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Operational characteristics of ion cyclotron resonance cells Woods, Ian Barry 1973

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OPERATIONAL CHARACTERISTICS OF ION CYCLOTRON RESONANCE CELLS by IAN BARRY WOODS B.Sc, Queen's University, 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1973 In presenting 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada D a t e I\U<X. »<J73. ( i i ) ABSTRACT: A prerequisite to the correct i n t e r p r e t a t i o n of experimentally observed r e s u l t s i n ion cyclotron resonance c e l l s i s the detailed knowledge of ion motions i n the c e l l under a l l operating conditions. Thus far the theories i n the l i t e r a t u r e do not s a t i s f y such a c r i t e r i o n and a more detailed development i s presented i n t h i s t h e s i s . A s i g n i f i c a n t r e s u l t i s the r e a l i z a t i o n that s h i f t s i n the cyclotron resonance f i e l d s give information concerning the s p a t i a l d i s t r i b u t i o n of ions i n the ICR c e l l . Such information i s v i t a l i n many experiments. In addition, the theory predicts and explains the experimental behaviour of the ICR apparatus under v a r i a t i o n of the operating parameters and hence replaces the available theories as being more comprehensive. The ICR c e l l i s used to measure an average cross + section for the photodissociation of H2 , and to place an upper l i m i t on the controversial photodissociation cross section of CHI". ( i i i ) CHAPTER I : TABLE OF CONTENTS INTRODUCTION: HISTORICAL RESUME THESIS INTRODUCTION PAGE 1 4 CHAPTER I I : PROPERTIES OF THE ICR C E L L : GENERAL CONSIDERATIONS THE DRIFT VELOCITY POWER ABSORPTION POTENTIALS AND E L E C T R I C F I E L D S ICR C E L L POTENTIALS LINEWIDTH CONSIDERATIONS 8 9 13 18 22 37 CHAPTER I I I APPARATUS: ICR C E L L VACUUM SYSTEM MODULATION TECHNIQUES LIGHT SOURCE AND CHOPPER SPECTROMETER OSCILLATOR S E N S I T I V I T Y 43 47 48 50 51 53 CHAPTER I V : PHOTODISSOCIATION OF P O S I T I V E IONS: OBSERVATION OF PHOTODISSOCIATION OF PHOTODISSOCIATION IN ICR THEORETICAL PREDICTIONS EXPERIMENTAL PROCEDURE PHOTODISSOCIATION OF CHI 56 60 61 64 72 BIBLIOGRAPHY: (iv) 74 APPENDIX A: ICR POTENTIALS 77 APPENDIX B: ICR ELECTRIC FIELDS 80 APPENDIX C: ELECTRON BEAM POTENTIALS 81 APPENDIX D: ENERGY SPREADS OF IONS FROM PHASE AND TRAPPING CONSIDERATIONS 8 2 (v) LIST OF ILLUSTRATIONS: FIGURE TITLE PAGE A E x H D r i f t of charged p a r t i c l e s i n crossed e l e c t r i c and magnetic f i e l d s 10 B Basic ion cyclotron resonance c e l l 12 C Low pressure ICR absorption lineshape of H £ 16 D A r + Ion Cyclotron resonant magnetic f i e l d s h i f t with trapping voltage and electron beam current , 28 E Graphical representation of the parameters f , (x) , f z (x) , g ( (x) and g ^  (x) from equations (37) and (38) solved for the " f l a t c e l l geometry" 30 JL. F Ar Ion Cyclotron resonant magnetic f i e l d s h i f t with trapping voltage and electron beam current 32 G Ar"*" Ion Cyclotron resonant magnetic f i e l d s h i f t 4. _ with d r i f t voltage Vd = V - V , and electron beam current 34 H Ar"*" Ion Cyclotron resonant magnetic f i e l d s h i f t with . Va = V + + V~ 35 I Graphical representation of the parameters f , ( x ) , f^(x) , h ( (x) and h z(x) from equation (56) solved for the " f l a t c e l l geometry" 39 (vi) -t-Ar Ion Cyclotron absorption signal linewidth v a r i a t i o n with trapping voltage Vj and electron beam current 41 K Anomalous s a t e l l i t e sideband structure of + He ion absorption signal i n aluminum c e l l 44 L Anomalous s a t e l l i t e sideband resonant magnetic f i e l d s h i f t with trapping voltage V-j- 4 5 M ICR Spectrometer c i r c u i t diagram 52 N H* population near the i o n i z a t i o n potential threshold, for p ~ 2 x l 6 " 5 t o r r 58 + 0 H z population near the i o n i z a t i o n p o t e n t i a l threshold, for p~10 t o r r 59 + + P Ez + hv. ^ H + H signal manifest v i a the H + ICR absorption signal 66 Q Photon density integration with respect to wavelength for the lamp used approximated by the black body ra d i a t i o n formula 7 0 +• +• R Change of the H 2 + hv—^*H + H with a pyrex f i l t e r incorporated i n the l i g h t beam 71 S D i s t r i b u t i o n of energies of ions i n the ICR c e l l due to the i n i t i a l random phase d i s t r i b u t i o n of the ions r e l a t i v e to the r f e l e c t r i c f i e l d 84 Variation of the maximum energy spread due to the i n i t i a l random phase d i s t r i b u t i o n of the ions r e l a t i v e to the r f e l e c t r i c f i e l d with atomic mass number and (E at) Variat i o n of the energy d i s t r i b u t i o n for ions due to formation i n the trapping plate pote n t i a l well ( v i i i ) ACKNOWLEDGMENTS: I wish to sincerely thank Dr. Meyer Bloom for his generous support and assistance during my stay at U.B.C. Dr. Bloom's e a s i l y shared physical insights have made working i n his lab a d e f i n i t e pleasure. I am also indebted to Dr. M.H. Tinker and Mr. M. Riggin for t h e i r interchange of ideas and c r i t i c i s m s which have been of enormous help to me. Fin a n c i a l support from the National Research Council of Canada i n the form of Scholarships i s g r a t e f u l l y acknowledged. This work was supported i n part by the National Research Council of Canada. INTRODUCTION: HISTORICAL RESUME: The essence of ion cyclotron resonance (ICR) has basic-a l l y resulted as a spin-off from the research and development of the omegatron instrument. ^  This apparatus exploits the fact that charged p a r t i c l e s possessing a v e l o c i t y component i n the plane perpendicular to a magnetic f i e l d are constrained i n t h e i r motion i n that plane to c i r c u l a r o r b i t s with a unique angular frequency defined by CO - flH . i f a n r f e l e c t r i c f i e l d with the same frequency i s applied i n the same plane as the ion o r b i t s , the component of the f i e l d r o t a t i n g i n phase with the ions l i n e a r l y accelerates them to higher v e l o c i t i e s and hence larger o r b i t s . Whereas the presence of charged p a r t i c l e s i s detected i n the omegatron by phy s i c a l l y c o l l e c t i n g the ions when the i r o r b i t s exceed a given radius, the ICR apparatus i s able to monitor the presence of ions i n the system by t h e i r absorption of energy from the o s c i l l a t i n g e l e c t r i c f i e l d without a l t e r i n g s i g n i f i c a n t l y the ion trajectory on a macroscopic or c l a s s i c a l basis. Subsequently, c o l l i s i o n broadening of electron cyclotron resonance l i n e s and c o l l i s i o n processes analyzed by ICR techniques were carr i e d out. The second property of ICR which made i t a unique (4) development was the adaptation by Baldeschweiler ' and Beauchamp ( 5) of a second r f e l e c t r i c f i e l d to s e l e c t i v e l y heat a p a r t i c u l a r i o n i c species i n a gas mixture. The e f f e c t of th i s v e l o c i t y increment on the c o l l i s i o n or reaction cross-section 2. with a second species i n the system i s simultaneously monitored by observing the c o l l i s i o n coupled e f f e c t on the population of the second species. This p a r t i c u l a r technique, known as ion cyclotron double resonance (ICDR) became immediately useful i n (5) sorting out complicated gas phase chemical reactions. ' The geometrical arrangement of the ICR c e l l i s such that a separate ion d r i f t region i s available between the ion source region and the actual analyzer region of the c e l l . In t h i s d r i f t region, s p e c i f i c ion species can be accelerated to prepare the ions i n a given k i n e t i c energy state before introduction into the analyzer region. As a r e s u l t , i t seemed i n i t i a l l y that the ICR apparatus had an immediate ap p l i c a t i o n to provide precise quantitative measurements of both the energy dependence of c o l l i s i o n and reaction cross sections, as well as the energy dependence of rate constants A ' A basic assumption for the successful extraction of precise quantitative data r e l a t i n g to the energy dependence of ICR observed processes i s that the experimenter has been able to prepare the ions i n a narrow, controllable energy range. Several factors seem, a c t u a l l y , to make thi s s i t u a t i o n quite d i f f i c u l t to achieve i n ICR over a large range of operating energies (usually £ 10 ev.) The ions are formed i n the source region by electron bombardment of the background gas i n the system. Usually i t i s reasonable to assume that these ions are i n fact produced with thermal v e l o c i t y energies. However, i t i s also obviously true that the ions are produced with a random phase r e l a t i v e to the r f e l e c t r i c f i e l d s . In c a l c u l a t i n g the power absorption, i t i s 3. (7) reasonable to assume that the phase angle term may be averaged to zero. However, as indicated i n appendix D, there may be a s i g n i f i c a n t d i s t r i b u t i o n i n the energies of the i o n i c system when heated by an r f e l e c t r i c f i e l d , due to t h i s phase angle spread. The actual d i s t r i b u t i o n i s given i n appendix D. In addition, the ions are constrained s p a t i a l l y i n the c e l l i n t h e i r motion along the magnetic f i e l d axis by the use of two trapping plates (see figure A). These plates w i l l trap ions of the same charge as the trapping plate p o t e n t i a l . The motion of the ions along the axis p a r a l l e l to the magnetic f i e l d i s thus roughly approximated by simple harmonic o s c i l l a t i o n s . Due to t h e i r formation at d i f f e r e n t positions i n t h i s potential well, there i s a d i s t r i b u t i o n of k i n e t i c energies which i s developed i n appendix D. The r e s u l t s indicate that most ions experience a small energy increment as a r e s u l t of t h e i r formation i n the po t e n t i a l well of the trap. The r e s u l t i n g change i n the k i n e t i c energy d i s t r i b u t i o n complicates further the problem of preparing the system i n a narrow energy range. Thus, u n t i l more work can be done to specify the energy spread of the i n t e r a c t i n g i o n i c species, i t seems quite tentative to extract quantitative r e s u l t s from the ICR apparatus which depend on knowing the precise energy of the prepared i o n i c state. Using the ICDR technique i n sorting out ion molecule reactions, i t i s impossible to derive the r e l a t i v e contribution of d i f f e r e n t reaction channels leading to the same product ion. However, making use of the ion o s c i l l a t i o n i n the trapping plate (e>) f i e l d , an ion ejection technique may be u n t i l i z e d to eject 4. s e l e c t i v e l y from the c e l l by applying an r f e l e c t r i c f i e l d to the second where vy i s the biasing voltage of the trapping plates and d i s t h e i r geometric separation. By ejecting d i f f e r e n t ions from the c e l l while observing the r e l a t i v e e f f e c ts on a secondary ion, the r e l a t i v e contributions of the d i f f e r e n t ions as precursors of the secondary ion w i l l be determined. There i s unfortunately a problem of resolution with t h i s method i n that several ions of similar mass are usually ejected at the same time. In practice, the experimentally determined ejection frequency d i f f e r s