c a l damping was achieved and the periodic noise eliminated. PERIODIC NOISE I I I 2ps/DIV. Fig. 24. The current flow i n the secondary winding of the SCR t r i g g e r transformer. Noise i s seen to occur each time the current passes through zero. { 82 2ps/DIV. Pig. 2 5 . The current flow In the secondary winding of the SCR t r i g g e r transformer i s shown when a long cable to the o s c i l l a t i o n i s used. Timing of A r r i v a l of Incident Laser Pulse A great deal of d i f f i c u l t y was experienced i n achiev-ing the required delay (6-12p.s) between the i n i t i a t i o n of the discharge of the amplifier and o s c i l l a t o r capacitor banks. I t was found that the e l e c t r i c noise, associated with the discharge of the ampl i f i e r capacitor bank, which reaches a maximum current of 48 KA, caused the o s c i l l a t o r SCR to f i r e . I n i t i a l l y i t was believed that the noise was coupled to the SCR unit v i a the grounding c i r c u i t and therefore the following improvements were made: 1. The o p t i c a l bench was used as the single ground conductor, one end being connected with heavy copper braid to the laboratory buss bar. 2 . The power supplies and capacitor banks were connected to the bench separately, using short cables. 3 . Grounding of the power supplies through the A.C. l i n e cables was eliminated. 83 4. A l l connections In the ground c i r c u i t were cleaned, and. tightened to minimize the contact resistance. The timing problem persisted. However, having made these changes i t was decided that impedance of the ground, c i r c u i t , and hence the noise s i g n a l , had been minimized and that no further improvements would be made i n t h i s system. The next series of experiments were therefore aimed at Improving the noise immunity of the delay and SCR un i t s . Measurement of the noise l e v e l at d i f f e r e n t locations i n the c i r c u i t was impossible since the signal i s so pervasive that i t appears on the oscilloscope even when no input cable i s connected. The noise causing the timing problem was found to occur during the i n i t i a t i o n of the arc i n the spark gap and the SCR unit was found to be triggered even when removed some distance from the l a s e r , i n d i c a t i n g that the coupling was, i n part, r a d i a t i v e . Shielding the spark gap made no noticeable difference and thus i t was concluded that the fla s h tube c i r c u i t acts as an antenna f o r the rad i a t i o n . Improved shielding and wiring to the printed c i r c u i t board, and the addition of small decoupling capacitors i n the SCR c i r c u i t to provide a low Impedance to ground for the 84 high frequency noise eliminated the problem, unless a cable was connected to the tr i g g e r terminal. Having excluded the noise from the SCH shielded can, a monostable delay, c a r e f u l l y shielded, was i n s t a l l e d within the unit so that for correct timing a t r i g g e r pulse would be required to a r r i v e before the noise s i g n a l . The c i r c u i t used did not function as required, since the noise reset the monostable. However, by making the delay only one and u t i l i z i n g the noise immunity of the input required to set the monostable, correct timing was achieved. The following additional improvements were also made: 1. The t r i g g e r pulse f o r the o s c i l l a t o r delay u n i t was derived from the l i g h t output of the ampl i f i e r f l a s h tubes v i a an optic f i b r e which Is immune to e l e c t r i c noise. 2. Flash tube l i g h t and an optic f i b r e were also used to tr i g g e r both oscilloscopes, thereby eliminating an addit i o n a l 15 feet of cable. 