1)llc FILE COPYNaval Research LaboratoryWuhton, DC 20S.80oo
NRL Memorandum Report 6295
AD-A200 399
Relativistic Focusing and Beat Wave Phase VelocityControl in the Plasma Beat Wave Accelerator
E. ESAREY AND A. TING
Berkeley Research AssociatesP.O. Box 852
Springfield, VA 22150
P. SPRANGLE
Plasma Theory BranchPlasma Physics Division
DTIC -
ELECTE
OCT 25 19881 September 22, 1988DcJ
Approved for public release; distribution unlimited.
J.../
SECURIty CLASSIFICATION OF THIS PAGE
REPORT DOCUMENTATION PAGE ormB 0704rov8d
la REPORT SECURITY CLASSIFICATION 1b RESTRICTIVE MARKINGS
UNCLASSIFIED ______________________2a. SECURITY CLASSIFICATION AUTHORITY 3 DISTRIBUTION/ AVAILABILITY OF REPORT
Approved for public release; distribution2b. DECLASSIFICATION / DOWNGRADING SCHEDULE unlimited.
4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5 MONITORING ORGANIZATION REPORT NLV-BERIS,
NRL Memorandum Report 62956a. NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a NAME OF MONITORING ORGANiZA' ONI (if applicable)Naval Research Laboratory Code 4790
6c. ADDRESS (City, State, and ZIP Code) 7b ADDRtESS (City, State arid ZIP Code)
Washington, DC 20375-5000
8a. NAME OF FUNDING/ISPONSORING J8b OFFICE SYMBOL 9 PROCUREMENT INSTRUMENT DENTIF-CAT ON N ;,MBE-'ORGANIZATION (if applicablIe)
U.S._Department ofEnergy _______ _________ ____________
Sc. ADDRESS (City. State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERS
*PROGRAM IPROET 31TASK VVORK uNITWsigoDC 20545 ELEMENT NO -983 NO IACCESSiON NO
WasingonDOE I A00411. TITLE (include Socursty Clasification)Relativiatic Focusing and Beat Wave Phase Velocity Control in the PlasmaBeat Wave Accelerator
12. PERSONAL AUTHOR(S)Esarey,* E., Ting,* A. and Sprangle, P.
13a. TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year. Month. Day) isAC ~Interim FROM TO ___ 1988 September 22 2 4
16 SUPPLEMENTARY NOTATION
*Berkeley Research Assoc., P.O. Box 852, Springfield, VA 22150
17. COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block nufller)
FIELD GROUP SUB-GROUP
19 ABSTRACT (Continue on reverse if necessary and identify by block number)
7 Relativistic focusing allows two colinear short pulse radiation beams, provided they are of sufficiently
high power, to propagate through a plasma without diffracting. By further accounting for finite radial beamgeometry, it is possible for the phase velocity of the radiation beat (ponderomotive) wave to equal the speedof light. This removes one of the limiting factors, phase detuning between the accelerated electrons and thebeat wave, in determining the maximum energy gain in the plasma beat wave accelerator.
00 Form 1473. JUN 86 P'revious editions ire obsoiete . -.
S/N I)I)T.LF..Iti.6or)I
CONTENTS
INTRODUCTION ................................................. I
ANALYSIS OF RADIATION FOCUSING AND BEAT WAVE PHASEVELOCITY CONTROL ....................................................................... 3
DISCUSSION.................................................................................. 6
ACKNOWLEDGEMENTS ................................. I................................ 6
REFERENCES ................................................................................ 7
DISTRIBU77ON LISTS.......................................................................13
ACC~On, tny,-
RELATIVISTIC FOCUSING AND BEAT WAVE PHASE VELOCITYCONTROL IN THE PLASMA BEAT WAVE ACCELERATOR
Introduction
Recently there has been much interest in plasma based accelerator schemes, such as
the plasma beat wave accelerator (PBWA),' - 3 for producing ultra-high energy electrons.
This has led to a renewed interest in the study oi the propagation of intense radiation beams
through a plasma.4 - " In the PBWA two colinear radiation beams of frequencies w1 ,W2are incident on a umiorm plasma. By appropriately choosing the difference il lhe i a.e
frequencies to be equal to the electron plasma frequency wp, Aw = wl - ,2 = wp, where
wP/w? << 1, it is possible for the radiation beat wave to resonantly drive large amplitude
electron plasma waves. In the ideal wave breaking limit,' 4 the maximum accelerating
electric field Em is given by E, (mtc 2 /e)wp/c " .97. ,yi eV/cm where np is the plasma
density in cm - . For example, np = 1.6 x 1016 cm - 3 gives Em _ 120 MeV/cm which
implies that an electron could be accelerated to 1.2 TeV in 100 meters.
To realize such an acceleration scheme it is necessary that i) the radiation beallis
propagate at high intensity over distances large compared to the Rayleigh length ZR =
r /2c, where r, is the radiation spot size, and that ii) phase resonance between the
accelerating electrons and the plasma wave be maintained over an equally large distance.