consider-ably from that predicted above. Some researchers a t t r i b u t e t h i s to f i e l d d i s t o r t i o n s ^ ) , It appears that other factors may also s i g n i f i c a n t l y s h i f t t h i s frequency. More w i l l be said about t h i s l a t e r . of the ICR method i s to be found i n the excellent compilation prepared by F u t r e l l e n t i t l e d Ion Cyclotron Resonance Mass spectroscopy, 1971, Department of Chemistry, University of Utah. THESIS INTRODUCTION: A major area of concern which has guided the research i n t h i s thesis has been the problem of explaining more prec i s e l y the behaviour of the ions i n the ICR c e l l . The basic motivation for t h i s work evolved as a r e s u l t of d i f f i c u l t i e s i n obtaining data consistent with that predicted by the theories i n the l i t e r a t u r e There were also extensive variations i n the measurements of our home made apparatus which were not predicted at a l l i n the l i t e r a t u r e . In addition, the measurements were not consistent on a day to day basis. trapping plates at frequency radians per A general review of the various chemical applications 5. The i n i t i a l impulse was of course to suspect the home made apparatus. However, after intensive e f f o r t s to r e c t i f y any technical.oversights i n the construction and/or operation of the equipment, the following problems remained e s s e n t i a l l y unexplained i n the l i g h t of the available theory, which was based on a guadrupole expansion of the potential f i e l d s i n an ICR c e l l . (i) The prediction of a unique v a r i a t i o n of the resonant magnetic f i e l d H c (or frequency) with the trapping voltage Vj was s a t i s f i e d only under some conditions, and only over a very li m i t e d range of trapping plate voltages. At voltages greater than 2-3 v o l t s , the predicted constant value of the slope A He. was no longer experimentally s a t i s f i e d . In addition when the electron beam current, used to ionize the gas being studied, was increased, the slope AH C s h i f t e d to a d i f f e r e n t value. ( i i ) I t was found that there was a considerable v a r i a t i o n of the resonant magnetic f i e l d with where V„ _ V + V" and V +, V~ are the d r i f t voltages applied a z to the top and bottom d r i f t plates i n the ICR c e l l to provide a controlled d r i f t v e l o c i t y for the ions down the c e l l . This d r i f t motion i s superimposed on the cyclotron o r b i t i n g motion i n the plane perpendicular to H. This v a r i a t i o n of H c versus was not predicted by the available theory. ( i i i ) It was found that there was also a considerable v a r i a t i o n of the resonant magnetic f i e l d with , where = V + - v" i s the e f f e c t i v e d r i f t p o t e n t i a l i n the ICR c e l l . This slope A He w a s n o t predicted by the available theory. (iv) It was observed i n many instances that when ions were accelerated by large r f e l e c t r i c f i e l d s both i n ICDR and ICR 6. techniques, that the ions seemed to a t t a i n o r b i t s leading to c o l l i s i o n s with the d r i f t plates, and hence were removed from the c e l l . The problem that arose was that the ions appeared to s t r i k e the plates with energies less than that required for t h e i r o r b i t s to be large enough for such c o l l i s i o n s to occur. (v) It was found that as the electron beam current was increased from minimum levels required to observe an ICR absorption signal to higher currents, the ICR absorption signal i n t e n s i t y (and hence presumably the number of ions of the species being monitored) increased over only a r e l a t i v e l y small current range, and then began to decrease. With continued increase of the electron current the absorption signal would completely disappear. Others had usually attributed t h i s c h a r a c t e r i s t i c to some sort of complicated space charge e f f e c t . I n i t i a l l y t h i s vague statement s a t i s f i e d us, but we l a t e r came to f e e l the need for a more quantitative explanation. (vi) One c o r r e l a t i o n we did notice i n these experiments was that when the ion population was increased by higher electron beam currents to the point where the ICR absorption signals disappeared, s e n s i t i v e electrometers indicated that i n f a c t the ions were disappearing mainly v i a the bottom d r i f t plates i n the source and reaction regions, but not v i a the top plates. (vii) Many experimentally derived quantities i n ICR work r e l y on measuring the ICR absorption l i n e width designated LI OO) as A n i . It was found that both at high and low electron beam currents, there was a marked v a r i a t i o n of with V T . This 2. 1 v a r i a t i o n was not i n f a c t l i n e a r , and at low voltages reversed the slope of the general v a r i a t i o n at higher voltages. Since no 7. va r i a t i o n at a l l was predicted i n the l i t e r a t u r e for the dependance of AHy^ on V-j-, t h i s behaviour was d i f f i c u l t to evaluate. B a s i c a l l y , the above seven problems along with other related, but less c l e a r l y defined issues, seemed to make much of the e f f o r t and work being put into assigning precise quantitative values to experimentally determined parameters s l i g h t l y premature to an adequate understanding of the motion and behaviour of the ions. The available theory did not provide explanations for the observed measurements of our apparatus. Part of thi s thesis thus develops the theory of ICR to the point where the observed behaviour i s explained. In so doing (Chapter I I ) , i t becomes evident that along with the previously mentioned importance of knowing the energy d i s t r i b u t i o n s , i t i s also extremely important to know the s p a t i a l d i s t r i b u t i o n of the ions. The s h i f t i n the resonant magnetic f i e l d (or frequency) appears to provide a tool to investigate s p a t i a l d i s t r i b u t i o n s of the ions i n ICR c e l l s . A second part of the thesis discusses some of the construction d e t a i l s of sign i f i c a n c e i n the development of a functional ICR apparatus. The t h i r d part of the thesis i s concerned with the investig a t i o n of photodissociation experiments where a beam of l i g h t i s used to dissociate one io n i c species into another, + •+-such as A + hV >• B + C. The apparatus was used successfully to measure the photodissociatxon of Hj, , and a value of an average cross section i s derived. F i n a l l y , the apparatus was used to look at the p o s s i b i l i t y of photodissociating CH"^ . which provides some i n f o r -mation r e l a t i v e to a contemporary discussion of the di f f u s e i n t e r s t e l l a r l i n e s . 8. CHAPTER II PROPERTIES OF THE ICR CELL GENERAL CONSIDERATIONS: One method of operation for an ion cyclotron resonance apparatus i s to create ions by electron bombardment of a gas contained i n the geometrically rectangular c e l l mounted between the pole faces of an electromagnet (Figure B). By applying the appropriate e l e c t r i c and magnetic f i e l d s to the c e l l plates and c e l l u l a r environment respectively, the ions created i n the source region of the c e l l are d r i f t e d down the c e l l i n a controlled manner, and the populations of the ionic species then are detected i n a subsequent analyzer region of the c e l l . The motion of a charged p a r t i c l e q of mass m moving i n a prescribed e l e c t r i c and magnetic f i e l d may be found d i r e c t l y by solving the lorentz force equation, for the n o n - r e l a t i v i s t i c case where i s the i n i t i a l v e l o c i t y of the ion. For the case of electron bombardment of a gas at room temperature, the d i s t r i b u t i o n of i n i t i a l ion v e l o c i t i e s i s close l y approximated by the thermal v e l o c i t y d i s t r i b u t i o n of the neutral molecules before i o n i z a t i o n . It w i l l be shown that i f an e l e c t r i c and magnetic f i e l d are applied simultaneously to the ions, with E J_ H, then the p o s i t i v e and negative charges w i l l d r i f t i n the same di r e c t i o n down the c e l l . A provision must be made to constrain the l a t e r a l motion of the ions being studied while d r i f t i n g down the c e l l . This provision i s provided by trapping plates which also f a c i l i t a t e the removal from the ion beam of ions of opposite charge to those being detected (Figure B). THE DRIFT VELOCITY: For convenience l e t If = li.j + XT and then a p a r t i c u l a r choice of T l j = £ * H c- causes (assume E and H are uniform) cancellation of a l l the forces of the Lorentz force equation except A V * H a n ( ^ e q U a t i o n (1) becomes 1 c a t " I c which gives the usual ion o r b i t i n g motion i n the plane perpendicular to H and at a c h a r a c t e r i s t i c cyclotron frequence U>c _ 4 H (2) ' IV\C Thus the motion of an ion i n mutually perpendicular E and H f i e l d s i s e s s e n t i a l l y made up of three terms: (a) any i n i t i a l v e l o c i t y Vp which the ion may have p a r a l l e l to H and which thus remains unaffected by the application of the. f i e l d s , (b) an o r b i t i n g motion about the magnetic f i e l d l i n e s with an angular frequency U)c = •*)•• and (c) a constant d r i f t v e l o c i t y ITJ _ ^ ^ * ^ (3) at r i g h t angles to E and H. From equation (3) i t should be noted that tfj i s independent of the charge, and thus both p o s i t i v e and negative charges w i l l experience a constant d r i f t i n the same d i r e c t i o n E x H. The motion of the ions i n the x - y plane i s represented by the o r b i t s i l l u s t r a t e d i n Figure A. In order to detect the presence of these ions d r i f t i n g and o r b i t i n g as described above, consider the application of an o s c i l l a t i n g r f e l e c t r i c f i e l d E = E 0 cos cu,"t perpendicular to the d i r e c t i o n of the magnetic f i e l d . Ions of a given JW r a t i o , and hence of a unique cyclotron frequency for the applied f i e l d H, FIGURE A Ex fit DRfFT OF CHARGED PARTICLES IN CROSSED FIELDS w i l l absorb energy when the frequency of the r f f i e l d , (radians), i s equal to U)c, the cyclotron frequency. This resonance phenomena i s the basis for the detection system i n an ion cyclotron resonance (ICR) mass spectrometer. 0 0 A schematic of the c e l l i s shown i n Figure B. The c e l l plates are fabricated from polished non-magnetic st a i n l e s s s t e e l , and the unit i s mounted between the pole faces of a magnet, such that H i s p a r a l l e l to the electron beam, and defines the - 2 axis. The system i s maintained at a high vacuum ( 6 x 10 torr to 10 torr) and i s f i t t e d with gas handling f a c i l i t i e s for c o n t r o l l i n g the introduction of selected gases for investigation. The ions are produced i n the ICR c e l l by bombarding the background gas with an electron beam which traverses the c e l l i n the source region. This source region i s defined geometrically by the top and bottom plates i n Figure B having voltages of 4- _ V s and V & respectively which provide the e l e c t r i c f i e l d E needed to cause the ions to d r i f t down the c e l l a f t e r formation i n the electron beam. This ion d r i f t i s maintained i n the analyzer region of the c e l l defined geometrically by the top and bottom plates i n Figure B with dc d r i f t voltages V* and respectively. The trapping plates with potential V^ . i n Figure B are necessitated by the otherwise unconstrained motion of the ions i n the 2 d i r e c t i o n . The poten t i a l of the trapping plates i s chosen p o s i t i v e or negative depending on whether i t i s desired to study p o s i t i v e or negative ions respectively. BASIC ION CYCLOTRON RESONANCE CELL In addition to serving as d r i f t electrodes, the top and bottom plates i n the analyzer region also form the capacitive element i n the tank c i r c u i t of a marginal o s c i l l a t o r (Chapter I I I ) . In analogy with NMR techniques, the resonant absorption of energy when lOi ui c i s detected by the change i n the Q of the tank c i r c u i t which manifests i t s e l f by a corresponding change i n the dc l e v e l of o s c i l l a t i o n of the marginal o s c i l l a t o r . Thus, i n t y p i c a l single resonanace experiments, the magnetic f i e l d or the marginal o s c i l l a t o r frequency i s swept through the resonance region (ie.