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usaec ltr, 16 jun 1971

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»*TtS AMT tllCT« ICS COMMAN»

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INVKSTIGATICH OF FAST «AVE

BEAM/PLASMA IimftACTIOHS

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PERSONNEL

Contract DA-28-O^5-AIIC-020^l(B)

for the period

1 June - 31 August, 1967.

Senior Staff

F. W, Crawford, part time

(Principal Investigator)

P. Dlament, part time

T. Fessenden, part time

R. 3. Harp, part time

S. A. Self, part time

Part Time Graduate Research Assistants

J. Lee

V. Rlstlc

D. St. John

J. Tataronls

•ll-

ABSTRACT

This report describes a program of work on beam/plasma Interaction.

Both electrostatic and electromagnetic wave amplifying mechanienns are

under investigation. For the former, studies in the absence of a «titic

magnetic field are directed towards verifying the theory for the canes

of finite beam/infinite plasma, and beam/sarface wave amplification,

when transverse modulation is applied. Two distinctly different lines

are being followed for interactions in the presence of a ststic Magnetic

field: Electrostatic cyclotron harmonic wave interaction is being ex-

amined, both tneoretically and experimentally, iud the potentialities of

electromagnetic wave growth in the "whistler" node are being Investigated.

-Hi-

FOREWORD

Thl. contract repre.ents a three-year prognun of research on "Fast

V.ve BWpla«. Interaction." which is proceeding in the Institute for

Kim Research, Stanford Univer.ity. under the direction of Prof. r*.

Crawford a. Principai mve.tigator. The worK is pa^t of ^ECT DEFESD^

and ... -ad. po..ible by the .upport of the Advanced Research Projects

Agency under Order No. 695- " l- conducted under the technical guid-

iMi of the Ü. 8. Ar.y «l.ctronic. Coa-nd. This is the sixth Quarterly

Report, .ad cover, the period 1 June to 51 Augu.t, 1961.

-I»-

-v-

CONTENTS

Page

ABSTRACT -HI'

FCÄEWORD -iv-

I. INTRODUCTION 1

II. BEAM/PLASMA AMPLIFICATION 3

(A) Theoretical studies of beam/plasma interaction , k

(B) Experimental work on beam/plasma interaction. 16

III, ELECTROSTATIC WAVE AMPLIFICATION IN MAGNETOPLASMAS ... 24

(A) Experimental studies 24

IV. ELECTROMAGNETIC WAVE AMPLIFICATION IN MAGNETOPLASMAE . . 28

(A) Theoretical studies 28

(B) Experimental studies ?8

V. FUTURE PROGRAM 36

VI. REFERENCES

PUBLICATIONS, LECTURES, REPORTS AND CONFERENCEb

t.TST OF riGURES

Page

8

9

1 surface Wave Propagation Characteristics.

a) (c/a) = 1.90

b) (c/a) =1.36

, ^amction oi the -"^»'"i: t^e' "fo Lcount. when the finite velocity of 1 -^t

3 spaoe-charge waves on beam obtained by Doppler 14

transformation of plasma waves.

5 Profiles of plasma density, n and self-consistent ^ potential. ^ as a function o¥ radius.

4.4^«. variation of phase and 6 Beam-surface wave interaction: Variatio

amplitude along the tube.

♦ ^ field configuration for study of 7 Modified magnetic fi*" '^ *on phenomena.

cyclotron harmonic amplification v

.~>rw^' Tnterferograras of 8 Whistler dispersion measUreme

t^thr^ the plMM. the microwave signal propagated through tn

theoretical curves (full line;

10 Density shadow cast by axial antenna.

♦ ■i,, field set-up for whiitler 11 schematic of high magnetic field set P ^

studies.

21

26

SO

n 32

-vi-

I, IKTOOIXJCTION

The wave amplification effect associated with the interaction of an

electron beam and a plasma has attracted considerable attention over the

last few years, particularly from microwave tube specialists to whom such

interactions offer possibilities of constructing very high gain devices

which should be electronically tunable over wide frequency ranges. Since

the plasma plays the role of a conventional slow-wave structure, the inter-

action region should be free of metallic structures, a particularly sig-

nificant characteristic if millimeter w.-ve operation is envisaged.

The work being carried out under this contract is directed towards

utilizing the beam/plasma amplification methanism in microwave device

applications. So far, despite the efforts of many groups, it has not

been found possible to realize this potential fully. The most serious

obstacles to progress are that efficient coupling of an rf signal into

and out of the Interaction region has been found difficult to achieve

and that the amplifiers are frequently very noisy compared with most con-

ventional microwave tubes. The necessity of providing the m«ans of plasma

generation within the device, and the presence of a relatively high back-

ground gas pressure, add constructional problems beyond those normally en-

countered with vacuum tubes. Although satisfactory engineering solutions

to these latter difficulties could certainly be found, the coupling and

noise problems still require considerable further study to determine

whether competitive devices can be developed.