In vacuum, radiation diffracts over distances on the order of ZR, which can be relatively
short. Hence, in order to maintain high intensity beams it is necessary to rely on focusing
enhancement from the plasma. In the PBWA the phase velocity of the plasma wave isequal to the phase velocity of the radiation beat wave which, in the 1-D limit, is given by
vp/c = Aw/Ak = 1 - w'/2w', where Ak = k, - k2 is the difference in th*. wave numbers
of the two beams. Since the velocity of an ultra-relativistic electron is approximately the
speed of light, the electrons out run the plasma wave and become "detuned" in a length"5
Ld A W A /w., where A1, = 21rc/wp. For wl/wp = 25 and np = 1.6 x 1016 cm - 3 , this gives
L," 16 cm and a maximum electron energy gain of AE - ELd - 2 GeV. In order to
increase the energy gain beyond this detuning limit, it is necessary to increase the phase
velocity of the plasma beat wave.
This paper addresses the two points mentioned above concerning the realization of
the PBWA. As is shown below, matched beam solutions are possible in which the two
radiation beams propagate with constant spot sizes provided the radiation is of stuffici ntlv
high power. This allows the radiation beams to propagate over distances larger than
the Rayleigh length while maintaining their high intensities. For example, two radiation
beams with equal spot sizes are matched provided t.h, power in each beam is P = P, 3.
Manuscrpt approved July 7, 1988.
IEEEI !U EE 11 I I i I - i -- I
where P, : 17 x 10'w 2/wP W is the power threshold for relativistic focusing of a single
radiation beam in a plasma. 4" In addition, by including finite radial beam profiles along
with relativistic focusing, the phase velocity of the beat wave can be tuned to the speed
of light. This is accomplished by appropriately choosing the initial spot sizes and powersof the radiation beams. Hence, phase resonance between the electron and beat wave can
be maintained beyond the 1-D detuning length Ld and, consequently, substantially higher
electron energies can be achieved. Figure 1 shows schematically the propagation of two
matched radiation beams through a plasma with the resulting beat wave phase velocityequal to the speed of light.
Focusing of radiation beams in a plasma occurs through the combined effects of rela-
tivistic, ponderomotive and thermal self-focusing.4 -13 Typically these processes occur on
widely separate time scales. Relativistic focusing 4- 8 occurs on the shortest time scale,rR - 1/w, which is the time scale at which the electrons respond to the radiation field.
Ponderomotive focusing -" depends on the expulsion of ions from the radiation chan-
nel and thus occurs on a time scale given roughly by 'rp r./C,, where C, is the ion
acoustic speed. Thermal focusing1'2 ,3 relies on heating of the plasma by the radiation
beam and typically occurs on an even longer scale. This paper is concerned with rela-
tivistic focusing, and hence the analysis is applicable to lasers with pulse lengths TL in
the range rR < -rL < -rp, which is the region of interest for the PBWA. Physically, rela-tivistic focusing arises solely from the relativistic electron quiver velocity, Vq = ca, /-r-L,
in the combined radiation field. Here aj = eA±/mc2 is the normalized radiation vector
potential and 'yj = /T + a2_ is the relativistic gamma factor for an electron in a helically
polarized radiation field. The focusing mechanism for a single beam is that a radiation
profile peaked on axis leads to an index of refraction profile, n 1 - (,p/w)2 /2-y±, which
has a minimum on axis. The radiation beam, therefore, focuses along the axis.' When
the radiation power is greater than the critical power P, for relativistic self-focusing, it is
possible for the envelope of a single radiation beam to propagate at a constant spot size.T
For two colinear beams, however, the situation is more complicated due to the coupling
of one beam to the other through the relativistic gamma factor. The analysis presented
below indicates that matched beam propagation for two beams is only possible for a finite
range of the parameter R, such that 1/(v/8 - 1) < R < 0 - 1. where R = (r,l /r,l )2 is
the square of the ratio of the spot sizes of the two beams. The radiation power required
to obtain matched beam propagation for two beams is near that for a single beani. P.
Control of the beat wave phase velocity is most easily understood by the following
heuristic argument. The finite radial extent of the radiation beams gives rise to a small
2
effective perpendicular wave number k1 . Here k1 is a function not only of the spot size
but also of the power due to the relativistic focusing effects. The existence of k1 gives
rise to an effective parallel wave number given by kll !:_ (1 - wp/2w2 - c2 k±/2w2 )w/c.
Hence, the parallel phase velocity of the beat wave is now given by vp/c 1_ 1 - w/2w2 +
(k21 - k2 2 )c2 /2wwp. By appropriately choosing the initial spot sizes and powers of the
two radiation beams, it is possible to have the last term in the expression for vp/c cancel
the second term thus providing vp = c.