^k* = ^« -Wc — 0) while some parameter of the c e l l which a f f e c t s the absorption signal i s modulated to allow use of phase sensitive detection methods to enhance the signal to noise r a t i o . T y p i c a l l y , the modulation could be made v i a the magnetic f i e l d , the spectrometer frequency, the d r i f t f i e l d s , the trapping potential or the i o n i z i n g electron beam energy. After the analyzer region, the ions may be co l l e c t e d by a set of electrodes i n which the trapping potential has been removed. POWER ABSORPTION: For frequency = (COc+ Su>) and for | Su> \ <5C c the k i n e t i c energy associated with if* and 1/tj aft e r a time t i s given by 0*) E(t) = 2|L + ttj2") (4) i e . E(t) = € 4- 2 ( £ £ 0 V / z - COS ("U.- ^ ) +• £ Q (5) where & 0 = i s the i n i t i a l k i n e t i c energy of the ions at time "to j i s the i n i t i a l phase angle of V~0 r e l a t i v e to the applied r f f i e l d E = E 0 cos to.t, and VL - &u> ("t -to) ±s a 14. defined resonance factor. Also e « e m u / ^ (6) where £ m = t < * It seems reasonable to assume that i n most cases of i o n i z a t i o n , ^ i s randomly d i s t r i b u t e d between 0 and 2-TT . Hence €,0 represents the average change i n energy due to the influence of the r f e l e c t r i c f i e l d . The quantity £ m i s the change i n the average energy obtained when the ICR resonance condition ?U) = 0 i s s a t i s f i e d . Then 'A E c it) * £ m + 2 ( € m € . « ) c o>V + e0 (7) Hence, for a given i o n i c species, there i s a cumulative power absorption, which at great enough f i e l d strengths (or long enough d r i f t times) i n the c e l l , the ions absorb enough energy to be l o s t by c o l l i s i o n s with the upper and lower d r i f t plates of the c e l l . This can i n fact be used to obtain a t o t a l ion current spectrum by monitoring the reduction i n t o t a l ion current as ions of d i f f e r e n t ^\ r a t i o are swept out of the analyzer region. From equation (6) cte _ <P -sUv .foo ( t - O (8) Under the condition that no c o l l i s i o n s take place during t r a n s i t of the ions through the c e l l , ta i s simply the time of entry of the ion into the c e l l . If c o l l i s i o n s do occur then t t f w i l l be interpreted as the time of the l a s t c o l l i s i o n . The power absorbed by the ions i s found by c a l c u l a t i n g g ( t / ) d t / , the f r a c t i o n of ions i n the c e l l which at any time t have moved f r e e l y under the influence of the e l e c t r i c and magnetic f i e l d s for a time between t and t + dt' , where t' = t - t . . 15. Thus _„ r oo 3 a') swcsw-fc') dt' where n i s the number of ions i n the c e l l at a given time, Assuming no c o l l i s i o n s , then q(t') , JL W o £ < t J K ' Hence A C ^ . ) _ 4 Z s ^ v , I 2 ) ( 1 2 ) Experimentally, spectra are seen at low pressures which do exhibit lineshapes similar to that described by equation (12). One such spectrum i s shown i n Figure C for at a pressure of ~4 x 10 t o r r , l*Jc = ZK x 3.576 x 10 radians, V T = + 0.98 vol t s and V. = V* - V„ =1.3 v o l t s . The c h a r a c t e r i s t i c absorption l i n e shape was obtained using lock-in detection with the trapping voltage being modulated. The s o l i d curve i s the t h e o r e t i c a l curve based on equation (12) f i t t e d to the peak amplitude and the l i n e -width at half the peak amplitude. The c i r c l e s are points taken (9) (10) where i f 1 i s the length of the analyzer region, then t - A ( I D 17. from the absorption signal recording. The width at half height can be found both for the case when the absorption signal i s measured d i r e c t l y and for the case when the derivative of the absorption signal i s measured, as when the magnetic f i e l d i s modulated. From equation (12), setting x = Sw'fc gives AC*) = 71 of C t- s t w z ( T ) z m x i e . AC*) _ A Co) I - <U>S * (13) where A(o") _ "ftfi £•» T" i s the power absorption at resonance. The half width X y2 = ( A C J ) ^ ^ (14) defined by A U Q = J_ was found to be A C ° ^ (AU>),/ 2t * 5 - 5 6 6 (15) for the absorption l i n e shape of equation (12). For the derivative of the absorption s i g n a l , i t i s easy to measure the "peak to peak" linewidth AtOpp which i s found by solving d AC*) _ o numerically, to be <J*Z A O J p p t ^ 5.ZIZ (16) Thus, for a magnetic f i e l d sweep of the signal given by equation (12) the linewidth i n gauss for the absorption signal (AH).L and for the derivative of the absorption signal (AH^pp i s given by AH y - 5-566 Tnc aou^<& ( 1 7 ) and AH p p s 5.212 7HC (18) where t i s given by equations (11) and (3). 18. THE ICR POTENTIALS AND ELECTRIC FIELDS: 04) In two recent publications, the e l e c t r o s t a t i c potentials i n the ICR c e l l have been investigated by making a quadrupole expansion of the f i e l d due to the trapping plates, and then superimposing t h i s potential upon that due to an i n f i n i t e plate capacitor, representing the top and bottom d r i f t plates. It i s c e r t a i n l y clear that t h i s i s only an approximation to the actual potentials i n the c e l l , the approximation being most v a l i d i n a region near the geometric centre of the c e l l . It i s in t e r e s t i n g that these authors i n fact were able to predict to a f a i r p r e c i s i o n c e r t a i n s h i f t s of the ion cyclotron frequency with changing bias of the trapping plates. However, as a r e s u l t of attempts to make similar predictions of our experimental res u l t s here at U.B.C. (and even more important, to have these r e s u l t s reproducible from day to day) i t became more and more evident that the approximations used by the above mentioned authors were not s u f f i c i e n t to describe or predict a l l the variations i n r e s u l t s which were consistently found. Hence, i n an attempt to comprehend better the ion dynamics i n the ICR c e l l , an exact solution of Laplace's equation was sought for the generalized biasing of V-j- on the trapping plates, V + on the top d r i f t plate, and V~ on the bottom d r i f t plate. As outlined i n Appendix A, the solution of the potential i s given by (for the o r i g i n taken as the c e l l ' s geometrical centre) (.19) no w The e l e c t r i c f i e l d s may be found d i r e c t l y from equation Thus E x - Z ^ K. n 2:^ (20) (19) by taking the p a r t i a l derivatives oto K.--o where 2^  K,n a r e given by equations B3 and B4 , i n Appendix B. For motion i n the x d i r e c t i o n , the Lorentz equation F= £j gives at 4 m + 1 1 ? 4%- - 4 m c 4. ^ _ (M-y = - to. (21) where U)g i s defined as an e f f e c t i v e frequency. (It i s c r i t i c a l to note at t h i s point the gross over-s i m p l i f i c a t i o n found i n the l i t e r a t u r e by writing only E x= E^x) rather than E^= E^XjZ). Thus the r e s u l t s being derived here r e f l e c t the misleading assumptions of the available theories for motion of ions i n ICR c e l l s . This w i l l be r e c t i f i e d i n the further developments i n t h i s chapter.) Thus 4- U3f and hence CO, CO, 4 2m COc (22) for // | which i s a condition always well s a t i s f i e d i n these experiments. Thus ALOc = COe - kOc i e . ACOc _ - 4 36* _ - C (23) Experimentally the absorption signals w i l l be observed keeping the frequency of the spectrometer fixed and varying the magnetic f i e l d . Thus, 2CO t 1% In deriving t h i s equation, there i s an assumption made i n writing equation (21) that jt Bx $ t (24) (25) This assumption i s i n fact s a t i s f i e d i f the ions t r a n s i t the analyzer region at an e s s e n t i a l l y constant value of the x co-ordinate. It i s of in t e r e s t to note that t h i s condition i s s t i l l s a t i s f i e d i f any v a r i a t i o n i n the displacement of the ions i n the x-direction has taken place before the ions enter the analyzer region. In the event that the ions undergo a net further displacement 21. i n the x-direction during t r a n s i t through the analyzer region, equation (21) w i l l not necessarily be a good approximation and a solution of the equation of motion can be carried out by the use of the Weierstrass e l l i p t i c integrals which keep only a (15} cert a i n number of terms i n the expansion of the p o t e n t i a l . Thus, i f these approximations are v a l i d for the experimental operating conditions (ie. by working with low energy ions.) then as shown i n equation (23) the e f f e c t of the e l e c t r i c f i e l d s i n the ICR c e l l i s to cause a s h i f t i n the ionn cyclotron frequency (H c held f i x e d ) , or i n the ion cyclotron resonant magnetic f i e l d (tOc held fixed) as indicated i n equation (24). In the majority of experiments i n i t i a l l y investigated by researchers using ICR, the actual magnitude of the r f of the observing o s c i l l a t o r i s kept quite low (£40 m i l l i v o l t s pp.) r e s u l t i n g i n small o r b i t s . It appears that at low r f values, there i s very l i t t l e coupling between the x and z motions and one may e s s e n t i a l l y regard the average ion motion as a "dc" experiment i n thinking of the ion t r a j e c t o r i e s inasmuch as the motion of the center of the ion o r b i t may be taken as representative motion of the ion. THE ICR CELL POTENTIALS: Equation (19) may be rewritten as OO + 4 I (- 1) CX>5><Xn V<J S u n k * * * TV M e 8 (2m + l) 2. (26) where \JA = V* - \T and V = V* + V~ (27) I t has become apparent that the v a r i a t i o n of some of the ion motions with z may occur with s u f f i c i e n t r a p i d i t y to j u s t i f y averaging them over z i n order to study th e i r dependence on x. One example of t h i s i s the d r i f t v e l o c i t y (<X- ) which may possibly be averaged i n a meaningful way i f the r e l a t i v e change i n the average d r i f t v e l o c i t y due to displacement i n the x-direction i s n e g l i g i b l e during one trap o s c i l l a t i o n . The f i e l d s h i f t may be averaged i f the v a r i a t i o n i n ion cyclotron frequency during one trap o s c i l l a t i o n i s small compared with the trap o s c i l l a t i o n frequency which gives r i s e to the frequency modulation. For F(j> = 2aCos[(tK+rt£]fK00 , from equation (26) i t i s clear that the average of any (time-dependent) observable F can be related to a sum of the form < F \ = I (28) for ^ = ^ 0Co5© , 6'Lot , and ^ ^ i s an average over >^ . Using the harmonic approximation, assume that the d i s t r i b u t i o n function for ions produced at ^ = ^ 0 i s that associated with simple harmonic motion i n the trap. 23. The d i s t r i b u t i o n function for the variable J- Co$ & , given that b(e) = constant, i e . = 2^.