18.6 COMPTON SCATTERING OF PHOTONS FROM ELECTRONS IN MAGNETICALLY INSULATED TRANSMISSION LINES* Sandia Laboratories, Albuquerque, New Mexico 87185

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1 COMPTON SCATTERING OF PHOTONS FROM ELECTRONS IN MAGNETICALLY INSULATED TRANSMISSION LINES* K. L. Brower and J. P. VanDevender Sandia Laboratorie, Albuquerque, New Mexico Abtract Self-magnetically inulated tranmiion line are ued for power tranport between the vacuum inulator and the diode in high current particle accelerator. Since the efficiency of the power tranport depeyd on the detail of the initial line geometry, i.e., the injector, the dependence of the electron canonical momentum ditribution on the injector geometry hould reveal the lo mechanim. We propoe to tudy that dependence experimentally through a Compton cattering diagnotic. The pectrum of cattered light reveal the electron velocity ditribution perpendicular to the direction of flow. The deign of the diagnotic i in progre. Our preliminary analyi i baed on the conervation of energy and canonical momentum for a ingle electron in the E and B field determined from 2-D calculation. For the Mite 1 accelerator with power flow along Z, the normalied canonical momentum, JJ, i in the range-.7 < JJ,S. For II?, and k II X', our analyi indicate that the catterea photon have 1.1 ev.s hv < 5.6 ev for ruby laer cattering and can be detected with PM tube. Introduction Self-magnetically inulated tranmiion line are being developed for power_ tranport in the particle beam fuion accelerator EBFA at Sandia. The efficiency of power and energy tranport i enitive to variation in line geomefry which occur at the input and output convolute. In thi paper we conider how the dynamic of electron flow might be probed by Compton cattering. The evaluation ha everal tep. Firt, the ditribution of the electric and magnetic field in the EBFA elf magnetically inulated line 1 are inferred from imulation2 and 1-D theory. 3 Then the relationhip be- tween.-..the energy of a photon cattered from an electron with an axial canonical momentum P i calculated at variou poition in the electron flow, for the E and B field from the 2-D imulation and for thoe from the 1-D theory. A comparion of the two relationhip illutrate the enitivity of the diagnotic to the model fore and B. The particle trajectorie for an aumed ditribution of canonical momentum P in the axial direction are then calculated at a given poition in the vacuum gap. Finally, the pectrum of cattered photon *Thi work wa upported by the U.S. Dept. of Energy, under Contract DE-AC4-76-DP789. for two different aumed canonical momentum ditribution are calculated to illutrate the diagnotic. Each tep will be examined in turn. Electromagnetic Field Calculation The triplate tranmiion line which i being incorporated into EBFA i repreented by an equivalent coaxial tranmiion line with rc =.7 m and ra =.8 m. Thi coax and the baic feature in the Compton cattering experiment are hown in Fig. 1. From imulation 2 of thi coaxial line, 1 the power flow i repreented by a boundary current IB, of 243 ka and a total current, IT, of 45 A at V = 2.4 MV. The current IE = IT-IB = 27 ka i carried by electron in the vacuum gap between conductor. TheE and B field for thi particular cae have been calculated previouly by Bergeron and Poukey with a 2-D electromagnetic particle imulation code. 2 The agreement between the experiment and the code reult for V, IT, and IB are excellent. We have alo calculated the E and B field for thee nitial condition from parapotential theory. We noticed that under thee con dition of power flow the value of c 1 a calculated by Eq. (29) and (36) in Creedon' paper 3 were inconitent. Thi theory require elf-conitency whih we achieved by optimiing N o that V m c( -l)/e i MV intead of 2.4 MV. Thi Fig. 1. Coax with baic feature of Compton cattering experiment. Direction of electron power flow (+Z), incident photon, and detector are all mutually perpendicular.