Analysis of Radiation Focusing and Beat Wave Phase Velocity Control
The analysis starts with the wave equation for the vector potential of the conibin'-d
radiation field, (V2 - c-8 2 /&tI)A± = -(4ir/c)J±, where J± is the transverse current
density. In order to study the effects of relativistic focusing alone, only the current resulting
from the electron quiver motion is needed, J± = -enpVq. The wave equation is then given
by(P 122 --1/2,
( _a±= a. (1 + alI' + ja 2 -L 21aIa 21cosA1/) (1)
where a± = a, + a2 . Throughout the following, a subscript 1 refers to the radiation beam
of frequency wl, and a subscript 2 refers to the radiation beam of frequency w2. The factor
within the square root is the relativistic gamma factor 7±, assuming helically polarized
radiation. Here, A4 = Pj -- t2 is the phase of the beat wave and ('1,2 = kl,-z-W l.t4 2 ,
where 01,2 is the slowly evolving phase of the radiation field.
In order to examine the qualitative diffractive properties of the radiation beams, it is
helpful to consider the index of refraction nl, 2 of each beam. The approximate index of
refraction associated with each beam is obtained in the following manner. First, tile I-D
limit of the left hand side of Eq. (1) is taken, assuming a - exp(i$I). Next, Eq. (1) is
divided by the phase factor exp(iZ) of either beam 1 or 2 and then averaged over a period
of the beat phase Al. In the mildly relativistic limit 1al,212 < 1, the index of refraction
for each beam is given by
n- klc/w = I -(w /2w)(1 - jai 12/2 - lal 2"), (2a)
n2= k 2 c/w 2 = 1 - (w/2w2)(1 - lai 1- a2 12 /2). (2b)
In the above expressions, the first term (the unity) represents vacuum diffraction while the
second term is the contribution from the ambient plasma. The remaining terms represent
focusing from the radiation fields. More specifically, a term proportional to (lai 2 2 la, 2) '2
3
results from the individual contributions of beam 1 and 2 to the relativistic factor 7±,
while the remaining term proportional to jai, 2 12 /2 results from the contribution of the
beat wave to -y. Radiation focusing occurs when cn/or < 0. Hence, the contribution
from the radiation terms to n1 ,2 provide focusing for radiation profiles peaked on axis. For
sufficiently high power, these focusing terms dominate the vacuum diffraction and provide
overall focusing of the radiation beams.
Envelope equations describing the evolution of the spot size r,(z) of each beam are
derived by applying the "source-dependent expansion" (SDE)1'6 17 to Eq. (1). This is
accomplished by expanding the normalized vector potential al,2 for each beam into a
series of Gaussian-Laguerre polynomials and using orthogonality properties to determinetheir coefficients. The SDE differs from the typical vacuum modal expansion in that the
parameters characterizing the Gaussian-Laguerre polynomials, such as the width of the
Gaussian, are functions of z which depend on the "source", i.e. the right hand side of
Eq. (1). Assuming that each beam is adequately described by the lowest order Gaussian
mode a = laoo Iexp[i/3 -(1 - ia)r 2 /rf], then the parameters lao0, 13, a and r, are given
by Iaoo(z)l = aor.o/r,(z), a(z) = (w/4c)dr2/dz along with the following equations:
4r 2 1 -8W 1\+ (3a)t wr~WI(1 + R)
d2 4c 2 [ w( 8W1 1 )]bdz-- s2 _ - 1- W, 1 W+ IR) (3b)Z2 ;22 r32 22(1+ R)2
d 2c 1 + - , 3 4W 2,R(l + 2R)0 11 = - -2- 2' " ' -+ ( 4 a )
dz 2, r., a 4c (2 W (1 +R) 2 /J 4.
2c 1 (3 4rj- wr~ [2 + -p, -, +_ -W 1W2 2 4c 2 (2 W1+ R 2)] (4b)
where the mildly relativistic limit was taken, Iai, 212 < 1. Physically, W = (Wpaoro/4c)2 =
P/Pc where P is the power in one of the beams and P, is the critical power necessary
for relativistic focusing of a single beam.7 Here aq and ro are the initial amplitude ofthe vector potential on axis and the initial 3pot size of each beam. The parameter a is
related to the curvature of the radiation wavefront and the parameter 3 is important in
that it represents a correction to the parallel wave number on axis k1 = ;/c + d3/dz. This
relation is used below to determine the beat wave phase velocity on axis.
Equations (3a) and (3b) describe the envelope evolution for each beam as it propagates
through the plasma. Setting the right-hand sides of Eqs. (3a) and (3b) equal to zero gives
4
matched beam solutions for which the beams propagate without diffracting. Matched beamsolutions are obtained for values of R in the range 1/(vi - 1) < R < v/g - 1 provided tilenormalized power W of each beam is given by
W, = [8R 2 (1 + R) 2 - (1 + R)4][64R 2 - (1 + R) 4 ]', (5a)
W2 = [8(l + R)2 - (1 + R)4 )[64R 2 - (1 + R) 4]- '. (5b)
This is illustrated in the following limits: For R = 1, then W, = W 2 = 1/3. As R -1/(v/8--1), then W, - 0 and W 2 --- 1. As R -- v/8- -1, then W, -. 1 and W2 - 0.Hence, it is possible for a beam close to the critical power to confine a second beam which
has a smaller spot size and a smaller power.