^ , O <. 9 4 JL i s given by b(co5 S ( c o s e") = j?C$) ^  ^  = f^C©) J^£.| Hence [>C^) = iL ^  ! - J ^ -for O ^ j ^ l . ^ (29) Thus <CO$O*<+0P\ = COS [ ( ^ ' ) P 3 cip (30) Gradshteyn and Ryzhik, page 419 #3.753.2 give the int e g r a l and thus (31) Assume that a l l values of P0 between -]L and JL are J 2. 2-equally probable, i e . p(^) s= JL ° ^  \° ^  \ ' Gradshteyn and Ryzhik. page 666, #6.511.6 give where IHI ^  i s a Struve function. Thus i t may be shown from tables for the Bessel and Struve functions that (tos[(2K+0j]N = _L ' (l+Alc) (32) where ^ ^ O. 2. Thus equation (2 6) when averaged over z subject to the above conditions y i e l d s 00 w V " U r n ••-1) and hence <^E*) = ~ — 7>x , i e . 2-V<1 C o s k c ^ * * Z ( .VT -V* . ) £i*iko(*w.X. 7. and also 24. (33) (34) From equation (24) which becomes AHc = — — for motion averaged over z. From equation (33) and equation (3 5) <y> ^ v T f Y d j U * ) + ( v v u f * c * ) (35) (36) (37) Equation (3 6) i s not t o t a l l y correct and must have an additional term added to describe the p o t e n t i a l i n the ICR c e l l when an electron beam i s used to form the ions by electron bombardment (lb) of the background gas. As Beauchamp noticed , an electron beam of quite small current actually produces an a t t r a c t i v e pot e n t i a l for the p o s i t i v e ions of several hundreds of m i l l i v o l t s . Hence as the ions are d r i f t e d out of the source region and into the analyzer region, the ions w i l l experience a s i g n i f i c a n t increase i n pot e n t i a l energy of i n t e r a c t i o n with the electron beam. This increase i n potential energy due to the electron beam must be compensated for by a decrease i n the k i n e t i c energy of the ions 25. and/or a decrease i n the potential energy of the ions i n the ICR potential f i e l d s . Thus equation (3 6) becomes and &WC «* V j + O r - V « J ) 92 00 The d i f f e r e n t i a l form of equation (37) i s (38) (37) (39) dv . It i s a reasonable assumption i n deriving t h i s that h ( ,T , * ) i - s n e g l i g i b l e i n the region i n which the ICR i s observed. There are three e a s i l y investigated variations to observe experimentally; ie, and J U M P V < J , V T , 1 which may be i d e n t i f i e d with the p a r t i a l derivatives of AHc . Thus from equation (3 9) T>VT J (40) a, GO + | ( v T - v « . ) d ^ c o + Vd i o i O O V ^ i . \ (41) Where the second terms i n the above expressions are corrections due to the displacement of the ions i n the c e l l caused by s p a t i a l (42) 1. 26. variations of V T , Vj or V^. Assuming the ions are produced at x=o and thus h(I,o) = h 0(I) = h D and also that h(I,x) = o i n the ICR detection region, and since the potential of the ions must be conserved i n going from the source region to the analyzer region, hence from equation (38) V T + Va f.CO + WT-VCL.) ^ .(O) + \\0 = V T a- Va f.G0 + C M T - ( 4 3 ) which i n d i f f e r e n t i a l form becomes Thus a* ax dx + (<i v <w*) f*c*} (44) va a f c*) + (v/ T-\/^ afzU) 1 dx d* J Vd ^ + 1 dfGO + (y T -v«. ) i f c w L dx. ; dx J dx (45) [ k M - t o ] (4 6) Vd df.C*> ax a^cx) ax [ f , M - f i M ] (47) 7>Vo. ax ' a* (48) where from equations (33), (35), (36) and (37) f. 27, * V (49) It should be noted that i n equations (46), (47) and (48) that the f i r s t term i s that term found by erroneously taking only the simple derivative expression from equation (35) inserted into equation (24). As w i l l be shown, t h i s i s quite misleading. Of course, the main point basic to thi s whole development i s that the centers of the cyclotron o r b i t s of the ions do not actually t r a v e l down the x=o plane of the ICR c e l l except i n special cases when h ( I , o ) s o . Since t h i s condition i s often not approximated i n practice, the development being pursued i n t h i s chapter i s quite necessary to understand the behaviour of ICR absorption signals. Consider now an experiment done with argon at an o s c i l l a t o r frequency of W c £ 2.175 x 10 radians per second i n a so c a l l e d " f l a t " geometry c e l l of dimensions h = 1.4 cm, and w = 2.5 cm. If the ions stay i n the x = o plane while d r i f t i n g through the analyzer region, equation (46) predicts which for exact i^m's gives 29 gauss/volt. 3 V T 28. FIGURE D 29. However, i t i s clear from equation (26) that for any mechanism which provides the ions with an e f f e c t i v e value of x ^ o when d r i f t i n g through the analyzer region, the contribution from functions dependant on x i s far from n e g l i g i b l e i n s h i f t i n g the cyclotron resonant frequency and resonant f i e l d . Figure D shows the r e s u l t s of varying the trapping voltage Vy with Vj = 1.0 v o l t and = 0 v o l t s . The top tracing was determined with a filament heating current of 2.7 amps which was about as low a current that would produce a detectable s i g n a l , and corresponded to a c o l l e c t o r current of /vlO amp. The electron beam was then increased ^10 f o l d , by increasing the heating current through the rhenium filament. The r e s u l t i n g v a r i a t i o n of &HC with changing was markedly altered r e s u l t i n g i n a slope of ~12 gauss/volt. Consideration of equation (46) w i l l indicate why t h i s v a r i a t i o n occurs. As the electron beam increases, h (I,o) increases which r e s u l t s i n the ions changing th e i r x-coordinate as they d r i f t down the c e l l . Thus the upper slope on figure D i s predicted by but for a non-negligible value of h (I,o) the f u l l expression for equation (46) must be used with x^o when the ions t r a n s i t the analyzer region. Consideration of figure E w i l l a s s i s t i n the proper in t e r p r e t a t i o n of the experimental r e s u l t s with theory. Clearly the term g ^  (x) i s not s u f f i c i e n t to describe the v a r i a t i o n of ^ f o r values of x ^ o since for either 31, po s i t i v e or negative going values of x, i t would predict a l^tAc. ^  Thus for values of p o s i t i v e l y increasing slope for x ^ o, the expression V,) must be included. The factor always posi for p o s i t i v e and negative values of x. t i v e a 6 , ( ^ - < o -for- tf.ii x . d * Vd <*f» (*) > o -fiv- AJI X dx d * < o jtsrv- X > O-jffV" X ^ O. •jirv- X < O. fry X > O-In these experiments Va. = 0 and thus since the slope of ~b£i\\c seems to be monotonically decreasing for increasing T>VT values of h (I,o), t h i s experiment tends to indicate x<o i n the analyzer. Figure F shows the same experiment repeated for Vj = 4 v o l t s and the same re s u l t s indicate x<o for the ion beam s p a t i a l d i s t r i b u t i o n i n the analyzer region. For very small values of vy, the slope w i l l be more or less independant of V T i f y V T and the electron beam i s quite small. 32. FIGURE F 33. At larger values of V-^  , the slope w i l l tend to decrease due to the increased dependence on the r a t i o ax / d* which for larger values of 1 ^ w i l l produce more marked ef f e c t s due to x being a larger value. This i s q u a l i t a t i v e l y observed i n Figure F. The next experimental r e s u l t s i n Figure G show the v a r i a t i o n described i n equation (47). For small electron beams and hence small values of x i n the analyzer, the slope i s seen to be zero. This i s as expected for g, (o). As the value of h (I,o) i s increased, the slope goes negative very quickly. I f only g t (x) was considered i n equation (47), the r e s u l t s would tend to indicate x>o i n the analyzer region. However, consideration of the factors i n the correction term following i n equation (47) again indicates that values of x ^ o give agreement between theory and experiment. A further experiment i s shown i n Figure H which i s done for a high electron current and v e r i f i e s equation (48) for x ^ o i n the analyzer region. As an experimental v e r i f i c a t i o n , electrometers were set up attached to the top and bottom plates i n the source region to c o l l e c t p o s i t i v e l y charged current. The electron beam i o n i z i n g the argon gas was then steadily increased r e s u l t i n g i n a gradually increasing p o s i t i v e ion current being c o l l e c t e d on the bottom plate, but none on the top plate. There was a "threshold" electron beam current required to produce t h i s e f f e c t of. the order of /v 10 amp?. 9087 35. FIGURE H 36. The ions are formed on r e l a t i v e l y large potentials along the z-axis i n the f i e l d of the trapping plates. As the ions are continually o s c i l l a t i n g i n t h i s f i e l d , there i s a condition of increasing and decreasing k i n e t i c and potential energies. A ca l c u l a t i o n done i n appendix D shows that for a trapping voltage of vy v o l t s , the p r o b a b i l i t y d i s t r i b u t i o n of the r e s u l t i n g k i n e t i c energies i n the trapping f i e l d predicts that about half the ions w i l l have k i n e t i c energies ^ 0.1 V electron v o l t s . Thus for reasonably low values of V T, there w i l l be l i t t l e opportunity for the ions to decrease t h e i r z - o s c i l l a t i o n energies v i a some coupling mechanism to compensate adequately for the increased potential energy due to the electron beam. Thus the only a l t e r n a t i v e l e f t for the ions i s to experience a decrease i n the poten t i a l f i e l d of the top and bottom plates. This i s i n fact achieved by the ion beam s p a t i a l l y s h i f t i n g below the x=o plane i n the c e l l to a lower d r i f t p o t e n t i a l . Hence for low energy ions, low biasing potentials and non-negligible electron beam currents, i t i s highly l i k e l y that the ions w i l l d r i f t down the analyzer region of the c e l l with t h e i r cyclotron o r b i t s centered about the non-zero negative values of their.x-coordinate. 37. LINEWIDTH CONSIDERATIONS: In the c o l l i s i o n l e s s regime, the expected linewidth for an ICR absorption signal i s given by equation (17) as AHi_ ~ 5.566 _ s.56k H ^ a acu*-4$. WcJl J On the basis of the proceeding discussion, the d r i f t v e l o c i t y when averaged over z may be expressed as where ^ E x ^ i s given for the ICR c e l l by equation (34). Thus A U y z <* <* Vd UCx} + (\!T-^) ( 5 1 ) and as before \^/^  i s given by equation (38). Thus d(AHy2) * dV dU,(x) + dV T kG0-dVxk( / )4 (Vf-V^WC*) fVd<)U*) j-L d* 00 where and cos la o< * (52) (53) (54) Thus from equation (52) d ( A % ) * KU) + av T dx d x dx dV r £* (55) where as before from equation (45) j x I - f U o ) - £ . ( * ) dM Vd + ( V r - V ^ i i l t x ) dx and f . U ^ t W are given by equation (4 9) dx. l e . d(AH'/ z) ^ k ( x ) dv/T , dig. GO , w x aVCx") Vd —3T - + ^ VV) ~aT~ 1 Vd d£Z*T a* ax ax (56) 38. Thus, i f the electron beam can be made small enough so as to not cause any s h i f t i n the s p a t i a l d i s t r i b u t i o n of the ions along the x-axis i n the analyzer region, then the linewidth predicted by A H ' / , = 5 . 