Of the many widely differing •s>ecta of bea«/plae»a Interaction,

thre« have been chosen for close examination under this contract. The

first of these la the interaction of an electron beam with a plaswa when

the modulating fields, *nd the w«»e growth, are in either the first sxi-

sywetrlc aode. or in the first aalouthtlly-vsryln« aode. Since with

transverse aotfulatlon several tntsrssttn« interaction and coupling osch-

anlsM bscoos possible. It is intended that • thorough investigation of

•uch pfcsinMSsna should be made under this contract.

Most previous work has been concerned with the thoore*lc*l descrip-

tion sad dsBonstratton of beo^plssoa interaction oechanlsos that wsn

-I-

be derived from cold plasma theory, i.e., from theory in which it is

assumed that the plasma electrons have no thermal or directed motions,

and that the injected beam is monoenergetic. When a dc magnetic field

is present, microscopic theory, in »hich single-particle behavior is

followed, predicts a much wider range of amplification mechanisms. Some

of these are simply modifications of those occurring in the absence of

the magnetic field, while others involve interaction of beams with trans-

verse energy with slow "cyclotron harmonic waves." This constitutes our

second area of interest, i.e., that of wave growth in magnetoplasmas when

the electron beam has a substantial component of transverse energy.

Our third area of interest is in electromagnetic wave amplification.

Theoretical studies show that, in addition to electrostatic wave growth

phenomena such as those Just described, there is the possibility of ob-

taining appreciable growth in the "whistler" mode when an electron beam

with transverse energy interacts with a magnetoplasma. This mode is a

right-hand, circularly-polarized electromagnetic wave, i.e., its electric

field vector rotates in the right-hand sense, which is also (conventionally)

the sense of rotation of the electrons about the magnetic field lines.

If a beam with transverse energy is moving along the field lines, there is

consequently a possibility of energy being transferred from the electrons

to the wave, and hence, for wave amplification to occur. The purpose of

our work is to demonstrate this type of interaction, and to examine its

potentiality for coupling to slow- end fast-wave circuits. Here "fast-

wava is interpreted to mean that the phase velocity of the wave is of

tt • order of the velocity of light.

Previous quarterly reports (QR) have described the background for

•ach of the topics in detail. Progress made during the reporting period

•111 be described in the succeeding sections.

-2-

II. BEAM/PLASMA AMPLIFICATION

Amplification due to interaction of an electron beam with an unmag-

netized plasma has been studied hitherto at Stanford and elsewhere.

Experimentally, electronic gains as high as 20 dB/cm, at frequencies up

to 1 GHz, have been observed In both m = 0 and m = 1 modes, and rea-

sonable agreement has been obtained with theoretical predictions. Although

electronic gain has been observed, however, the achievement of net gain

between an input and an output appears to be an elusive goal due to the

difficulty of achieving efficient coupling between the beam/plasma system

and external circuits. One of the principal aims of this study is to in-

vestigate coupling methods in the hope of realizing net gain.

Consider a system consisting of a beam of radius a interacting with

a plasma of radius b (b s a) . In practice, the plasma will be confined

in a dielectric tube which may itself be surrounded at some larger radius

by a conducting waveguide. For the present purposes,the specification of

the system outside the plasma radius, b , is unimportant. The usual quasi- 1 2

static analysis of this system exhibits a peculiar ambiguity ' in that

it apparently admits of two distinct mode types which have been called the

solenoidal and nonsolenoidal modes. This question has been examined in

detail in the past quarter and, as is reported in Section A below, it is

concluded that the nonsolenoidai lode is fictitious. It arises purely as

a result of the approximationa made in the usual analysis.

This result justifies the hitherto tacit assumption that it is the

solenoidal mode of quasistatic theory that gives the correct description

of the interaction for nonrelativistic beams. In this mode, there is no

time-varying space-charge within the volume;, but there is effectively a

surface charge due to rippling of the beam surface. This surface charge

acts as a source for the electric fields and for frequencies less than

the plasma frequency, when growth occurs, the fields are concentrated near

the beam surface.