Matched beam propagation occurs when R, W, and W2 are specified as indicated
above. For example, once R is chosen in the range 1/(v/8 - 1) < R < v/8 - 1, then W1
and W2 are given by Eqs. (5a) and (5b). The actual magnitudes of the spot sizes r,1 andr, 2 are undetermined and only their ratio has been specified. Specifying a value for r,gives a value for the radiation beat wave phase velocity on axis according to the relationc/vP = 1 + cAfI /Aw, where A,8' = do3/dz- d/32/dz. Alternatively, requiring vp = C
for a given set of matched beam parameters R, W, and W2 specifies r, 1 . For example,
as R - v/8 -1, requiring vp= c gives k2r, - 5w,/Aw, where k , = wp/c. For R = 1,requiring v, = c gives k r, :-- 2. As R -- 1/(v/8- 1), it is not possible to have t, = c. For
applications in the PBWA, it may be desirable to have kprl >> 1. This implies that itmay be desirable to choose a matched beam case with R > 1. For example, R = 1.5 gives
W, _ 0.7, W 2 : 0.1 andk~r, = 2.6w,/Aw.
As a final illustration, the above results are applied to parameters similar to those inthe UCLA beat wave excitation experiment," where wl _ 2.0 x 1014 sec - 1 and Aw w _9.7 x 10- 2 (which implies n, 10"7 cm- 3 ). A test electron with intial energy given by
70 = 50 is accelerated by plasma waves generated in the following two special cases: i) Amatched beam case with the beat wave phase velocity tuned to the speed of light, v, = c.where R = 1.5, rsl = 8.3 x 10- 3 cm, P, = 1.3 x 1012 W and P, = 1.6 < 1011 W; and
ii) the same parameters as case i) only now the beat wave phase velocity is given by the
1-D limit, vp/c = 1 - w/2w2, and the radiation beams are assumed to undergo vacuum
Rayleigh diffraction, r8 = r0(1 + :2/4 )1/a. The results of case ii) are shown in Fig. 2and the results of case i) are shown in Fig. 3. Figure 2 indicates that the test electron
outruns the plasma wave and begins to be deaccelerated after approximately 0.5 cm witha maximum energy gain of A-y = 210. In Fig. 3, however, phase resonance between the
5
electron and beat wave is maintained which allows an energy gain of AY a- 6500 in 8 cm.
This energy gain continues in a linear fashion until it becomes limited by some non-ideal
effect such as pump depletion.19
Discussion
In summary, it has been shown that two colinear, short-pulse, Gaussian radiation
beams can propagate through a uniform plasma without diffracting due to relativistic
focusing. This occurs for values of R in the range 1/(v/8 - 1) < R < v'8 - 1, provided W,
and W 2 are specified according to Eqs. (5a) and (5b). In addition, it is possible to tune
the phase velocity of the radiation beat wave to the speed of light for cases where R > 1.
This is accomplished by appropriately choosing r,,. In an actual PBWA, Aw = WP and the
envelope behavior of the radiation beams becomes more complicated due to the presence
of large amplitude resonantly driven plasma waves.2" However, the analysis presented here
remains valid for the front of the radiation pulse (the first several plasma wavelengths)
where the amplitude of the plasma wave remains small. In the small amplitude linit, the
phase velocity of the plasma wave is equal to that of the radiation beat wave.21 Assuming
that the phase velocity of the plasma wave remains fixed to its initial value, then the above
analysis indicates that it is possible to tune this phase velocity to the speed of light. This
implies that phase detuning between the plasma wave and the electrons can, in principle,
he avoided which results i. a substantiallv higher energy gain in the PBWA.
Acknowledgements
The authors would like to acknowledge useful discussions with C.-M. Tang. This work
was supported by the U.S. Department of Encrgy.
I
4,
6I
References
1) T. Tajima and J.M. Dawson, Phys. Rev. Lett. 43, 267 (1979).
2) C. Joshi and T. Katsouleas, eds., Laser Acceleration of Particles, AlP Coulf. Proc.
No. 130 (Amer. Inst. Phys, New York, 1985).
3) T. Katsouleas, ed., IEEE Trans. Plasma Sci. PS-15 (1987).
4) C. Max, J. Arons and A.B. Langdon, Phys. Rev. Lett. 33, 209 (1974).
5) P. Sprangle and C.-M. Tang, in Laser Acceleration of Particles, ed. by C. Joshi and
T. Katsouleas, AlP Conf. Proc. No. 130 (Amer. lust. Phys, New York, 1985). p.
156.
6) G. Schmidt and W. Horton, Comments Plasma Phys. 9, 85 (1985).