5 6 6 _ C / E A (57) should be found experimentally to be constant, and independent of the trapping voltate, V-j-. For non-negligible electron beam potentials, equation (56) predicts the expected v a r i a t i o n of d C AH \/-^) _ Figure I provides the required functions used to inter p r e t equation (56). Equation (56) may be rewritten where = dh*U) dx d x d * f 4 M _ d - fUx ) (58) dX and = 0 i n these experiments. It has already been shown that for increasing electron beam currents, x<o. Thus, from Figure I, i t i s clear that for non-zero values of x, K * U ) £ o k 4 G0 > o hiM <. o (59) f * G 0 > o UM >, o -fsGO > o Thus i t i s clear from a combination of equations (58) and (59) that for non-negligible contributions from the s p a t i a l d i s t r i b u t i o n of ions that the value of + contributions FIGURE I 40. dependent on Vj . For small values of V T, i t would be expected that h,(x) w i l l predominate and £L^H.kL w i l l be negative. At higher values of V T, the contributions to d(- k^ '/z.) dv-f dependent on V T w i l l tend to be comparable with and then exceed contributions from hj(x) thus leading to p o s i t i v e values of cKkVWP a t higher values of V T. This general behaviour should be shi f t e d to higher . values of for increasing values of electron beam current and hence x. The experimental investigation of thi s predicted behaviour i s shown i n Figure J for the ICR argon absorption signal for COc ^  2.175 x 10 , 1 = 6.1 cm. , and W = 2.5 cm. For these operating parameters, equation (58) predicts a minimum linewidth of 29.53 gauss. However, for a filament heating current of 2.7 amps, the lower data points of open c i r c l e s i n Figure J i l l u s t r a t e s p r e c i s e l y that behaviour indicated by equation (56) for the case of x being non-zero and negative. The upper tracing of s o l i d c i r c l e s i n Figure J indicates the s i g n i f i c a n t s h i f t i n the r e s u l t s for increased electron beam currents. At a trapping voltage less than 2.0 v o l t s , the signal disappeared as most of the argon beam was col l e c t e d on the bottom d r i f t plates. I t i s now clear that i n the presence of an electron beam, considerable influence i s noted on many of the measured parameters i n detecting an ICR absorption s i g n a l . In p a r t i c u l a r , the ions i n the ICR beam have their s p a t i a l d i s t r i b u t i o n altered 41. FIGURE J S t—. <r> o o CO a E IX. ii O o o o o o o o o o o o CO CD _ to N o o o o (ssne6) H10/M3N/1 i n leaving the source region and mainly before entering the absorption region. This displacement of the ions i n the v e r t i c a l d i r e c t i o n also explains why several labs have reported losing the ions to the negative d r i f t plate by cumulative energy absorption from heating o s c i l l a t o r s at peak to peak r f l e v e l s lower than expected assuming x = o i s the plane along which the centers of the o r b i t s d r i f t . Extreme caution must be exercised i n using ICR c e l l s i n i n terpreting quantitative data, e s p e c i a l l y that r e l y i n g on measurement of linewidths, and d r i f t v e l o c i t i e s . As previously mentioned, although the r e s u l t s of this i n v e s t i g a t i o n indicate forebodingly the p r e c i s i o n a v a i l a b l e for exact energy measurements in ICR, the q u a l i t a t i v e benefits of the instrument i n the analysis of ion-neutral c o l l i s i o n problems i s well attested to by the l i t e r a t u r e . CHAPTER III THE APPARATUS: ICR CELL: The basic ICR c e l l i s of a rectangular or square cross-section r e s t r i c t e d i n width to approximately 2.54 cm. i n order to f i t i n the pole gap of the 15" Magnion magnet. A schematic of the ICR c e l l b u i l t i n t h i s laboratory i s shown in Figure B. Although many c e l l s and prototypes were b u i l t , t h i s was the general design. The f i r s t c e l l b u i l d was aluminum mounted on t e f l o n spars. However, the aluminum plates appeared to r a p i d l y oxidize and form in s u l a t i n g surfaces on which d i r t and stray charges c o l l e c t e d . These proved to be serious effects and d r a s t i c a l l y altered the ICR single resonance lineshapes. It was of i n t e r e s t that the f i r s t aluminum c e l l yielded optimum resonance signals only with trapping voltages over 20 v o l t s . The lineshapes were unique and puzzling. There appeared to be 3 or 4 "sidebands" which d i s t r i b u t e d equally on both sides of the main ICR single resonance l i n e . The size of the sidebands was large enough to r u l e out contributions due to low pressure lineshapes as given by equation (12) and Figure C. Figure K shows a t y p i c a l trace with the aluminum square geometry ICR c e l l of a helium ion absorption s i g n a l . There were also additional sidebands appearing further out on both sides. The fascinating point to note i s that these sidebands had i n d i v i d u a l l y d i f f e r e n t variations with changes i n any of the parameters which produce a s h i f t of the cyclotron frequency or linewidth. For example, Figure L shows the v a r i a t i o n of the cyclotron frequency for a v a r i a t i o n of the trapping voltage. I i I i I i I i I i . I i l , l , L 0 20 40 60 80 LOWFIELD SIDEBAND SHIFT (gauss) The frequencies involved are not compatible with a possible coupling mechanism between the cyclotron frequency and plasma frequencies. S i m i l a r l y , a beating between the cyclotron frequency and the trap o s c i l l a t i o n frequency i s ruled out. There have been various models of ICR c e l l s constructed following the f i r s t c e l l to investigate the operating advantages of d i f f e r e n t materials and/or geometries. For the experimental r e s u l t s of Chapters II and IV, the c e l l used was constructed of (-^ j) " non-magnetic stainl e s s s t e e l sheeting that had been prepolished commercially on one side. Supporting rods on which the basic c e l l and electron beam assembly were mounted were General E l e c t r i c Lucalox p o l y c r y s t a l l i n e alumina rods. These have p a r t i c u l a r l y s a t i s f y i n g properties of homeostasis under conditions of temperature or pressure v a r i a t i o n s . The filament consisted of a 0.0 05" diameter rhenium wire about 1.25" long and mounted i n a filament holder machined from boron n i t r i d e , which i s r e a d i l y a v a i l a b l e , machines n i c e l y and has good e l e c t r i c a l i n s u l a t i o n . The filament assembly was mounted on the lucalox ceramic poles and produced an electron beam by thermionic emission when heated by a Kepco amplifier (model KS60 - 5M, 0 - 6 0 v o l t s , 0 - 5 amps) operating i n the current regulated mode. The electrons were accelerated by a g r i d of non-magnetic st a i n l e s s s t e e l mesh (wire diameter approximately 0.003" and mesh transparency about 67%.) incorporated into the boron n i t r i d e assembly. Similar s t a i n l e s s s t e e l grids were used to cover the holes i n the two trapping plates. These provided for a planar equipotential i n the region of the trapping plate holes and prevented penetration of the biasing potentials i n the filament assembly into the ICR c e l l . When the filament was run for periods of several weeks or for shorter times but at white l i g h t emission temperatures, i t was found necessary to clean the c e l l trapping plates and grids as well as the boron n i t r i d e assembly. Acetone seemed to be an adequate solvent and did not necessitate more elaborate cleaning procedures. Wiring connections to each plate were made v i a stainless s t e e l size oo screws and nuts. The wires were introduced to the vacuum system v i a Amphenol multiple feedthroughs, type 182-11. A l l voltage biasing of the d r i f t plates was done by in d i v i d u a l batteries run i n p a r a l l e l with low noise potentiometers and appropriately biased to ground. THE VACUUM SYSTEM : The system i s e n t i r e l y constructed of glass and stainl e s s s t e e l . The actual pumping i s done with two CVC six inch blue l i n e o i l d i f f u s i o n pumps coupled to two six inch Granville -P h i l l i p s l i q u i d nitrogen cooled traps. The o i l d i f f u s i o n pumps are backed with two Welch duo seal vacuum pumps, model 1402. The o i l d i f f u s i o n pumps are water cooled. The l i q u i d nitrogen traps seem to e f f e c t i v e l y hold t h e i r l i q u i d for approximately 12 hours and contribute a factor of about 10 i n the ultimate background vacuum attainable, which i s of the order of 10 ^ torr as measured on CVC i o n i z a t i o n 48. gauges. These gauges unfortunately are dependent upon the gas i n the system, since the electron cross-section for i o n i z i n g various gases varies s i g n i f i c a n t l y from element to element. Hence the p o s i t i v e ion current i n the gauge w i l l also vary for d i f f e r e n t gases at the same pressure. The background pressure quoted was for hydrogen gas. There are a series of valves on the system to allow i n d i v i d u a l control of the pumps, and also to allow flushing of the system with any gas. On the c e l l end of the apparatus, a fine gauge stainless s t e e l variable leak control has been mounted. It i s manufactured by Granville - P h i l l i p s and allows a controlled introduction of any desired gas. Proximal to t h i s needle valve i n the gas handling system, a Matheson two-stage regulator i s incorporated on the gas bottles to allow a reduction i n pressure i n the gas l i n e from approximately 2000 p s i to atmospheric before entering the variable leak. MODULATION TECHNIQUES: In detecting a signal with the ICR apparatus i t i s necessary to u t i l i z e phase sensitive detection to pick out the small signals from the spectrometer noise. Hence i t i s also necessary to provide a modulation signal to the apparatus such that t h i s signal w i l l i n turn modulate the ion population and hence provide a reference source for the l o c k - i n amplifier. It i s a somewhat gratuitous feature of the ICR apparatus that application of a modulating signal to almost any dc bias w i l l have an e f f e c t on the ions and give a suitable reference. The basic method of modulation i s by the app l i c a t i o n of a sinusoidal voltage to helmholtz c o i l s coaxial with the magnet poles containing the ICR c e l l i n the i r gap. Thus the main magnetic f i e l d has a simusoidal f i e l d superimposed. A magnet f i e l d compensating device must be used i n conjunction with the main magnet f i e l d regulator so that i t w i l l not try to follow the varying f i e l d . F i e l d modulation provides the c h a r a c t e r i s t i c derivative of the absorption s i g n a l , and hence the corresponding change i n the peak-to-peak linewidth read from the derivative signal y i e l d s the linewidth as derived i n equation (18). The o actual size of the f i e l d modulation i s quite s i g n i f i c a n t and w i l l d i s t o r t the l i n e i f the modulating f i e l d i s larger than the natural width of the l i n e , under the operating conditions. A l l other forms of modulation w i l l y i e l d a pure absorption signal with linewidth given by equation (17). ('7) One modulation technique which could be p a r t i c u l a r l y appealing involves modulation of the accelerating voltage of the electron beam. The g r i d can be biased to accelerate the electrons through the trapping plates, but the application of even extremely small ac voltages to the gr i d seems to produce adequate modulation to the electron beam and hence the ion population. As Henis points out ^ '"^  , modulation of the d r i f t plates w i l l y i e l d a signal but i t w i l l be subject to the r e s t r i c t i o n of ions squi r t i n g from the d r i f t region