When b is appreciably greater than a (say (b/a) > 1.5), then the

field at the radius b is very small.and the coupling to external regions

is very weak. Under these conditions the interaction is similar to that

for an unbounded (infinite^ plasma and is effectively due to coupling

-5-

between the beam modes and plasma oscillations. For this ctse, to

achieve efficient coupling it would be necessary to introduce coupling

circuits either into or close to the beam, i.e. within the plasma, and

this raise« a vsriety of difficult practical problems. One poF^'ble

■jans of overcoming this difficulty in the case of the m = 1 :.iode was

s>iggeated in QR 3, through the use of a locally enhanced plasma density

in the coupling regions,such that these regions are resonant in the di- 1/2

pole mode (at <u /2 ) for a frequency close to the local plasma fre-

quency in the main interaction region. Experimentally^ however, it

proved difficult to achieve the necessary control over the plasma density

profile along the axis.

«Then, however, the beam fills, or nearly fills, the plasms region,

((b/a) ma l) , the fields penetrate appreciably into the region external

to the plasms. Under y^ese conditions, provided the plasma is bounded

by a dielectric (with or without an additional external conductor), then

the Interaction is effectively between the space-charge waves of the

beam and the surface waves of propagation on the plasma column. In this

ess«, it should be possible to couple efficiently to circuits external

to tha plasma. This is highly desirable from the practical point of

view. For this reason we are studying, both theoretically and experi-

mentally, a« reported in Sections B and C below, a system in which the

beam and plasma fill a dielectric tube.

(A) Taeoretical Studies of Beam/Plasma Interaction,

Solenoidal and Nonsolenoidal Modes: In the usual quasistatic theory

of interaction between a cold electron beam of fini e radius and a cold, i y

uniform, unmagnetized plasma of the same or greater radius, it appears '

that there are two distinct uncoupled solutions which have been callfd

the Kolenoidal and nonsolenoidal modes. They have the following char-

«ct«ri«f,ics:

(i) Solenoidal Mode - This mode is characterized by

having zero time-varying volume space charge so that the

electric field ha* zero divergence, i.e. it is solenoidal.

Ho.ever, there is a surface charge on the beam surface.

This acts as a source for the electric fields, which are

-k-

non-zero both within and outside the beam. The dispersion

relation comes from solving the eigenvalue problem when

the fields inside and outside the beam i-.re mat hed, and its

form depends on the particular configuration JS regards the

external boundary of the plasma. For the simple case of an

unbounded plasma, the dispersion relation may be written,

2 2 CD (JD

l.-f.-Ji— 03 (ü) - ßv. )

— F 2 1

= 0 (1)

wherp the space-charge reduction factor F = ßa l'(ßa)K (ßa)

m is the azimuthal mode number, and I and K are modi- m i.i

fied Bessel functions, the prime demoting diiferentiation

with respect to the argument. There is a complete set of

normal mode solutions to Eq. (l) with different ß's , cor-

responding to the various raiial modes of the system.

(ii) Nonsolenoidal Mode - This is characterized by

the fact that there is no electric field external to the

beam, and there is a time dependent volume space-charge

within the beam, as well as a surface charge. The rf poten-

tial, 0 , within the beam is arbitrjry provided 0(a) = 0

at the beam surface. The dispersion relation for tl is mode

is 2 2

-E 5 ^ (ffi - ßvj2

= o (2)

which is the same as that for one-dimensional motion in an

infinite beam/plasma system.

The appearance of two distinct modes is disquieting and, in partic-

ular, the appearance of the nonsolenoidal ir-.de \ th a dispersion rela-

tion independent of the geometry, and with no fields outside the beam,

is suspect. The predictions of the two mode, concerning what would be

observed in a practical system are quite disparate,and one is led to in-

quire whxch mode would be excited and observed in practice. Furthermore,

since one requires fields outside the beam in order to facilitate coupling

-5-

into and from the system, It is particularly important to resolve this

issue. In the past, it has been tacitly assumed that the appropriate

mode in a finite beam/plasma system is the solenoldal one, and the ex-

istence of the nonsoienoidal mode has 1een neglected.

In the past quarter, we have examined this problem in detail and

find that the occurrence of the two mode types Is a degeneracy intro-

duced into the analysis through the use of the quasistatic approximation.

By making an exact analysis from the full Maxwell equations, including

relativistic effects, one finds Just a single mode type which, under

appropriate approximation, reduces to the solenoidal mode of the quasi-

static analysis. It appears that the nonsoienoidal mode of the quasi-

static theory is an artefact introduced through making the quasistatic

assumption ab initio.

This result is reassuring in that it justifies the neglect of the

nonsoienoidal mode. Furthermore, the full analysis gives precise mathe-

matics conditions, in the form of inequalities, under which the quasi-

static dispersion relation, Eq. (l), for the solenoidal mode is valid.