7) P. Sprangle, C.-M. Tang and E. Esarey, IEEE Trans. Plasma Sci. PS-iS. 145 (1987).
8) G.Z. Sun, E. Ott, Y.C. Lee and P. Guzdar, Phys. Fluids 30, 526 (1987).
9) P.K. Kaw, G. Schmidt and T. Wilcox, Phys. Fluids 16, 1522 (1973).
10) C. Max, Phys. Fluids 19, 74 (1976).
11) F.S. Felber, Phys. Fluids 23, 1410 (1980).
12) D.A. Jones, E.L. Kane, P. Lalousis, P. Wiles and H. Hora, Phys. Fluids 25, 2295
(1982).
13) A. Schmitt and R.S.B. Ong, J. Appl. Phys. 54, 3003 (1983).
14) M.N. Rosenbiuth and C.Q Liu, Phys. Rev. Lett. 29, 701 (1972).
15) T. Katsouleas, C. Joshi, J.M. Dawson, F.F. Chen, C.E. Clayton, W.B. N'lori. C'.
Darrow, and D. Umstadter, in Laser Acceleration of Particles, ed. by C. Joslii and T.
Katsouleas, AIP Conf. Proc. No. 130 (Amer. Inst. Phys, New York, 1985), p. 63.
16) P. Sprangle, A. Ting and C.-M. Tang, Phys. Rev. Lett. 59, 202 (1987).
17) P. Sprangle, A. Ting and C.-M. Tang, Pliys. Rev. A 36, 2773 (1987).
18) C. Joshi, C.E. Clayton, C. Darrow and D. Unistadter, in Laser Acceleration of P tr-
tidles, ed. by C. Joshi and T. Katsouleas, AlP Conf. Proc. No. 130 (Amier. hist.
Phys, New York, 1985), p. 99.
19) W. Horton and T. Tajima, in Laser Acceleration of Particles, ed. by C. Joshi and T.
7
Katsouleas, AlP Conf. Proc. No. 130 (Amer. Inst. Phys, New York, 1985), p. 179.
20) C. Joslii, C.E. Clayton and F.F. Chien, Phys. Rev. Lett. 48, 874 (1982).
21) C.-M. Tang, P. Sprangle and R.N. Sudan, Phys. Fluids 28, 1974 (1985).
>N
EN
mo
06 oSr --
o-
0)0
0))
0 -0
0 <
CL -
140
0 100-
4W
00
,w
60
iI
25 MeV
20 1 , 1 I I
0 2 4 6 8
z (cm)FIG. 2. Test electron acceleration with the same parameters as Fig. 3 except the phase
velocity is given by the 1-D limit and the radiation beams undergo vacuum Rayleigh
diffraction.
10
>2
CP
WI
25 MeV
0 1 1
0 2 4 68
z (CM)FIG. 3. Test electron acceleration for a matched beam case with t',p C, Where R 15
rj= 8.3 X 10-3 CM, p1 = 1.3 x 1012 W and PA = 1.6 x< 10" W.
DISTRIBUTION LIST*
Naval Research Laboratory4555 Overlook Avenue, S.W.Washington, DC 20375-5000
Attn: Code 1000 CAPT V. G. Clautice1001 - Dr. T. Coffey1005 - Head, Office of Management & Admin.2000 - Director of Technical Services2604 - NRL Historian4603 - Dr. W.V. Zachary4700 - Dr. S. Ossakov (26 copies)4710 - Dr. C.A. Kapetanakos4730 - Dr. R. Elton4740 - Dr. V.M. Manheimer4740 - Dr. S. Gold4790 - Dr. P. Sprangle4790 - Dr. C.M. Tang4790 - Dr. M. Lampe4790 - Dr. Y.T. Lau4790A- V. Brizzi6652 - Dr. N. Seeman6840 - Dr. S.Y. Ahn6840 - Dr. A. Ganguly6840 - Dr. R.K. Parker6850 - Dr. L.R. Whicker6875 - Dr. R. Wagner2628 - Documents (22 copies)2634 - D. Vilbanks1220 - 1 copy
Records I copy
Cindy Sims (Code 2634) 1 copy
* Every name listed on distribution gets one copy except for those whereextra copies are noted.
13
Dr. R. E. Aamodt Dr. B. BezzeridesScience Applications Intl. Corp. MS-E5311515 Walnut Street Los Alamos National LaboratoryBoulder, CO 80302 P. O. Box 1663
Los Alamos, NM 87545Dr. B. Amini1763 B. H.U. C. L. A. Dr. Leroy N. BlumbergLos Angeles, CA 90024 U.S. Dept. of Energy
Division of High Energy PhysicsDr. D. Bach ER-221i/German townLos Alamos National Laboratory Wash., DC 20545P. 0. Box 1663Los Alamos, NM 87545 Dr. Howard E. Brandt.