under p i l e -up conditions imposed when the d r i f t voltage i s pulsed to zero. Very successful operation of the c e l l occurs for modulation of the trapping voltage. In fact when one trapping plate i s set at vo l t s and the other trap modulated 50. by ±V-y v o l t s , then a signal of p o s i t i v e ions w i l l be observed only when the modulated trapping plate i s +VT. Furthermore, by changing the steady trapping plate to -V T v o l t s and changing the phase of the lock-in amplifier by 18 0 , then the negative ion spectrum i s available. The frequency of the square wave modulated trapping voltage must be low enough to allow the ions to traverse the analyzer region i n the time available i n the "trapping half cycle". Another nice method of modulating i s v i a the bias of the filament. This technique would allow you to vary the filament bias above and below the i o n i z a t i o n p o t e n t i a l of the gas being studied. This would be es p e c i a l l y useful i n looking at appearance potentials and possible v i b r a t i o n a l l e v e l structure of ions near th e i r i o n i z a t i o n threshold. Unfortunately the power supply being used to heat the filament i n our apparatus has a rather complex capacitive f i l t e r network on the output stage, and as a r e s u l t , t h i s l a s t method was not f e a s i b l e with the available supply, without s i g n i f i c a n t a l t e r a t i o n s . Since the other techniques work quite well, there was no reason to try to"proceed to make these a l t e r a t i o n s . LIGHT SOURCE AND CHOPPER: There are many s i g n i f i c a n t experiments available to ICR involving photodissociation of both p o s i t i v e and negative ions. In these methods, a steady state ion signal would be maintained i n the ICR c e l l , and then a beam of l i g h t directed down the ICR c e l l to intera c t with the ion cloud. Any in t e r a c t i o n of the l i g h t beam with the ions which af f e c t s the population of the ions w i l l be detected by an increase or decrease i n the 51. absorption s i g n a l . Since i n fact the cross-sections for such reactions are extremely small ((T—10~ i e > cm1) i t i s advantageous to modulate the l i g h t beam by f i r s t sending i t through a PAR model 222 l i g h t chopper which can be phase locked to the driv i n g frequency from the in t e r n a l o s c i l l a t o r i n a PAR model JB-4 or HR-8 phase sensi t i v e detector. Again, the frequency of the modulation must be low enough to permit at least one generation of ions to d r i f t the length of the c e l l during one of the chopper "half cycles". The l i g h t sources were Hanovia and PEK short arc lamps mounted i n an a i r cooled housing. The l i g h t was focused into the ICR c e l l by a quartz lens i n order to allow good transmission into the u l t r a v i o l e t . The window on the end of the ICR c e l l housing was a 1.5" O.D. quartz disc THE SPECTROMETER: The spectrometers u t i l i z e d to detect the absorption of energy by the ions i n t h i s experiment are based on the (19) excellent low r f lever o s c i l l a t o r designed by Robinson. The o s c i l l a t o r spectrometer consists of a tank c i r c u i t followed by three pentode amplifier stages, a l i m i t e r and an audio frequency stage. Feedback to the tank c i r c u i t originates from the plate of the l i m i t e r stage. A change i n the voltage across the tank c i r c u i t i s e s s e n t i a l l y diode detected at the input to the l i m i t e r stage, and t h i s change i n the l e v e l thus manifests i t s e l f by a change i n the operating l e v e l of the audio frequency stages, (see Figure M). +240 v H Q a ICR SPECTROMETER The coupling capacitors are adjusted to provide spectrometer operation i n the lin e a r or plateau region of a Bode amplifier p l o t . This i s p a r t i c u l a r l y important at low operating frequencies of 4 300 khz. At high frequencies > 15 Mhz the bypass capacitors would have to be increased to remove high frequency o s c i l l a t i o n s on the output stage i n i t i a l l y due to squegging. ROBINSON OSCILLATOR SENSITIVITY IN ICR The ion absorption signal may be considered as a change i n voltage across the tank c i r c u i t which i s b a s i c a l l y diode detected. This signal may be calculated as follows: 'R The current I may be given as I = At resonance, an ion absorbs power A(u>) causing a (60) change i n E„ and hence a change i n Q0 i f the o s c i l l a t o r i s considered to be e s s e n t i a l l y a constant current source. With no ions present i n the c e l l , the power absorbed i s -o  ZR zaw L (61) where E = E D cosWt i s the applied r f e l e c t r i c f i e l d across the detection plates i n the ICR c e l l . Thus Power DL&I R> ZR + T i e . Q ^ Qc Thus to J r A Q « GL AV = c o L l (Gi - Qo) - 2R. KCco} 54. (62) (63) ie. (64) At the same time, the e f f e c t i v e voltage due to noise across the c e l l i s given by V* = ( 4 k T F B f c V / z (65) * (4kTF Ba.fe)' / 2) , / i = ( 4 l c T F B>CU fitY2- (66) Thus the minimum number of ions required to produce a signal to noise of 1:1 i s given by 71 a* (67) For the Robinson o s c i l l a t o r , for r f level s i n the order of 100 m i l l i v o l t s or les s , then F ^ l . n ' Equation (13) predicts that under resonance conditions 8>m 4 6o cj r (68) subject to the condition that (69) where r = (o.5) (height of the c e l l ) to saying Equation (69) i s equivalent Recalling the experiments on argon mentioned i n -lb Chapter I I , t y p i c a l values for A (u>) would be ^6 x 10 watts for an r f l e v e l of ~25 m i l l i v o l t s pp. across the tank c i r c u i t . Thus from equation (67) and (68) YlmU.. - l.zk * \09 (_C (71) CO V L / Thus for the argon experiments, Ylml/w • — 27 ions. In these c a l c u l a t i o n s , Q c $L 100, B = bandwidth = 30 hz., T ~ 273 °K, C = 100 pf. and L = 20yull . I t i s clear that several of these parameters could be adjusted to y i e l d a lower value for TlmUi. and hence provide a more sensitive instrument. It should be noted that i n doing any experiment i n which c o l l i s i o n s with the walls are to be avoided, then i t i s necessary that E 4 ^ 2 C v * - V ) ( 7 2 ) as well as having a very small electron beam potential to avoid s p a t i a l d i s t r i b u t i o n s as outlined i n Chapter II. 56. CHAPTER IV PHOTODISSOCIATION OF POSITIVE IONS It i s of in t e r e s t to investigate the use of the ICR c e l l as a means of producing and c o n t r o l l i n g p o s i t i v e ions within the ICR c e l l geometry while attempting to photodissociate some or a l l of these ions during t h e i r c e l l t r a n s i t time. The major problem i n doing t h i s form of experiment i s to maintain a cluster of ions i n the region i r r a d i a t e d by a l i g h t beam for a reasonably long period of time. OBSERVATION OF PHOTODISSOCIATION OF H* : (*>) Photodissociation has been used as a means of s e l e c t i v e l y aligning H 2 molecular ions. The ions were s p a t i a l l y OO constrained by electrodynamic trapping techniques. Some experiments indicated that intense commercial l i g h t sources were available which under the operating conditions would give detectable photodissociation effects i n t r a n s i t times as short as 100 milliseconds. (23) Dunn commenced an experiment to measure the 4- + photodissociation cross-section for the process + hv" ^ H + H and after approximately 10 years was able to get f a i r l y good (2.40 agreement ' with his theory for predicting the wavelength dependence of the photodissociation cross-section (T'C'X). One of the major problems i n looking for exact experimental agreement i s to prepare the H 2 ion population i n the correct v i b r a t i o n a l l e v e l d i s t r i b u t i o n by electron bombardment. One of the main problems Dunn has i n matching experiment to theory i s not knowing the i n i t i a l state populations of the H 2_ 10ns . 57. (25) There has been d i r e c t evidence that the f i r s t 4- 2-r- + three v i b r a t i o n a l l e v e l s of H Z ( 2.^  ) are populated i n accordance with the Frank - Condon r u l e s . However, there have also been several experiments performed which did not seem to be i n agreement with these r e s u l t s , hence lending considerable doubt to the method of using the Frank-Condon p r i n c i p l e to +• . . . populate the v i b r a t i o n a l l e v e l s prior to photodissociation. In the ICR c e l l , an attempt was made to measure the v i b r a t i o n a l l e v e l s of H j ions prepared i n the c e l l by electron bombardment. There i s a major problem i n ICR i n obtaining monoenergetic electrons,from the filament assembly, primarily due to the very limited space of ^ o.25" i n which to construct the filament housing. Hence i t was not f e a s i b l e to introduce any electron optics into the system other than simple grids and collimating holes. However an attempt was made to look at the f i r s t few v i b r a t i o n a l levels by sweeping the electron filament biasing voltage from just below the i o n i z a t i o n p o t e n t i a l for H z to just above i t . The output from the Robinson spectrometer was accumulated i n a Fabri Tek model 1062 instrument computor (time averager). -S At a pressure ~2 x 10 t o r r , the structure of the + H 2 ion production versus electron beam energy showed quite a smooth onset with no apparent d e t a i l r e l a t i n g to the v i b r a t i o n a l l e v e l s as shown i n figure N. -6 However at ~10 t o r r , as c o l l i s i o n s i n the c e l l no longer occur, some d e t a i l did i n f a c t repeatedly show up as shown in Figure O, where 100 channels correspond to ""0.21 ev. I t i s tempting to assign v i b r a t i o n a l structure to the l e v e l s detected but t h i s should be done with the following cautions; FIGURE N 58. -\600 »2 -5 p = 2xlO torr \500 1400 g 500 {2 I o o Iroo ^ 400 500 CHANNEL 600 700 800 FIGURE 0 59. —I I I 1 I L_ 300 4 00 500 600 700 800 CHANNEL 60. (a) even though only a small portion of the electron filament i s actually the source for the electron beam, there i s s t i l l a s i g n i f i c a n t potential drop due to the heating current and t h i s corresponds to a spread i n the energy d i s t r i b u t i o n of the electron beam. (b) over a change i n the filament biasing of 1 ev. there i s c e r t a i n l y an e f f e c t on the number of electrons being focused into the ICR c e l l . Although i t would not seem reasonable to expect such a behaviour.to occur i n steps, i t i s d i f f i c u l t to assign exact v i b r a t i o n a l populations to the supposed v i b r a t i o n a l l e v e l s even though the energy spacing of 0.265 ev., 0.248 ev. and + 0.235 ev. for the f i r s t three v i b r a t i o n a l levels of H x as measured from Figure O are i n reasonably good agreement with the th e o r e t i c a l values of 0.269 ev., 0.254 ev. and 0.239 ev. The r e s u l t s c e r t a i n l y indicate that experimental parameters such as density can e a s i l y wipe out any structure such as shown i n Figure N. This may be s i g n i f i c a n t for several researchers. PHOTODISSOCIATION IN ICR: Several i n t e r e s t i n g facts seem to have emerged from the work of R. Dunbar who has investigated the photodissociation of p o s i t i v e ions i n the ICR c e l l . I t i s ess e n t i a l i n doing photodissociation to maintain the ions i n the c e l l for as long as possible. For as yet unexplained reasons, Dunbar finds as I have that one can successfully trap ions i n a square c e l l geometry but not a f l a t c e l l (h~1.4 cm.,W~2.5 cm.) arrangement. Trapped ions C*2>) have been detected a f t e r 60 seconds i n the square c e l l . 