3 . The t r i g g e r and noise signal appearing at the mono-stable input was clamped by a zener diode. Since the noise occurs as an o s c i l l a t i o n about the d.c. l e v e l of the tr i g g e r pulse, t h i s clamping at a low voltage w i l l eliminate much of the noise s i g n a l . Although t h i s system i s now functioning as required, some triggering d i f f i c u l t i e s may be encountered when the f i n a l a m p l i f i e r i s operated. Changing the integrated c i r c u i t used i n the SCB un i t from a retriggerable to a latched monostable (e.g., F a i r c h i l d type 9 2 0 3 ) , w i l l enable the c i r c u i t to be operated as proposed, providing a much improved noise immunity. Preliminary Experiments with the Complete System Preliminary experiments with the apparatus i n the present stage of construction were performed i n order to check the operation of the entire system, including the diagnostics, and i d e n t i f y possible d i f f i c u l t i e s which may be encountered i n the future. At present the apparatus has a 20^4 capacitor bank, uses quartz l a s e r tubes, and operates i n the low voltage regime. In order to perform the experiments and avoid the d i f f i c u l t i e s associated with the shock waves in e v i t a b l e with the device i n i t s present form, a s p a t i a l f i l l e r was used to l i m i t measurements to the undisturbed beam centre. Operating at low pressure, i . e . , without any buffer gas, the l a s e r pulse was passed through the am p l i f i e r at various times during the pump pulse (see Figure 2 6 ) . 86 LASER PULSE CURRENT PULSES lOOns/DIV. 5ps/DTV. Pig. 2 6 . The amplified l a s e r pulse and the o s c i l l a t o r and amp l i f i e r current pulses are shown. The additional pump energy delivered to the active medium i s seen not to increase the system gain. The system gain was found to reach a maximum value early i n the pump pulse and thereafter remain e s s e n t i a l l y constant u n t i l the termination of pumping, a f t e r which i t began to f a l l slowly. (See Figure 27) 87 GAIN 3 . • • PUMP CURRENT (KA.) _ - — _ - -• — _ • • • S • i i A / / / ; / / / / 3 / / / '* / / /  / ; •/ / 2 / ; / 1 / / • o O 2 . 4 8 I O 12. 14 l b 1 8 TIME (f-S.) F i g , 27. The temporal behaviour of the pump current and the subsequent system gain for a zero buffer gas pressure i s shown for the am p l i f i e r i n i t s present state of construction. This behaviour i s consistent with theory which predicts that at t h i s low pressure the inversion i s quickly pumped to the threshold for p a r a s i t i c o s c i l l a t i o n and i s held at t h i s l e v e l by the radiative losses. A f t e r the pump pulse has terminated the inversion f a l l s below this threshold and chemical deactivation slowly depletes the inversion. I t was found that, contrary to theory, the addition of any buffer gas reduces the system gain, i n i t i a l l y , i t was believed that the buffer gas was contaminated and therefore additional chemical deactivation was occurring. However, a thorough cleaning of the gas system and a new buffer gas supply f a i l e d to eliminate the problem. I t i s now believed that improper mixing of the gasses r e s u l t i n g i n regions of high and low concentrations i s the cause and i n the future a mixing chamber must be used. '89 CHAPTER VIgyl CONCLUSIONS Achievements A gain switched o s c i l l a t o r and a preamplifier stage, together with the diagnostics required to monitor the performance of the entire l a s e r and i t s sub-systems have been constructed and shown to function as required. The gain of the preamplifier i n i t s present stage of construction has been studied and has been shown to behave i n accordance with theory, unless a buffer gas i s added. Improper mixing of the active and buffer gasses i s suggested as a reason for th i s discrepancy and a mixing chamber has been constructed. Using a 20p.f capacitor bank charged to 12 KV and a zero buffer gas pressure, a maximum gain of 6 has been demonstrated. (See Figure 28) INTENSITY O . I 2. 