2 Report Documentation Page Form Approved OMB No Public reporting burden for the collection of information i etimated to average 1 hour per repone, including the time for reviewing intruction, earching exiting data ource, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding thi burden etimate or any other apect of thi collection of information, including uggetion for reducing thi burden, to Wahington Headquarter Service, Directorate for Information Operation and Report, 1215 Jefferon Davi Highway, Suite 124, Arlington VA Repondent hould be aware that notwithtanding any other proviion of law, no peron hall be ubject to a penalty for failing to comply with a collection of information if it doe not diplay a currently valid OMB control number. 1. REPORT DATE JUN REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Compton Scattering Of Photon From Electron In Magnetically Inulated Tranmiion Line 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Sandia Laboratorie, Albuquerque, New Mexico PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 1. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public releae, ditribution unlimited 11. SPONSOR/MONITOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES See alo ADM IEEE Puled Power Conference, Diget of Technical Paper , and Abtract of the 213 IEEE International Conference on Plama Science. Held in San Francico, CA on June 213. U.S. Government or Federal Purpoe Right Licene 14. ABSTRACT Self-magnetically inulated tranmiion line are ued for power tranport between the vacuum inulator and the diode in high current particle accelerator. Since the efficiency of the power tranport depeyd on the detail of the initial line geometry, i.e., the injector, the dependence of the electron canonical momentum ditribution on the injector geometry hould reveal the lo mechanim. We propoe to tudy that dependence experimentally through a Compton cattering diagnotic. The pectrum of cattered light reveal the electron velocity ditribution perpendicular to the direction of flow. The deign of the diagnotic i in progre. Our preliminary analyi i baed on the conervation of energy and canonical momentum for a ingle electron in  the E and B field determined from 2-D calculation. For the Mite1 accelerator with power flow along Z, the normalied canonical momentum, JJ, i in the range-.7 < JJ,S. For II?, and k II X, our analyi indicate that the catterea photon have 1.1 ev.s hv < 5.6 ev for ruby laer cattering and can be detected with PM tube. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR a. REPORT b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 4 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Precribed by ANSI Std Z39-18

3 43 value of V give a elf-conitent et of parameter V, Lr, IB, and Z for parapotential theory and i wel1 within experimental error in the meaurement and the numerical fluctuation in the computational reult. TheE and B field from 2-D calculation and the elf-conitent (SC) parapotential theory are hown in Fig. 2. E l l. 3.7 R (m) o CALCULATION -SC PARAPOTENTIAL (a) R (m) (b) Fig. 2. Plot of E and-b field extrapolate from data point of Bergeron and PQukey and according to SC parapotentialj theory. The Photon Energy a a Function of Electron Canonical Momentum In order to calculate the frequency of a Compton cattered photon, the velocity vector of the cattering electron need to be known. From the conervation of nergy and momentum for a ingle electron, Mendel ha hown that where = [l+(r)] -1- [a(r)+] 2 Vr 'Y v= radial velocity component, (rj'=: normalied calar a(r) = potential (= e/mc 2 withe= -V), -component of normalied vector potential ( e.a(r)/mc withb... VXA), : Z-component of normalied canonical momentum (= ep/mc with -y : t-;)-!;a)i!n:(r) (by energy conervation). In Eq. (1) a new parameter,#, i int5oduced which (1) i the normalied canonical momentum. For teadytate electron flow in a tranmiion line in which 3/oZ +, # i a contant of the electron motion. If the electron originate from the cathode where "' V... a.., then JJ=. Conequently, it i often aumed that = for all electron in the flow. However, elf-magnetically inulated tranmiion line have a tranition ection between the weakly, electrically treed vacuum inulator and the highly treed line. In the tranition ection, 3/oZ + and # i not a contant of motion Conequently, electron with JJ can be injected into the uniform line, and produce a ditribution. F() with a finite width IJ#, for the electron flow. It i thought that the detail tructure in F(#) determine the power trangprt in long, elf magnetically inulated line, and the tability of the electron flow may be undertood by tudying F() under variou condition. Stable orbit correponding to olution of Eq. (1) for which Vr in the gap can be found for variou value of JJ In Fig. 3 we have plotted the radial poition of the lower and upper turning point for table orbit a a function of J-1 Thee reult how hat the orbit are very imilar for calar and vector potential baed on parapotential and 2-D calculation. We alo ee that fo JJ =, the orbit are contained within the heath and return to the cathode urface. Orbit with JJ :'i have upper turning point beyond the heath and tend to remain iolated from the cathode urface. The minimum JJ correpond to thoe orbit whoe upper turning point jut grae the anode. According to Compton cattering theory for the geometry hown in Fig. 1, the energy of the cattered pot n, h11, i related to V ( r 1, JJ ) by the expre1.on (2)