61. Regardless of the empirical d i f f i c u l t y i n using the f l a t c e l l , I have attempted to look at several photodissociation + + processes with i t . The reaction H z + hv + H was successfully observed with the f l a t c e l l after much work. THEORETICAL PREDICTIONS: The available lamp was a Hanovia 500 watt Xenon arc lamp whose spectral d i s t r i b u t i o n i s such that i t s emission curve may be approximated by Planck's d i s t r i b u t i o n , where U.(tO,T)du) i s the mean energy per unit volume of photons i n the frequency range from W to (J + du) , i e . HCOJ.T) d60 _ _h ^ ! era5 The i n t e n s i t y of the d i s t r i b u t i o n i s given by (73) 4-1a Jco (74) At a distance r from the lamp, the in t e n s i t y d i s t r i b u t i o n becomes j? 4 l t r l (75) where I-j^to^ = I and P i s the lamp power i n ergs/second. Thus, o 62. or I(W,T,0 <±U> _ P / 1$ ^ du> (76) I ( V l » < f t _ P /ft \ 4 i * ^ 2 i r c ^ ^ (77) The lamp temperature T may be calculated by solving for A max T = h-£ , the universal constant for black body radiatio n and where Amax i s the wavelength of the peak lamp i n t e n s i t y . Thus, the number of incident photons per cm?" per second between A and A + dX w i l l be ) 1 W ^ X ( 7 8 ) / he The number of photons absorbed by ions with cross section <rO0 i s then (TJX) \1(A) C\\ , X ^ I C X ^ A where I i He ^ Kc (23) (79) i s a defined average cross section. In the ICR system i t has been shown i n equation (9) that the power absorbed by a system of ions may be written as 00 AGO) = Y l | <j(t') £d6 j <#' (80) where g(t') dt' i s the f r a c t i o n of ions i n the c e l l which at any time t have moved f r e e l y for a time between t' and t ' + dt' where t' = t - ta and dfe = of E z ^ $LQtl'--k*) ( 8 1 ) In the c o l l i s i o n l e s s regime g(t') = J_ where t = _k (82) The e f f e c t of photodissociation w i l l be to a l t e r t h i s g(t') since with a given p r o b a b i l i t y W for photoabsorpiton (and dissociation) g(t') then becomes g(t') ~ _L e (83) Thus the number of ions i n the c e l l when the Xenon l i g h t i s on i s X xo . i e W t d t ' . (• - e " w t ) ( 8 4 ) i e . A T V « T L - X O - e ~ w < k ) - W^-K ^ Wt«.i. ( 8 5 ) where the t r a n s i t i o n p r o b a b i l i t y i s given by W, and may hence be related to the experimental absorption signal given by equation (13) Thus (86) x 2 % *»C Thus the average cross section for photodissociation may be written as (87) 7. _ *. 7^1, 4-rrr* VkT/ "H"4 (88) i e . Z =• &.\(o * 10 AU 64. -9 ^ I t f ^ (89) X. where f ' i s the f r a c t i o n of l i g h t transmitted through the quartz lenses and window into the ICR c e l l , Xi and ^ j , are the bandpass l i m i t s for the quartz optics. EXPERIMENTAL PROCEDURE: The i n i t i a l experimental attempt was to detect the photodissociation + +• H z + hV 3» H + H since the experimental cross section could then be compared with the work of Dunn. The lamp used was a 500 watt Xenon arc lamp focused through a quartz lens and window into the c e l l . The t o t a l quartz thickness was 25 mm. A small frequency doubling mechanism was constructed and incorporated to allow rapid monitoring by the spectrometer + + of both the H 2 and the H absorption s i g n a l . The system was operated i n the c o l l i s i o n l e s s pressure regime. No evidence could be seem in d i c a t i n g the " f l a t c e l l " geometry could operate i n the trapped ion mode with zero d r i f t v e l o c i t y . The d r i f t times through the analyzer region were of the order of 5 msec. Magnetic f i e l d modulation was used to tune up on the and H + normal ICR absorption signals. The magnetic f i e l d modulation was then turned o f f and the Xenon arc lamp focused into the c e l l . The l i g h t beam was chopped at ^ 5 1 hertz. + + The signal due to photodissociation of H ^ to H + H was seen by sweepmg throught the H signal resonant f i e l d and detecting the absorption by a phase sensitive l o c k - i n amplifier referenced to the chopping frequency of the l i g h t beam. The signal disappeared when the l i g h t was blocked from entering the c e l l . S i m i l a r l y the signal disappeared by reverse biasing the elctron beam hence proving that the signal was not due to photoionization of H x > H + = H. (V^ A/ - 45 v o l t s l Figure P shows a trace of the absorption signal of due to photodissociation of H^ when the magnetic f i e l d was swept through the H + resonant f i e l d . The signal seemed to maximize at a pressure of -b ~2 x 10 t o r r . At lower pressures the signal was reduced, i t s linewidth remaining constant. At higher pressures the signal was also reduced i n peak amplitude but with an increased linewidth. A series of trap ejection experiments i n the source region proved conclusively that the H + signal was due to the photodissociation phenomena only. Over a period of two months, i t was not possible to increase the signal to noise past 8:1 using the PAR HR-8 phase sen s i t i v e detector working at a time constant of up to 3 0 seconds. Thus using the f l a t c e l l i t was not possible to try to make a comparison with theory ^ of the wavelength dependence of the photodissociation cross section However, the ICR method did y i e l d r e a d i l y the average cross section as defined by equations (7 9 and (88). FIGURE P 66. 67. From equation (13) AC^°) Eo t a n d hence i n comparing the r e l a t i v e absorption signals of H + and Hj_ under i d e n t i c a l c e l l operation at the same magnetic f i e l d but by a l t e r i n g the frequency of the detecting o s c i l l a t o r , then A ( w U + TTIiU+ This expression r e l i e s on the assumption that the spectrometer s e n s i t i v i t y w i l l not change s i g n i f i c a n t l y between the two frequencies involved. Under the c e l l biasing used for the photodissociation experiments, the experimentally observed single resonance absorption signals at the same magnetic f i e l d were ACU^HZ* - ZO i e . yitiJ 4o A M H + 1 7 U + 1 In these experiments the electrons were being accelerated to ~55 electron v o l t energies. The experiment of Rapp et a l indicates that for 55 ev. electrons, there should be 3.8 % of H + r e l a t i v e to Hj . The ICR population of ^2.5% indicates that approximately 35% of the H + ions produced are l o s t before entering the analyzer region. This i s due mainly to the high energy at which H i s produced. It was found experimentally that no photodissociation + +-s i g n a l for the process H 2 + hV H + H could be detected by monitoring , but a signal was seen by monitoring H , y i e l d i n g a signal to noise r a t i o of 8:1. If the noise contribution were purely from the s t a t i s t i c a l v a r i a t i o n of the ion population, then 68. I 71 TtSl + + assuming also that a l l the photodissociate to H ions detected i n the analyzer region of the c e l l . Caution must be exercised i n accepting t h i s l a s t expression since other factors may well contribute s i g n i f i c a n t l y to the noise of the observed s i g n a l . The spectrometer, for example, w i l l have a d i f f e r e n t Q at the two frequencies and t h i s w i l l a l t e r the noise pattern. However, on a purely s t a t i s t i c a l basis as well as experimentally, i t would appear to be easier to monitor the 4* + H population than the H 2 population to detect the photodissociation s i g n a l . In the expression for X given i n equation (88), AYl "4" 4 PT- i s for H -> ions. However AH. i s the same for H 7 or H and thus . / A / \ i \ * hi 4o \ M*>) J tfr where A (u>) represents the experimentally observed absorption signal with the l i g h t beam on and modulated for reference, and A(<0) i s the absorption signal for the t o t a l number of H + ions present when the l i g h t i s o f f . Experimentally, i t was observed that ( ATI ^  , AJ 7 x 10 ^ The distance from the lamp to the \ 71 /Hi quartz lens which focused the l i g h t into a p a r a l l e l beam entering the ICR c e l l was ^ 6 cm. The d r i f t time for the ions i n the c e l l was taken as 5 x 10'^ seconds based on linewidth measurements and p o t e n t i a l biasing'of the c e l l d r i f t plates. Thus equation (88) y i e l d s Z H + ^ i-t>& * \o~[C) cm1. (90) X C^O ° \ s -t ° where +^0.4 for 25 mm. of quartz optics and Zooo A. < A x 10,000 A. In evaluating equation (88) the i n t e g r a l was numerically solved, and i t s solution shown i n Figure Q. The o e f f e c t i v e wavelength transmission cut-offs of quartz are ^2100 A and Jo,000 A , and i t i s clear from Figure Q that they have l i t t l e e f f e c t i n respect to the i n t e g r a l . Thus the value of the i n t e g r a l II -3 was taken as. 3.02 x 10 cm . As a q u a l i t a t i v e t e s t of the experiment, and for the , 11 i n t e g r a l of Figure Q, a -L- piece of pyrex glass was introduced i n the l i g h t beam while a photodissociation signal + of H was being detected. The pyrex glass has a low wavelength cut-off i n the region of 3500 A, and hence a drop i n signal of the order of 10% was anticipated on the basis of the pyrex thickness and bandpass. Figure R i l l u s t r a t e s the r e s u l t . The value of Z. 2s: 1.68 x 10 cm. i s i n quite good agreement with Dunn and s i g n i f i e s that the ICR i s suited to rough measurements of 2, as defined by equations (79) and (88). FIGURE Q 70. NO H O a PYREX FILTER + ATTEMPT TO OBSERVE PHOTODISSOCIATION OF CH^ : There has been considerable discussion regarding the (>2.) astrophysical o r i g i n of the d i f f u s e i n t e r s t e l l a r l i n e s . One of the conjectures i s that C H 4 may be involved i n these phenomena. Thus i t was hoped that the ICR c e l l might be able to detect at l e a s t a p o s i t i v e i d e n t i f i c a t i o n of a photodissociation of CH^ Hence the apparatus was used for an i d e n t i c a l + + experiment on CH4 as performed on H z , both performed at -fa p i ! 2 x 10 t o r r . Unfortunately the r e s u l t s were negative and the most that could be done was to assign a l i m i t i n g value to ]E. on the basis of equations (79) and (88) and t h i s yielded 2 cul ^ S * ,0"2° c m Z - <91> In.the experiment on CH4 , the lamp was also replaced by a Xenon 1000 watt arc lampw The r e s u l t s for CH4 may also be expressed i n terms of an e l e c t r i c dipole matrix element cm which appears i n (33) the expression for an e l e c t r i c dipole t r a n s i t i o n p r o b a b i l i t y v Wif _ IC<Ocf .T,0 l < i k l f M * See."' (92) where ^ i\ -Combining equations (92) and (8 6) y i e l d s * ^ 4 1 T Y K ^ . i - . r ^ tf (93) where i s now given by equation (77). Simplifying equation (93) gives 'Vet I ^ H f M * = 4.S4 * io" 8 An f; 7 \ s ( e -\) cm7- ( 9 4 ) 71 t For X = 4430 A, and the other parameters as discussed previously for the attempted CH^ photodissociation, hence K M H f ^ 2 - < l.fc* < IO"'9 CM." ( 9 5 ) o The wavelength of 443 0 A was chosen from the discussion by Herbig and Herzberg regarding the o r i g i n of the d i f f u s e i n t e r s t e l l a r l i n e s . Of course, equation (94) assumes the CH 4. 10ns i n t h i s experiment to a l l be i n th e i r ground state which i s c e r t a i n l y not correct, but may serve to give a f e e l i n g for the e l c t r i c dipole moments involved. As previously mentioned, to the experiment was then repeated for P~10 ergs/sec. with s t i l l a negative r e s u l t . 