3 4 5 fc 7 8 «* IO TIME ( X 100ns.) Pig. 28, The temporal p r o f i l e of the Intensity of the Incident (broken l i n e ) and amplified ( s o l i d l i n e ) l a s e r pulse i s shown. Suggestions f or Future Work The following suggestions are offered f o r the future development of the Iodine l a s e r system at U.B.C. The duration of the pumping pulse must be reduced or a Q switching device must be incorporated so that the energy density of the l a s e r pulse i s s u f f i c i e n t to achieve reasonable extraction r a t i o s from the preampli-f i e r stages. This improvement i s p a r t i c u l a r l y important i f a mode locking and a pulse cutting system are used to produce sub nanosecond pulses. Germisil tubes must be used i n place of the quartz glass l a s e r tubes i n the preamplifier stage. Short Duration. High Power Laser Pulse (Explosive Compression Experiments) Active mode locking and pulse cutting systems must be included i n the o s c i l l a t i o n stage i n order to generate a l a s e r pulse of 1 ns. duration. The preamplifier stage with an active volume 1 cm. i n diameter and 1 m. long, at present under construction, should be used to raise the energy of th i s pulse to the required 100 mJ. A f i n a l a m p l i f i e r must then be designed and b u i l t to store the t o t a l energy required, i n the l a s e r pulse. I t must have s u f f i c i e n t bandwidth to accomodate the 1 ns. incident pulse. When the construction of the o s c i l l a t i o n and amp l i f i e r chain has been completed the operating conditions of the amp l i f i e r designed i n t h i s paper must be chosen to saturate the f i n a l a m p l i f i e r . I n i t i a l l y , i t should be operated at a pressure of 70 Torr CP3I and 400 Torr C0 2 with a 40 p f capacitor bank charged to 14 KV. I f the Incident energy at the f i n a l a m p l i f i e r i s above the saturation density then the changing voltage should be reduced. I f not, then the incident energy should be calculated for the maximum stored energy i n the capacitor bank of 6 KJ. I f the saturation energy can be achived at th i s higher l e v e l of stored e l e c t r i c energy then the l i f e t i m e of the fla s h tubes must be found experimentally or from data supplied by the manufacturer. The reduced flash tube l i f e t i m e may be tolerated or an additional preamplifier stage must be b u i l t to achieve the required saturation energy density of the f i n a l a m p l i f i e r . Long Duration Laser Pulse (Ablative Compression Experiments) The design process outlined i n t h i s paper i s appro-pr i a t e for an o s c i l l a t o r having modelocking and pulse cutting systems such that the pulse has a duration of approximately 1 ns. Without these systems the duration of the f i r s t pulse i s t y p i c a l l y 3 0 0 ns., (see figure 2<f) and therefore l a s e r i n t e r a c t i o n experiments requiring long duration pulses may be performed. iSSSI&UBBlj l 200ns/DIV. Fig. 29. A long duration l a s e r pulse generated by a gain switched o s c i l l a t o r stage, without a modelocking system, i s shown. The design compromises and the operating conditions of an am p l i f i e r f o r long pulses are dif f e r e n t to those required f o r a 1 ns. pulse. A reduced bandwidth, and. consequently a lower buffer pressure, i s appropriate. However, t h i s pressure i s no longer defined by the band-width requirement since the corresponding maximum stored energy, and hence the gain, i s unreasonably small. In t h i s scheme the buffer gas pressure i s chosen such that the small signal gain i s just below the threshold value for p a r a s i t i c o s c i l l a t i o n s , f or a pump pulse which can be achieved reasonably e a s i l y . This contrasts with the design procedure f o r a sub-nanosecond pulse where the pump pulse i s defined, i n d i r e c t l y , by the bandwidth requirement. Thus, i f i n the future experiments requiring long duration l a s e r pulses are to be performed, the preamplifier should be operated and should function as described below. The 40 