Department of the ArmyDr. D. C. Barnes Harry Diamond LaboratoryScience Applications Intl. Corp. 2800 Powder Mill RoadAustin, TX 78746 Adelphi, MD 20783
Dr. L. R. Barnett Dr. Richard J..Briggs3053 Merrill Eng. Bldg. Lawrence Livermore National LaboratoryUniversity of Utah P. 0. Box 808, L-626Salt Lake City, UT 84112 Livermore, CA 91550
Dr. S. H. Batha Dr. Bob BrooksLab. for Laser Energetics & FL-1ODept. of Mech. Eng. University of WashingtonUniv. of Rochester Seattle, WA 98195Rochester, NY 14627
Prof. William CaseDr. F. Bauer Dept. of PhysicsCourant Inst. of Math. Sciences Grinnell CollegeNew York University Grinnell, Iowa 50221New York, NY 10012
Mr. Charles CasonDr. Peter Baum Commander, U. S. ArmyGeneral Research Corp. Strategic .Defense CommandP. 0. Box 6770 Attn: CSSD-H-DSanta Barbara, CA 93160 P. 0. BoxO1500
Huntsville, AL 34807-3801Prof. George BekefiRm. 36-213 Dr. Paul J. ChannellM.I.T. AT-6, MS-H818Cambridge, MA 02139 Los Alamos National Laboratory
P. 0. Box 1663Dr. Russ Berger Los Alamos, NM 87545FL-10University of Washington Dr. A. 'J. ChaoSeattle, WA 98185 Stanford Linear Accelerator :en[er
Stanford UniversityDr. 0. Betancourt Stanford, CA 94305Courant Inst. of Math. SciencesNew York University Dr. Francis F. ChenNew York, NY 10012 UCLA, 7-31 Boelter Hall
Electrical Engineering Dept.Los Angeles, CA 10024
14
Dr. K. Wendell Chen Dr. Paul L. CsonkaCenter for Accel. Tech. Institute of Theoretical ScieacesUniversity of Texas and Department of PhysicsP.O. Box 19363 University of OregonArlington, TX 76019 Eugene, Oregon 97403
Dr. Pisin Chen Dr. Chris DarrowSLAC, Bin 26 UCLAP.O. Box 4349 1-1.30 Knudsen HallStanford, CA 94305 Los Angeles, CA 90024
Dr. Marvin Chodorow Dr. J. M. DawsonStanford University Department of PhysicsDept. of Applied Physics University of California, Los AngelesStanford, CA 94305 Los Angeles, CA 90024
Major Bart Clare Dr. Adam DrobotUSASDC Science Applications Intl. Corp.P..O. Box 15280 1710 Goodridge Dr.Arlington, VA 22215-0500 Mail Stop G-B-1
McLean, VA 22102Dr. Christopher ClaytonUCLA, 1538 Boelter Hall Dr. D. F. DuBois, T-DOTElectrical Engineering Dept. Los Alamos National LaboratoryLos Angeles, CA 90024 Los Alamos, NM 87545
Dr. Bruce I. Cohen Dr. J. J. EwingLawrence Livermore National Laboratory Spectra TechnologyP. 0. Box 808 2755 Northup WayLivermore, CA 94550 Bellevue, WA 98004
Dr. B. Cohn Dr. Frank S. FelberL-630 11011 Torreyana RoadLawrence Livermore National Laboratory San Diego, CA 92121P. 0. Box 808Livermore, CA 94550 Dr. Richard C. Fernow
Brookhaven National LaboratoryDr. B. Cole Upton, NY 11973Univ. of WisconsinMadison, VI 53706 Dr. H. Figueroa
1-130 Knudsen HallIDr. Francis T. Cole U. C. L. A.Fermi National Accelerator Laboratory Los Angeles, CA 90024Physics SectionP. 0. Box 500 Dr. Jorge FontanaBatavia, IL 60510 Elec. and Computer Eng. Dept.
Univ. of Calif. at Santa BarbaraDr. Richard Cooper Santa Barbara, CA 93106Los Alamos National Laborat)ryP. 0. Box 1663 Dr. David ForslundLos Alamos, NM 87545 Los Alamos National Laboratorv
P. 0. Box 1663Dr. Ernest D. Courant Los Alamos, NM 87545Brookhaven National LaboratoryUpton, NY 11973
15
Si
Dr. P. GarabedianCourant Inst. of Math. Sciences Dr. G. L. JohnstonNov York University NY16-232New York, NY 10012 M. I. T.