74. BIBLIOGRAPHY (1) H. Sommer, H.A. Thomas, J.A. Hippie, Phys. Rev. 78, 806 (1950) (2) K.D. Bayes, D. Kivelson, S.C. Wong, Jour. Chem. Phys. 37, 1217 (1962) (3) D. Wobschall, J.R. Graham, D.P. Malone, Phys. Rev. 131, 1565 (1963) D. Wobschall, Rev. S c i . Instr., 36, 466 (1965) D. Wobschall, R. Fluegge, J.R. Graham, Jour. Chem. Phys., 47. 4091 (1967) R. Fluegge, Technical Report, CAL Report UA-1854-P-1 Cornell Aeronautical Laboratory, 1967 (4) J.D. Baldeschweiler, Science, 159, 263 (1968) (5) J.L. Beauchamp, L.R. Anders, J.D. Baldeschweiler, Jour. Amer. Chem. S o c , 89, 4569 (1967) (6) R.P. Clow, J.H. F u t r e l l , Intern. Jour, of Mass Spectr.& Ion Phys., 4, 165 (1970) L.R. Anders, Jour. Phys. Chem., 73, 469 (1969) R.C. Dunbar, Jour. Chem. Phys., 52, 2780 (1970) R.C. Dunbar, Jour. Chem. Phys., 47, 54 45 (1967) (7) S.E. B u t t r i l l , J r . , Jour. Chem. Phys., 50, 4125 (1969) (8) J.L. Beauchamp, J.T. Armstrong, Rev. S c i . Instr, 40, 123 (1969) (9) J.L. Beauchamp, Phd. Thesis, Harvard University (196 7) S.E. B u t t r i l l , J r . , Jour. Chem. Phys., 50,4125 (1969) J.L. Beauchamp, J.T. Armstrong, Rev. S c i . Instr., 40, 123 (1969) T.B. McMahon, J.L. Beauchamp, Rev. S c i . Instr. 42, 1632 (1971) 75. (10) S.E. B u t r i l l , J r . , Jour. Chem. Phys., 50, 4125 (1969) J.L. Beauchamp, Jour. Chem. Phys., 46, 1231 (1967) (11) L.R. Anders, J.L. Beauchamp, R.C. Dunbar, J.D. Baldeschweiler, Jour. Chem. Phys., 45, 1062 (1966) (12) M. Bloom (in collaboration with I.B. Woods) Proceedings of 2nd annual Conf. on Atomic Physics, Oxford Univ. (1970) (13) G.H. Dunn, L.J. K i e f f e r , Phys. Rev., 132, 2109 (1963) (14) J.L. Beauchamp, J.T. Armstrong, Rev. S c i . Instr., 40, 123 (1969) T.B. McMahon, J.L. Beauchamp, Rev. S c i . Instr., 42, 1632 (1971) (15) T. Knott, M. Riggin (to be published) (16) J.L. Beauchamp, Phd. Thesis (Harvard University 1967) (17) J.M.S. Henis, W. Frasure, Rev. S c i . Instr., 39, 1772 (1968) (18) T.B. McMahon, J.L. Beauchamp, Rev. S c i . Instr, 42, 1632 (1971) (19) F.N.H. Robinson, Jour. S c i . Instr., 36,481 (1959) (20) H.G. Dehmelt, K.B. J e f f e r t s , Phys. Rev., 125,1318 (1962) C.B. Richardson, K.B. J e f f e r t s , H.G. Dehmelt, Phys. Rev., 165, 80 (1968) (21) R.F. Wuerker, H. Shelton, R.V. Langmuir, Jour. Appl. Phys. 30, 342 (1958) (22) W. L i n l o r , C.F. Barnett, R. Reinhardt, University of C a l i f . Radiation Laboratory "Report, #UCRL 4917 (1957) (23) G.H. Dunn, Atomic C o l l i s i o n Processes, edited by M.R.C. McDowell, p. 997 (1963) (24) F. von Busch, G.H. Dunn, Phys. Rev. A, 5, 1726 (1972) 76. (25) P. Marmet, L. Kerwin, Can..Jour. Phys., 38, 972 (1960) Frost, McDowell, Vroom, Phys. Rev. Letters, 15, 612 (1965) (26) J.W. McGowan, M.A. Fineman, E.M. Clarke, H.P. Hanson, Phys. Rev., 167, 52.(1968) D.D. B r i g l i a , D. Rapp, Phys. Rev. Letters, 14, 245 (1964) (27) M.E. Wacks, Jour, of Res., N.B.S., 68A, 631 (1964) (2 8) R.C. Dunbar - private communication (2 9) D. Rapp, P. Englander - Golden, D.D. B r i g l i a , Jour. Chem. Phys. , 42, 4081 (1965) (30) G.H. Dunn, L.J. K i e f f e r , Phys. Rev., 132, 2109 (1963) (31) CRC Handbook of Chem. & Phys., 52nd Edi t i o n , P. E-224. (32) I.A.U. Symposium, 31, P. 87 & 91, 1967. (33) L.I. S c h i f f , Quantum Mechanics, 3rd Edit. P. 405. 77. APPENDIX A ICR CELL POTENTIALS: The dc plate potentials i n the c e l l may be depicted as follows: K V which i s equivalent to w v+-vT V, Thus V ( X , B ) = V T + V ' (x,z) Assuming the plates to be i n f i n i t e i n the y d i r e c t i o n and the solution i s found from Laplace's equation V 2 V - o l e . and d * Z ( * > + = o. Equation A-5 i s solved by setting The boundary conditions for the problem give = o -for £ = o ^ 2:= W V(<,2^= V " - V T ftv x» o V (x. >e) = V 4 " - V T 4W x = k A - l A-2 A-3 A-4 A-5 A-6 Thus V(x,o) = o gives B = o and V(*>^) = O gives kw = 1\TC , H =• l,2,S, • • Thus £ = A. sin 2 0 1 5t n = I, z., 3, - - • W (The TV=0 term i s omitted since i t refers to zero f i e l d ) Then equation (A-4) becomes and then For For and c e + 3) e X = O 78. A-7 A-8 A-9 A-10 A - l l A-12 Combining A-10, A - l l and A-12 gives i e C' - - 3>' C + 3> _ V i - v e - 7VTflyx I - \J e Thus A-13 A-14 i - v e C - G + ve - ve A-15 i e i - v e -ntrh/, 00 w - S'twK TIT* J SMa rme A _ 1 6 w The general solution consists of an i n f i n i t e sum of such solutions 00 Sw "HIV-2 w A-17 79. To evaluate the c o e f f i c i e n t s Qn, use the boundary condition Q» V ( - w in \ I Vv 1 J nTrVl/vo - v e 7VIT2: A-18 W Using Fourier's analysis, multiply both sides by s i n 771 IT 2 where m i s an integer and then integrate from Z=o W to z=w. oo | ( \ T - V T > ) S^Wf? d* = | - I The solution of A-19 i s W W cte A-19 \ - v e Gin _ 4-(V " - V T ) W 71 odd. A-21 7MI ' = o for n even. Thus combining A-2 0, A-17 and A - l gives for the generalized p o t e n t i a l i n the ICR c e l l as TVtffc V(v,i) = V T - £(V-V T) J, ~w TT n , -mrU odd Vv A-21 80. APPENDIX B ICR CELL ELECTRIC FIELDS: Taking equation A-21 and transforming the co-ordinate system o r i g i n to the geometric centre of the c e l l y i e l d s 0 0 ire V(*,2} - V T - 4. (V + -V T ) 7. (-0* oos U ™ + 0 ~w~ IfVt and 1>x Thus, i n general where for \< even B-l B-2 & = -4- (v +-V-) 2 C-Omcos^lC^^+',) cos (z-m+O K n x ' — i I E B-3 and for kl odd V0 n* I i .\ irk 2 C o s U ( ^ + 0 H B-4 81. APPENDIX C ELECTRON BEAM POTENTIALS: Beauchamp shows i n his Phd Thesis (Harvard 1967) that the space charge depression AV of the poten t i a l i n an electron beam i s , o Av _ a. = _ i . 1 c-i where C i s the capacitance per unit length between the electron beam and the d r i f t plates. Morse and Feshback Vol. I I , equation (10.1.11) yields' 1 £ _ I esu. C-2 for a wire of radius o at a distance ij« from a conducting plate. T y p i c a l l y C ~ 5.1 x lO - 1 4" farads when both d r i f t plates i n the ICR are considered with a beam of radius 0.006 cm. -i> For a current of 2 x 10 amps and an electron accelerating bias of 15 v o l t s , then &V * i 0.148 v o l t s . Thus, s i g n i f i c a n t space charge potential depressions can be created i n the electron beam which w i l l s i g n i f i c a n t l y a f f e c t the ion beam. 82. APPENDIX D THE ENERGY SPREAD DUE TO THE PHASE ANGLE SPREAD OF ION VELOCITIES RELATIVE TO THE r f ELECTRIC FIELD The k i n e t i c energy associated with motion i n the x-y plane aft e r a time t i n the analyzer region i s given by £ = € : + • 2 ( £ £ o ) V z - COS +- £o from equation (7) where £ _ Q E<> X. «^nd £o = 22l2*£ 1 D-l where If. i s the i n i t i a l v e l o c i t y of the ion. Thus the f r a c t i o n a l spread i n energy due to the phase d i s t r i b u t i o n i s given by A£ ^ £ D-2 The d i s t r i b u t i o n of the plase angle tf* may be written as D-3 V(X) A* B d ^ TT wi th ^ ^ * x , and hence PCE^ d£ - POO de From equation D-l with E £ -4- AE Cos Thus de E - £. PCe)d£ = d£ TV be for £ - A £ < & 4- A E D-4 D-5 83. Setting E - d£ = d*' 6. At « \> £ lecuU TO D-6 de \ d*' d*' i l l f or I - j? 4 *' £ I + In-set t i n g *' - I = d*' - d Hq) d 3 for Setting 3 J ° 3 -M 3 s h PCs') d£ = leads to I leads to ds for where E - £ A6 D-7 D-8 D-9 D-10 Figure S i l l u s t r a t e s the d i s t r i b u t i o n of energies due to the phase d i s t r i b u t i o n . It may be v e r i f i e d by integration of equation D-10 that 0.5 of the ion population f a l l i n the energy range - O.-jS J to ^ 6 + 0-"]5 It i s of i n t e r e s t to calculate the maximum percentage deviation an ion can have from £ . Since > = i f * ' £ 4 mifo and If. may be regarded as the thermal v e l o c i t y l e . o- 9 5 m D-11 D-12 D-13 84. 85. where m i s i n amu, EQ i n m i l l i v o l t s / c m . , and t i n milliseconds. T y p i c a l l y consider an experiment on argon for which E» ^  z o HH^L, Crw-and t ~ 5 msec. Then ^ 5.88%. Thus i t i s extremely important i n experiments involving the r f heating of a p a r t i c u l a r ion to a given energy to know from equation D-12 the extent of maximum spread i n the energy of the ions for a given r f l e v e l , time of heating and molecular species. Figure T shows some t y p i c a l values of the maximum energy spread of ions due to the phase d i s t r i b u t i o n for various value of EQ{.-Keeping i n mind half the ions w i l l have energies with deviation of the energy >|o.75 &EJ from €. , Figure T indicates some requirements to maintain the energy spread due to phase d i s t r i b u t i o n s to a minimum. THE ENERGY SPREAD ASSOCIATED WITH OSCILLATION IN THE TRAP: Although there are exceptions, many ions are formed at e s s e n t i a l l y thermal energies, and the following discussion i s applied to those low energy ions. The t o t a l k i n e t i c energy of the ion motion may be written E = (kinetic energy),. + (kinetic energy) D-14 i e . E = 6 + TWti* a-For low values of the r f l e v e l , i t i s a good approximation to assume ne g l i g i b l e coupling of the xy motion to the z motion. An ion formed randomly along the electron beam w i l l experience an o s c i l l a t o r y motion i n the z d i r e c t i o n s a t i s f y i n g the r e l a t i o n 86. FIGURE T 87. where WT i s the angular frequency of o s c i l l a t i o n i n the potential w e l l . Thus i ( t ) = 2o Cos u> Tt D _ 1 6 and I d£ \ « O. ie = Tvx (tOr^p S i m u>^t )^ D_17 7Y1 V s lw 1 , U ) T t . Thus E - ^ + ™ V s V ^ T t D _ 1 8 for e < E 4 e +- V. For the ions produced between z and z + dz with i n i t i a l p o tential energy V and i n i t i a l k i n e t i c energy o, the d i s t r i b u t i o n of t o t a l k i n e t i c energies after a given time i s found as follows. (Assume that the ensemble can be associated with the d i s t r i b u t i o n . of k i n e t i c energies i n time giving equal s t a t i s t i c a l weight to each time element dt.) F i r s t consider a l l ions produced at a given z and convert the time dependence of the t o t a l k i n e t i c energy into a s t a t i s t i c a l d i s t r i b u t i o n of energies assuming random phases. Set & = C ^ T t . For the i n t e r v a l 0^ 9 £ y take equal a p r i o r i p r o b a b i l i t y , i e . b(e) 6& - Z. de and since D-19 1 TC de = ?Ce) d e l 6t de 1 TT V <>u^e cos e D-20 or for G. 4 E ^ £ + V Consider the d i s t r i b u t i o n function for the ions' p o t e n t i a l energy V. For the c e l l of width w, set w=2a, and P = where O < P 4 I. V(y) can be approximated roughly by Vo ^  where Vo i s the trapping well depth. Hence for equal numbers of ions d produced i n equal i n t e r v a l s d^ », thus However dv ?($) dj> dV = dv 2-V0 s and thus ( P ( v ) d< dV •4 and t h i s i s the p r o b a b i l i t y d i s t r i b u t i o n that V can take on values between 0 and V 0 . Thus for a given pot e n t i a l V, we know the p r o b a b i l i t y . d i s t r i b u t i o n for the energy P(E), and knowing the p r o b a b i l i t y d i s t r i b u t i o n for the potential energie we can calculate the p r o b a b i l i t y d i s t r i b u t i o n for the energy E as follows: ^ \ ?(e,v) (Ptsi) dv dV 89. i e . &Ce) s Set X' _ E - £ and solve for where 5 G O x de Thus 3 irx' D-26 D-27 where € ^ E i <£ -I- V„ i e . ° 4 *' ^ The d i s t r i b u t i o n for g(*') i s shown in Figure U. It i s evident that for a trapping voltage of say 1 v o l t , half the ions w i l l experience k i n e t i c energies less than 0.1 v o l t i n the trapping p o t e n t i a l f i e l d , i e . i 3 and 3 G O = FIGURE U 

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