p-f capacitor bank must be charged to 14 KV, thereby operating the fl a s h tubes within the recommended l i m i t s , and the buffer gas pressure required to y i e l d the maximum gain, found experimentally. The ampli f i c a t i o n w i l l increase with pressure as successive p a r a s i t i c modes are eliminated thereby increasing the stored energy l e v e l achieved. A further pressure increase above that required to surpress the p a r a s i t i c modes w i l l r e s u l t In a reduced a m p l i f i c a t i o n as the small signal gain,and hence the extraction r a t i o , w i l l f a l l . I t i s hoped that operating the o s c i l l a t o r stage In the high voltage regime and using the preamplifier designed i n t h i s paper to amplify the r e s u l t i n g long duration l a s e r pulse w i l l produce s u f f i c i e n t power to complete the evalua-t i o n of the fog c e l l o p t i c a l i s o l a t o r developed i n t h i s laboratory by B. Ahlborn, S. Ariga and D. Friedman ( 2 6 ) . I f t h i s device proves to be successful then the design com-promises necessary to achieve o p t i c a l i s o l a t i o n w i l l not be required and an improved l a s e r w i l l r e s u l t . , Using an e f f e c t i v e o p t i c a l i s o l a t o r , the apparatus designed i n t h i s paper could be operated as a f i n a l a m p l i f i e r , thereby y i e l d i n g an estimated 18 Joules i n 1 ns. Useful laser-plasm i n t e r a c t i o n experiments could be performed with t h i s 18 GW pulse. 95 B I B L I O G R A P H Y 1. D. Porrett & C. F. Goodeve. Proc. Royal Soc. Al6*? 31. (1938). 2. J.V. V. Kasper & G. C. Pimental. Appl. Phys. L e t t . £ 231, (1964). 3 . M.A. Pollack. Appl. Phys. L e t t . 8, 3 6 , ( 1 9 6 6 ) . 4. A.J. DeMarie & C.J. Vltee. Appl. Phys. L e t t . 9_, 67 (1966). 5 . K. Hohla. Springer Series i n Optical Sciences, Vol.9; High Power Lasers & Applications. Sprlnger-Verlag, N.Y. (1978). 6. Laser-Fusion Research Progress Report, January-June 1976. Issued by the Directorate of Physical Research Sandia Laboratories, Alberquerque, N.M. 7. R.D. Franklin, Wright Patterson AFB, Dayton, Ohio; Technical Report, ARL 73-0071, A p r i l 1973. 8. T.L. Andreeva, S.V. Kuzretsova, A.I. Maslov, I . I . Sobel'man & V.N. Sonokin. JETP L e t t . 12, 449, (1971). 9. R. G. Derwent, D. Husain & J.R. Wiesenfeld. Chem. Phys. L e t t . 2, 591, (1971). 10. K. Hohla. J . Appl. Phys. 4Z, No. 12, 5360 (Dec. 1976). 11. V. Jaccarlno et a l . Phys. Rev. 9_4, 1798, (1954). 12. W. Fuss & K. Hohla. Max Planck I n s t i t u t e Fur Plasma-physik, IPP IV, 6 7 , (1974). 13. T.D. Padnik & R.E. Palmer. J . Chem. Phys. 62, 3350, (1970). 14. R.E. Palmer, T.D. Padrik & E.D. Jones. Society of Photo- Opt. I n s t r . Engs. 3 6 , 3 2 , (1976). 15. D.W. Gregg, R.E. Kidder & C.V. Dobler. Appl. Phys. L e t t . II, 297, (1968). 16. K. Hohla. Max Planck I n s t i t u t e of Plasma Physics: Report No. IPP-IV/33. December, 1971. 17. G. Brederlow, K.J. Wltte, E. F i l l , K. Hohla & R. Volk. I.E.E.E. J . of Quant. Elec. QE-12, No. 2, 152 (1976). 96 18. I.M. Belousova, O.B. Danllov, I.A. S l n l t s l n a & V.V. Sperodonov. JETP. H , No. 5 , 791 (1970). 19. E. F i l l & K. Hohla. Optics. Comm. 18, No. 4, 431 (1976) 20. K. Hohla, W. Fuss, R. Volk & K.J. Witte; Optics Comm. 11, No. 2, 114, (1975). 2 1 . K. Hohla. R. Volk, K.T. Witte. I.E.E.E. J . Quant. ELec. QE-9. 764, (1974). 22. S. Arlga & B. Ahlborn. J . Appl. Phys. 4 Z , No. 3 ( 1 9 7 6 ) . 2 3 . J.W. Olsen. J . Appl. Phys. 4Z, No. 12, 536O (Dec. 1 9 7 6 ) . 24. K. Witte, G. Brederlow, E. F i l l , K. Hohla & R. Volk. Laser Interaction and Related Plasma Phenomena. Vol. 4A Plenum P u b l i s i n g Corp. (1977). 2 5 . J.F. Hol z r i c h t e r & A.L. Schawlow. Reprint from the Annuls of the New York Academy of Sciences, Vol. 168, A r t i c l e 3 , pp. 703-14. 26. D. Friedman, S. Arlga & B. Ahlborn 0 J . Appl. Phys. 50. 5998, (1979). 

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