4 l p Fig. 3. \ LOWER lurning POIN;; <" UPPER TURNING POINTS--... ', -2 CALCULATION R!ml Plot of p v. the poition of lower and upper turning point. The dotted line wa calculated by parapotential theory uing ame IB, IT, and V a wa ued for 2-D calculation. where r 1 i the radial poition of the incident laer beam in the gap. Scattered photon energie a a function of p are plotted in Fig. 4 for variou value of r 1 with hvi = ev from a ruby laer. The value of V (rl,jl) needed in Eq. (2) were determined from Eq. f1) uing potential from 2-D calculation with 11lower.S. Jl.S. tlu er Thee reult indicate that for thi geomet??, optical detection i required..725 '----2 CALCULATION.735 '.745 PARA POTENT! AL ' Calculated Spectra for an Aumed F(Jl) The number of cattered photon with energy between E, E +de i given by the expreion where dn de UL hv i D(ri.)F(P) l dg-1 fda - -do de do U = energy of incident laer pule, L = interaction length of beam and electron plama viible t the detector. D(r ) =number of electron/m at r 1 from. Ref. 2 F(JJ) =fraction of electron with normalied G( r 1,E) do dtl canonical momentum JJ, = normalied canonical momentum at ome n poition in the gap, r 1 (3), a a function of cattered photon energie (ee Fig. 4), and - Compton gifferential cattering cro ection. In uing Eq. (3) to.calculate the cattered pectra, we aume the laer energy i 1 joule, the collector ytem ubtend one terradian of gol angle, and the electron number denity i 1 1 m For a uniform canonical momentum ditribution, dn/de veru E (=hv 5 ) i plotted in Fig. 5 for everal poition of the probing laer beam. The total number of cattered photon i alo noted a NP in thee plot. We alo aumed a Gauian ditribution, exp(-.5(p-p )/SJJ) ), with P = and hij = Ool; the reult of the calculation uing thi ditribution i plotted in Fig. 6o. 715 _-...:: > 3..!!: "'..c: > "' Vi :I: c.. Q ::: >- >- <( u VI ::: IXl :::;;: ='... "C> p. Fig. 4. Plot of cattered photon energie v. p for variou poition for the field from the 2-D computation and, of the laer probe beam. The dotted line ha hv 5 (JJ) from the field from the elf-conitent parapotential calculation at r 1 =.725 m for comparion. Fig hv (evl Plot of dn/ de v. h.v for uniform ditribution in Po

5 432 P.o= O...ip.=-1 =.75 m r..--- Np = 3. 2 X 1 5 =.7!5 m Np = 3. X 1 5 =.735 m Np = 6. X 1 4 The electron produce a bremtrahlung x-ray pule that will produce a ignal on the detector. The cattered light can be optically delayed until the detector recover from the x-ray pule o the x-ray background can be tolerated. The limiting factor to the Compton cattering diagnotic to meaure F(JJ) appear to be the background light from the plama on the cathode. A ignificant amount of light can be expected, but no meaurement have been made of it intenity or pectral ditribution. The ratio of cattered light to plama light improve a the bandwidth bv of the cattered ligt decreae. If the width 6JJ of F(JJ) i 7 1, a recent calculation have indicated, the cattered light ha a wavelength pread of only 3 A", which would give a very favorable ratio of cattered light to plama light. Concluion The Compton cattering diagnotic i capable in principle of reolving the canonical momentum ditribution F(JJ) in elf-magnetically inulated electron flow. The limiting factor i the ratio of background plama light from the cathode plama and the cattered light, which i trongly dependent on the width of F(JJ) itelf. h v ievl 4 Reference 1. J. P. VanDevender, J. Appl. Phy. SO, No. 6 (1979). Fig. 6. Plot of dn/de v. hv for Gauian ditribution in JJ centered about JJ = with &JJ = K. D. Bergeron and J. W. Poukey, Appl. Phy. Lett. 32, 8 (1978). 3. J. M. Creedon, J. Appl. Phy (197S). Dicuion In the propoed experiment to meaure F(JJ) in an EBFA-I elf-magnetically inulated tranmiion line, tge total number of collected photon will be Np"" 1 The photon will be in the viible region of the pectrum and they will be pectrally reolved with a grating and recorded with a photomultiplier and ocillocope combination for each data channel. Aume that the pectrometer ha a tranmiion efficiency f =.2, the photomultiplier ha a unatum efficiency fpm =.3 and a gain G = 1 If the data i recorded in a t = 1 n pule into Ne = S data channel, then the average ignal into a SO ohm ocillocope will be 4. C. W. Mendel, J. Appl. Phy. 2Q, No. 7 (1979). S. J. D. Jackon, Claical Electrodynamic (Wiley, NY, 197S), p J. P. VanDevender, Proc. 2nd Int'l. Conf. on Puled Power, Lubbock, TX (1979). 7. E. L. Neau and J. P. VanDevender, ame a Ref c. Ward and R. E. Pechacek, Phy. Fluid. 222 (197 2). v Npffpm Ge 5 N At =.6 volt c which i eaily recordable. The funct:ional relationhip between hv and Jl feature a reaonably trong correponjence of F(hv ) 5 to F(JJ) for the propoed experiment and the interpretation of the data i reaonably inenitive to the aumed model for the electromagnetic field ditribution in the electron flow.