Cambridge, MA 02139Dr. Walter Gekelman
UCLA - Dept. of Physics Dr. Shayne Johnston1-130 Knudsen Hall Physics DepartmentLos Angeles, CA 90024 Jackson State University
Jackson, MS 39217Dr. Dennis GillLos Alamos. National Laboratory Dr. Mike JonesP. 0. Box 1663 MS B259Los Alamos, NM 87545 Los Alamos National Laboratory
P. 0. Box 1663Dr. B. B. Godfrey Los Alamos, NM 87545Mission Research Corporation1720 Randolph Road, SE Dr. C. JoshiAlbuquerque, NM 87106 7620 Boelter Hall
Electrical Engineering DepartmentDr. P. Goldston University of California, Los AngelesLos Alamos National Laboratory Los Angeles, CA 90024P. O. Box 1663Los Alamos, NM 87545 Dr. E. L. Kane
Science Applications Intl. Corp.Prof. Louis Hand McLean, VA 22102Dept. of PhysicsCornell University Dr. Tom KatsouleasIthaca, NY 14853 UCLA, 1-130 Knudsen Hall
Department of PhysicsDr. J. Hays Los Angeles, CA 90024TRWOne Space Park Dr. Rhon Keinigs MS-259Redondo Beach, CA 90278 Los Alamos National Labortory
P. 0. Box 1663Dr. Wendell Horton Los Alamos, NM 87545University of TexasPhysics Dept., RLM 11.320 Dr. Kvang-Je KimAustin, TX 78712 Lavrence Berkeley Laboratory
University of California, BerkeleyDr. J. Y. Hsu Berkeley, CA 94720General AtomicSan Diego, CA 92138 Dr. S. H. Kim
Center for Accelerator TechnologyDr. H. Huey University of TexasVarian Associates P.O. Box 19363B-118 Arlington, TX 76019611 Hansen WayPalo Alto, CA 95014 Dr. Joe lindel
Los Alamos Nationai LaboratoryDr. Robert A. Jameson P. 0. Box 1663. MS E531Los Alamos National Laboratory Los Alamos, NM .7{>5AT-Division, MS H811P.O. Box 1663 Dr. Ed KnaopLos Alamos, NM 87545 Los Alamos National Laboratory
P. 0. Box 1663Los Alamos. NM 97545
16
Dr. Peter Kneisel Prof. Kim MolvigCornell University Plasma Fusion CenterF. R. Nevan Lab. of Nucl. Studies Room NV16-240Ithaca, NY 14853 M.I.T.
Cambridge, MA 02139Dr. Norman H. Kroll
University of California, San Diego Dr. A. MondelliSan Diego, CA 92093 Science Applications Intl. Corp.
171.0 Goodridge DriveDr. Michael Lavan McLean, VA 22101Commander, U. S. ArmyStrategic Defense Command Dr. Warren MoriAttn: CSSD-H-D 1-130 Knudsen HallP. O. Box 1500 U. C. L..A.Huntsville, AL 35807-3801 Los Angeles, CA 90024
Dr. Kenneth Lee Dr. P. L. MortonLos Alamos National Laboratory Stanford Linear Accelerator CenterP.O. Box 1663, HS E531 P. 0. Box 4349Los Alamos, NM 87545 Stanford, CA 94305 0
Dr. Baruch Levush Dr. John A. NationDept. of Physics & Astronomy Laboratory of Plasma StudiesUniversity of Maryland 369 Upson HallCollege Park, MD 20742 Cornell University
Ithaca, NY 14853Dr. Chuan S. Liu
Dept. of Physics & Astronomy Dr. K. C. NgUniversity of Maryland Courant Inst. of Math. SciencesCollege Park, MD 20742 Nev York University
New York, NY 10012Dr. N. C. Luhmann, Jr.7702 Boelter Hall Dr. Robert J. NobleU. C. L. A. S.C1A.C., Bin 26Los Angeles, CA 90024 Stanford University
P.O. Box 4349Dr. Clare Max Stanford, CA 94305Institute of Geophysics& Planetary Physics Dr. J. NoremLawrence Livermore National Laboratory Argonne National LaboratoryP. 0. Box 808 Argonne, IL 60439 0Livermore, CA 94550
Dr. Craig L. OlsonDr. B. D. McDaniel Sandia National LatoratcrieqCornell University Plasma Theory Division IZ41Ithaca, NY 14853 P.O. Box 5800
Albuquerque, NM 87185Dr. Colin McKinstrieLos Alamos National Laboratory Dr. H. DonaP. 0. Box 1663 MS-E554Los Alz;nos, NM 87545 Los Alamos National Laboratory
P. 0. Box 1663Los Alamos, NM 87545
I
17
Dr. Robert B. PalmerBrookhaven National Laboratory Dr. Harvey A. Rose, T-DOTUpton. NY 11973 Los Alanos National Laboratory
Los Alamos, NM 87545Dr. Richard PantellStanford University Dr. James B. Rosenzweig308 McCullough Bldg. Dept. of PhysicsStanford, CA 94305 University of Wisconsin
Madison, VI 53706Dr. John PasourMission Research Corporation Dr. Alessandro G. Ruggiero8560 Cinderbed Rd. Argonne National LaboratorySuite 700 . Argonne, IL 60439Nevington, VA 22122