This equation is very much simpler to solve for k(üD) } or ^(k) , than

the full dispersion relation, and one may use it, rather than the latter,

provided one checks a posteriori that the exact conditions for its val-

idity are indeed fulfilled. A full report on this work is in preparation

and will be issued shortly.

Surface Wave Interaction: We are concerned here with developing the

theory for interaction between an electron beam and a plasma both filling

a dielectric tube ( f. = e ) of radii a , b , surrounded by an air-spaced

waveguide of radius c . 'he quasistatic dispersion relation for this

system was given in QR 5 (Eqs. 1 to 5). The numerical analysis of the

equations is complicated by the large number of parameters a, b,c,K =

(e /O etc., and the types of solution may change quite markedly with g 0

change of the parameters. Much insight may be gained, however, through

the use of the mode coupling formalism whereby one considers the inter-

action as due to coupling between the modes which can exist independently

on the beam and plasma. For this reason, we first consider the structure

of the surface wave modes for the plasma alone.

3 9ji§ • Jil . cu

«■ I , «i «• «• VMIM (*/•! , C«/»l •••nil«» ar« fiaa« «tuu« • «vtM»

IIM <uttwn l*r «»• firti

praciiMt wimm I • %4 , f^«l •I.I» •**

(l/*) . IW i|»nno —o ••©

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m^Mf rr«i«MitiM ii»MXt«< «•

If pr«9*t»(« Ift • ««PfM* *

•»• *•#!•«« I* • ).

I* «rwti««. tftft flfM

i« ft*. I tar «w

Mwiftit f«Maw. par^iftiftt «• «ft«

<!•»««*»•» «!•«««•. **•<! »r» ««•«««•« «• ft«M^»lMM IMWWiM

«fttai«*« e» 1m\tmm*

fm f - • . •II ell

U» • - .t«» «11 «ftl««» ftt »ft* ft**««»««»«

•

• «ft .

•f-

or K=4,6

(b/a)= 1.18 (c/a)= 1.90 a = 127cm

<&

12

070

0 35

0175

fp=500MHz

Vb =1180 VOLTS

Vb ^400V0LTS

Vb =100 VOLTS

• 25 VOLTS

fp=IOOOMHz

Vb=4700 VOLTS

Vb=l600 VOLTS

Vb= 400 VOLTS

Vb= 100 VOLTS

/3a

1 (•) Surface Wave Propagation Characteristics. (c/a) =1.90

-8-

3l3a

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"SpB tp*900KHt yoooi*«

070

099

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^•400\O.T9

vb-oovaTs ^•29VXTS

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1 (b) Surface Wave Propagation Cbaracierlatlea, fc/al • I.J

1

••v«» mm IM• f*l «l^p* mt l*m • • 0 «l*p«r*iMi carv«

fr» ^. (t) •• t»«« f«r Ift* pMM v«l«cliy «Mr UM orifla

« I« «artM* !• i»« ««••••«•tu •pproMlMtloo,

•I M «If «arrw« if •<<•,»• VCIMII» of Itfht. la

IM», mm t—m A • ((I I4vt) • ^fc/«))/»^ i.

•*«» «aitt( «• «• wi i»«« (• •) < < • . TIUS MMS

!«■■•» tor id»

to Mitoftto«

tat '•

i «f to. (^) t« to «arract. iai* ««atflllaa la •Xmmf likaly ta

£•0. tt^O.avMi

• ^•^^»MV«)^) • (Ha/*)* 'Ifl-'b'c)^)/'

(5)

to*. (*) Mi (to) II 1« «laa» ttot topatolaf aa ■. I.

(•^) «to (•<%) , MM Ma f . o cat-^fa. »^ , af Ma

•rtoa «MM My IM ato»a m tolM Ma tart«-^ •■yar-

(• -%*' i •»•»■• '*••. raa»a««l»alf, to Mckvara or

•**•• 9m ... •«..- t . b .«a (c^b) . M la «M« •• M Mat Ma M"*"* it

m*rm tor at#l

la «M «M* at • MU aal IM aiaia«tric tub«, a ^ fc ,

ffi 1 + K cm

cO

11/2

! . tH- (b/c)2m1 [l - (b/c)2"1]

(6)

From this it is clear that if (c/b) > [(K + l)/(K - l)]1/2

the cut-offs CD for all modes are greater than ü) ' cm p > and all the higher modes are backward. As (c/b) is reduced

then first the m = 1 mode, and successively, in order

higher modes become forward waves. Thus in Fig. l(a) for

(c/a) = 1.90, the m = 1 and all higher order modes are

backward, whereas in Fig. l(b), for (c/a) = I.36 , the

m = 1 mode is a forward wave, but higher modes are still

backward. It should be mentioned here that the nonzero

cut-offs, üi^ , for ß = 0 , for the m ^ 0 modes, appear

only in the quasistatic approximation. If CD tends to a

nonzero value as ß - 0 , it is implied that the phase vel-

ocity (ui/k) -«» f and one must expect the quasistatic

approximation to break down as the dispersion curve approaches

the light cone (ü)/k) = c . This is illustrated in Fig. 2,

where it is seen that in an exact analysis for the m / 0

modes, as ß -. 0 , the dispersion curve becomes asymptotic

to the light cone and passes through the origin while addi-

tional fast electromagnetic waves appear within the light

cone.

(ii) Surface Waves for the Beam Alone; For the three-region sys-

tem under consideration, the dispersion relation for the beam alone may

be written

a>2 b

(03 - ßy ) = F

m(ß,a^,c,K) . (7)

b'

It is clear that the modes of the beam alone may be obtained from the

modes of the plasma alone by replacing ^ by ^ , and performing a

-11-

2 Modification of the dispersion curve for a mode m ^ 0 when the finite velocity of light is taken into account.

-12-

in«», • • §• • ^J . At« •« n !«•«#•««• tar 9*9

• • 0 Mi • • I ■■tu i* »i«. ', I«HI mi<t»t i» tta p»

•« fi«. !(•). fw «M* •-«•Iw. «tar» »r» •«• witaw «•••» m

•M«fe »r» ■■it« •«•« ta • • C»»fc • *^1 ta» pa»M»*« «Mp

Ita «i*pw»i«» <tni—ii 9m %*•

— »n. I» »rtar •• ta tai». I« la

•ta «*• taftMiif (»^ •) . ita twi ta—«M»

•!••■» taMitf. »at i» p»»«ti«*l »i..

•rvita »!•«■• •?••«• •• »r» m%m *M«rtaMi<*>i« i» UMit ta ta

ci«»i> !••• tta« «Ulf. CWM««aMlf. ita nfirn«» ml **• nm tata

•»Ic» <M frf —*-> i* MiMlfta •• • .

•IM» tta iffii«» ta UM taM «tata i« «wii. uw» «ill tata u»

•»ic» ceMtllM «a» MpMt« Ita fMMIkllMt ta «r«»t» ♦•«*••

II t« nffffttaMM «• mir» uw »tata ta ift» ii»» rapfwwMtta ife» IM

v*l»riif, (•/?) • • , vti» i»» taiii»! »I»«». * ta «»• • » »

it*»» fef «i.(ta). If »^ < ta » , tta i»i»f»»«ii«» «««r« •«•

t» t» tiw • • o «ata I« m-mr, »taf»»t if »^ » ta^«

I» »» t»(»r»««tl»». »ta »• gtwm\m '••• ••t»«l«M. Ita f«»ffl«l»»l

A ■ ((■( i» c^) • ta(ta»))/3«)>/f iijuii «• it« •••»•trt. r», *«.

p»r«M«»r« of ri«».l(») MM l(») II 111 ■■ i tta »»IM» O.M »M

fMpwuvtaf«

dtff»r»«t MIMM »f (%A'Ä*) ••"• itaic»!»«. t»(l««i»g ita liMiiat

o»»» that mn Jas« !••««•« I AI I« Ita • • 0 MM».

.,.-

/<**

SLOW -CHARGE

WAVES

•t pimm »mm. r tr«Mf*r«B(i«Ht

•I*

corresponding to these lines are shown for two assumed values of the

plasma frequency, namely 500 and 1000 MHz, in the inset tables.

For the higher-order modes, m s 1 , it is clear that the beam

modes always intersect the plasma modes and interaction will always

occur, '/wo distinct types of interaction are possible according to

whether the plasma mode is a forward wave or a backward wave at the

point of intersection. In the first case, as for example the m = 1

mode in Fig. l(b), the mode coupling theory leads one to expect a con-

vective instability, that is to say, a wave growing in space in the? beam

direction, so that one might use it in an amplifier. In the second case,

as for example the m = 1 mode in Fig. l(a), mode coupling theory leads

one to expect a nonconvective, or absolute instability, so that the sys-

tem will behave like a backward-wave oscillator. These statements, how-

ever, need to be qualified as follows. In the case of a forward-wave

interaction, if there is sufficient reflection at the ends of the system

and there is a wave which can propagate in the reverse direction, then

the system will oscillate if there is some frequency for which the total

phase charge around the system is an integral of Sbt. and the loop gain

Is greater than unity. In the case of a backward-wave interaction, the

system will only oscillate if it is greater than a critical length.