Dr. R. D..RuthDr. Samual Penner SLAC, Bin 26Center for Radiation Research P. 0. Box 4349National Bureau of Standards Stanford, CA 94305Gaithersburg, MD 20899
Dr. Jack SandveissDr. Claudio Pellegrini Gibbs Physics LaboratoryNational Synchrotron Light Source. Yale UniversityBrookhaven National Laboratory 260 Whitney AvenueUpton, NY 11973 P. 0. Box d666
New Haven, CT 06511Dr. Melvin;A. PiestrupAdelphi Technology Dr. Al Saxman13800 Skyline Blvd. No. 2 Los Alamos National LaboratoryWoodside, CA 94062 P.O. Box 1663, MS E523
Los Alamos, NM 87545Dr. Z. PietrzykFL-10 Prof. John ScharerUniversity of Washington Electrical-& Computer Engineering Dept.Seattle, VA 98185 University of Wisconsin
Madison, WI 53706Dr. Don ProsnitzLawrence Livermore National Laboratory Dr. George SchmidtP. 0. Box 808 Stevens Institute of TechnologyLivermore, CA 94550 Department of Physics
Hoboken, NJ 07030Dr. R. RatovskyPhysics Department Dr. N. C. SchoenUniversity of California at Berkeley TRWBerkeley. CA 94720 One Space Park
Redondo Beach, CA 90278Dr. Charles V. RobersonOffice of Naval Research Dr. Frank SelphDetachment Arlington U. S. Department of Energy800 North Quincy St., BCT # I Division of High Energy Physics. ER-224Arlington, VA 22217-5000 Washington. DC 20545
Dr. Stephen Rockvood Dr. Andrew M. SesslerLos Alamos National Laboratory Lawrence Berkeley LaboratoryP. 0. Box 1663 University of California. BerkeleyLos Alamos, NM 87545 Berkeley, CA 14720
18
Prof. Ravi SudanDr. Richard L. Sheffield Electrical Engineering DepartmentLos Alamos National Laboratory Cornell UniversityP.O. Box 1663, MS H825 Ithaca, NY 14853Los Alamos, NM 87545
Dr. Don J. SullivanDr. John Siambis Mission Research CorporationLockheed Palo Alto Research Laboratory 1720 Randolph Road, SE3251 Hanover Street Albuquerque, NM 87106Palo Alto, CA 94304
Dr. David F. SutterDr. Robert Siemann U. S. Department of EnergyDept. of Physics Division of High Energy Physics, ER-224Cornell University Washington, DC 20545Ithaca, NY 14853
Dr. T. TajimaDr. J. D. Simpson Department of PhysicsArgonne National Laboratory and Institute for Fusion StudiesArgonne, IL 60439 University of Texas
Austin, TX 78712Dr. Charles K. SinclairStanford University Dr. Lee Teng, ChairmanP. 0. Box 4349 FermilabStanford, CA 94305 P.O. Box 500
Batavis, IL 60510Dr. Sidney SingerMS-E530 I Dr. H. S. UhmLos Alamos National Laboratory Naval Surface Warfare CenterP. O. Box 1663 White Oak LaboratoryLos Alamos, NM 87545 Silver Spring, MD 20903-5000
Dr. R. Siusher U. S. Naval Academy (2 copies)AT&T Bell Laboratories Director of ResearchMurray Hill, NJ 07974 Annapolis, MD 21402
Dr. Jack Slater Dr. William A. WallenmeyerMathematical Sciences, NW U. S. Dept. of Energy2755 Northup Way High Energy Physics Div., ER-22Bellevue, WA 98009 Washington, DC 20545
Dr. Todd Smith Dr. John E. Walsh •Hansen Laboratory Department of PhysicsStanford University Dartmouth CollegeStanford, CA 94305 Hanover, NH 03755
Dr. Richard Spitzer Dr. Tom WanglerStanford Linear Accelerator Center Los Alamos National LaboratoryP. 0. Box 4347 P. 0. Box 1663Stanford, CA 94305 Los Alamos, NM 87545
Mr. J. J. Su Dr. S. VilksUCLA Physics Dept.1-130 Knudsen Hall 1-130 Knudsen HallLos Angeles, CA 90024 UCLA
Los Angles, CA 90024
19
• mon m re a n n m midm mm H E E tmmimmmiimmmnau
Dr. Perry B. WilsonStanford Linear Accelerator CenterStanford UniversityP.O. Box 4349Stanford, CA 94305
Dr. V. WooApplied Science DepartmentUniversity of California at DavisDavis, CA 95616
Dr. Jonathan VurteleN.I.T. PNV 16-234Plasma Fusion CenterCambridge, MA 02139
Dr. Yi-Ton YanLos Alamos National LaboratoryNS-K764Los Alamos, NM 87545
Dr. M. YatesLos Alamos National LaboratoryP. 0. Box 1663Los Alamos; NM 87545
Dr. Ken YoshiokaLaboratory for Plasma and FusionUniversity of MarylandCollege Park, MD 20742
Dr. R. W. Ziolkovski, L-156Lavrence Livermore National LaboratoryP. 0. Box 808Livermore, CA 94550
20
Top Related