Otherwise it will behave like a backward-wave amplifier with the ampli-

tude of Jhe wave Increasing in the direction opposite to the beam.

It should be pointed out that the foregoing ideas concerning the

instability types to be expected from an examination of the uncoupled

modes are based on the simple theory of the coupling of two modes. This

is at best an approximation, and can lead to incorrect conclusions con-

cerning the instability type to be expected. Consequently there is need

to carry out a thorough analysis for the particular systom under considera-

tlon, employing .he rigorous criteria for the determination of instabil-

ity and wave types. This we propose to do in the forthcoming reporting

period.

(iv) olutions for the Beam/Plasma System: The waves that can

propagate on the combined beam/plasma system are given by solutions of

the dispersion relation.

■15-

2 2

i '-I-- ^-p = r(ß) . (8) ü)2 (tt . ßvb)

2 m

This equation may be regaroad as a quartic for ü3(ß) or as a transcen-

dental equation for ß(^) . Because F is real whjn ß is real^ one

may find the solutions for simple propagating waves, i.e. with ü) and

ß both real, by solving for the real roots of the quartic ^ (ß real) .

Such solutions for the m = 0 mode, for the «jeometry of Fig. l(b)

and for (ü> /a) ) = o.Ol. (v^/^'a) =0.092 are shown in Fig. k as full op ' b p '

lines. These parameter values are chosen to correspond, as well as can

be Judged, to the experimental values reported below. There are three

such simpla propagating waves indicated: First, a mode propagating in

the positive (beam) direction, which is asymptotic to the plasma mou'e

for ü) < a« ' and asymptotic to the fast beam mode for CD > ü) ' ; second, P p '

a mode propagating in the positive direction which is asymptotic to the

plasma mode near ü) = ü) ' , and asymptotic to the slow beam mode for

ü) > ü) ' , and third a reverse mode, i.e. one propagating in the negative P

direction (opposite to the beam). This is effectively a pure plasma

mods since it is almost unaffected by the presence of the beam.

Besides these real-ü) real-ß roots, there are, for 0) < CD ' an in- P

finite set of complex-ß roots for real CD , The first of this set is

also indicated on Fig. 1|, as Mode (k). One may interpret this root as

corre .ondlng to an amplifying wave, but this interpretation is only

tentative since the system may possibly be absolutely unstable, and a

full stability analysis is necessary to settle this point. In the next

quarter is is planned to examine this question in detail and also to

study numerical solutions for the m = 1 mode.

(B) Experimental Work on Learn/Plasma Interaction.

The Beam/Plasma Tube: The discharge tube designed for the experi-

mental study of beam/plasma Interaction employing surface modes, illus-

trated in Fig. 5 of QR k, employs a beam-generated plasma in mercury-

vapor. An electron beam of a few hundred volts energy, and a few milll-

amps current, is formed in a planar triode gun, and passes into the

mercury-vapor (pressure ^ 2 mTorr at room temperature). Under these

-16-

o ca.

<\j G) O

J8 it

o , , ü ID o Q.

o ■; si 1 M * o *"■

£^ Sß' 5 __ H II ^^

-R JD a ■s 3 3 n

> cr o ÜJ X

< UJ

-S£

a: LU UJ

R P y O X X , X QJ lil - UJ

I o

II

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ü h H 0

h 8 y t, I

J= U c u 11 M X n 4, H (S c a t) z t a ** > d e » o i

ä - r » 3 0

-17-

5 conditions a steady-state theo.rv shows that the oeam nay travel the

length of the tube with little colllsional scattering, yet create by

lonlzatlon a iasma whose number density, n , nay be one or two orders

of magnitude higher than the number density ol the beam, IL . Prevloua

experience at Stanford with such beam-generated plasaas, In «hieb tbe

beam only partially fills the tube, have confirmed this, and furtbenore

have shown that such systems may be quiescent provided the growth of

spontaneous noise fluctuations due to beam/plasma Interaction does not

reach large-flgnal level In the tube length. This offera an advaniege

over the alternative arrangement, In which a beam la fired Into a sep-

arately maintained discharge, since the latter la frequently oolay.

Ideally, the electron gun operates auch like a vacuua tried« tn a

space-charge limited condition. In which the current Is controlled by

the first grid. In practice, however, the cathode la sore or leee le»-

perature-llmlted. It in then necesaary to atablllte tbe beater power to

a high degree and to operate the tube for soae coosldereblt ftae before

stable conditions are reached, alnce tbe eelaelon la set ee • beleoc» be-

tween activation and poisoning due to positive ton boaberOaent.

The ateady-atate theory of a besa-geoerated pltmm ahowa that, al-

though the bean density and hence the voluae tonlsetloo rate ere «aifor»,

the plasaa density Is nonunlfora, decreasing wltb radius a* abeea la

Fig. 5, Tbe plasaa denalty first falls slowly with redlus. sed tbe«

quite rapidly In tbe sheath region, the latter being of tbe order of

aeverel electronic Debye lengtbs froa tbe tub« «ell. figar« % aloe

abuwa ?he profile of tbe self-conelateat poteatlal, § , «bleb boa •

alallar fora to that of tbe doaeity profile an« attalas et tbe aall e

value 8o*e (> kT^/e) volte below the value «a aale, obere f ta tbe

plaaae electro« teaperatur« (« I eV} . rbe aaaaalforaity la pleMM

deaaltjr is laportenk la tbat It «111 reduce tbe grweta ret« «arba<l|

belea the valwee MlOttiaMi on tee beeta a« e «aiffana plMaa Tble

point la diarussetf furtlwr beloo.

tie of bave-eref f»tloa To elady »ae« prapegatlae mm tfce

fltf«d with I

m • •|>. MM Mlf-«M»|«lMt p»l#«||*l. #.

!♦•

touching the glass tube, and may be used to excite and detect either the

symmetric (m = O) or dipole (m = l) modes, through the use of suit-

able phase-shifts in the connecting lines. The detecting coupler may be

moved along the tube to allow measurements of phase and amplitude to be

made as a function of position.

In early experiments, the diameter of tue surrounding waveguide was

relatively large ( (c/a) = I.90) , the corresponding plasma mode disper-

sion diagram being Fig. l(a). Subsequently, the guide was reduced in

diameter to make (c/a) = I.36 , the corresponding plasma mode disper-

sion diagram being Fig. l(b). This was done in an attempt to avoid inter-

action in the m = 0 mode, so that interaction in the m = 1 mode might

be more easily observed. However, it appears that even with the smaller

guide diameter, because of a limitation of the beam voltage to less than

about 500 volts due to the onset of arcing in the gun, it is not possible

to avoid the possibility of interaction in the m = 0 mode for plasma

frequencies in the interesting range of 500 ~ 1000 MHz. In order to

avoid m = 0 interaction with low beam voltages and high plasma frequen-

cies. It would be necessary to reduce the discharge tube diameter a .

An incidental effect of reducing the ratio (c/a) is also to convert

the m = 1 plasma mode from a backward wave into a forward wave, as is

clear from Figs. l(a) and l(b).

Since, for the experimental conditions attainable with the L sting

tube, int-raction in the m = 0 mode cannot be avoided, it was decided

to take measurements for both the m = 0 and m = 1 modes, starting

with the symmetric mode. Some preliminary measurements of the m = 0

mode were reported in QR 5. Further measurements have been made in the

past quarter. Figure 6 shows the phase and amplitude of the m = 0 wave

as a function of position along the tube, as the detecting coupler is

moved aray from the exciting coupler, for a range of frequencies between

5I4O and ij-TO MHz. While the amplitude increases with distance, indicating

growth, there is a pronounced interference effect due to a beating of

waves with different propagation constants. This effect has been studied

and a satisfactory explanation has been developed as follows. Referring

to Fig. 4, it is clear that for frequencies a» < a» ' there are two P

-20-

CO

3

<

>

UJ er

«•O

KAM vaTMÄ eDVCLTf

4 6 AXIAL POSITION

4 6 8 AXIAL POSITION (cm)

Beam-surface wave interaction: amplitude along the tube.

Variation of pttamm mmt

-21-

«M pMpa*»«« »it» pMiti** f . i.«. i« UM taaa «lr«ctlea.

». «tift «»UUfMM, M ttw» «Itt M !• prtcitc«, lAt» «111 b« e«-

• inpM MM«. ?*• ■iM>i< •«*«, utM»ii«« («) t» • gr««««

l«l«t •«#•«» MMI •» «9MI«t %m «sell« b*tli «•*••, til«

IM««* «f «a« «■» «•<#«• «apaaiitg «a IIM «abet gt—ttry,

r, •••. I« »ppMr» itei •!••• i« m* ««««Ur. IIM iiapiti mv«

(!) I« fMiMUMW, tot tlBt t«rf»w »iMt «*• !•*• «*• gnwiAf v«v« (%)

pr«MM«»l«». Mi« «^iMa» «•? 1*« ji—-tm—ti clMr«ci«rt«tic« of

^»#. * *«■•*• tHUT «M «■»tlM. «fife • •■ill •!•»•, corrMpMtfta« to tM«

«•)!«* § of tto mm$m§ oo««. «M •■■— • Ur«or »lo^o •! Urg« tfl«-

llOg »O IftO ISff« # Of !%• ttWtOg OOVO.

%m Wm *mm ml mm 0*** itxo—o «orvo for mail «od

•IOM for $t for OMb oovo My too

oil» «fto tiMoroiiool «isporoioa MTVO, •• la

•o f 1«. *, I« mm%m «»• ««■p»n«M, iw frmoooey MOIO tea

fIM«« •» mmmmmt «»•« •«* >» Mü. *tl« • «UM fit to m« tiMory

loo off «a« aosuag «ffwi.

ij , M «««orMao« ftoo U« «lopo of

•la» M^II 11 mm u» itmn to rig. k, tHilo gr««tk it «>t«r>«< i«

I« «wr mm* Urn mmm «M itatIIIMI «oioo. far • • 1^7 «■, tte

iMtooo««iif to« ofeoioo» tvoot» foio (oi 4fe «i) I« o« Mr« IM« ? M/M.

• .«n «Mil IOM tftM prMiciM lanriUMll». m« My M

kit« MO» O «tfMg loffloMM I« pTMltM. TIM prlMlp«!

te mm $mmmmm mmm 11 i« tiMiy MOI »• »«•«•»«•«•« •ff«t< iiottiag

•• •••••• *mm to M« fIOOM itfnwgMHiif. to aw oorfM» •««• i»t«r*

•««Mo. mm fl«l* or« ilgMHotM MW IM »l«MO-«lolMtri( M«9««rr

and it is here, because of the presence of a sheath, that the inhomoge-

neity is greatest. A further effect is that strong radial electric fields

in the sheath are likely to deflect the relatively slow beam electrons

away from the surface where the interaction should be strongest.

In the measurements of propagation and growth in the m = 0 modb

it is observed that while a growing wave is measured for some distance

along the tube, the signal reaches a maximum and then decays past a cer-

tain point. This was illustrated in Fig. 1| of QR 5 and was interpreted

as being a result of beam b.-eak-up due to some signal on the beam having

reached large signal level. However, in view of the small growth rates

observeil in the m = 0 mode, it seems unlikely that the effect is due

to beam break-up in the m = 0 mode. It is possible, however, that it

is a result of beam breakup due to growth in some other mode e.g. m = 1 .

Certainly, the limitation of the signal indicates that the steady-state

conditions are not uniform along the length of the tube, though whether

the nonuniformity is due to beam breakup, or to some other effect, is not

entirely clear yet. It is intended to investigate this effect more fully

in the coming quarter, and also to make propagation studies in the m = 1

mode.

-23-

III. ELECTROSTATIC WAVE AMPLIFICATION IN MAGNETOPLASMAS

When the beam and/or plasma have directed or thermal motions in the

transverse and axial directions, it is necessary to derive the appropriate

dispersion relations using a Boltzmann equation formalism. The results

of doing so were discassed rather generally in QR 1 where it was pointed

out that, for a high enough value of the parameter (üU/OJ ) . i.e. the be' ,

ratio of beam plasma frequency to electron cyclotron frequency, even an

ion-neutralized electron beam could be unstable, and that in the presence

of a background plasma the instability threshold for the beam density

could be reduced. The purpose of this project is to investigate such inter-

actions, and to determine their potentialities for microwave applications.

Numerous theoretical predictions of the instabilities have been na de

at Stanford and elsewhere. Basically, the theory predicts growth in pass-

bands centered on the electron cyclotron harmonic frequencies (rtu ) . No

further computations will be carried out under this project until our ex-

perimental parameters have been measured. Those computations carried out

to date are being summarized in a Ph.D. thesis being written by J. A.

Tataronis, and which will be completed during the coming reporting period.

So far, few controlled experiments have been carried out to check the

theory, though observations of strong noise emissions from ir.agnetoplasmas

containing charged particles with appreciable transverse velocities pro-

vide significant support for the existence of the predicted mechanisms.

The studies planned under this contract are intended to provide results

under refined experimental conditions, and to put the theory on a firm

quantitative basis. In particular, we wish to verify the dispersion rela-

tion for the realistic case of a delta-function beam interacting with a

warm plasma.

(A) Experimental Studies

The aim of the experimental work under this project is to excite

growing waves by means of an electron beam injected into the plasm«, and

to study the variation of the growth rate as a function of the longitudi-

nal and transverse energies of the beam. The first, and slBplest, way of

imparting transverse energy to the beam is to inject It through an increas-

ing magnetic field into the interaction region. This does not create the

-24-

delta-function tran»v«r»« velocity dtstntMttoo «ftte* «Mt« Im mm% ••*

ilrabl« (or diocklac «laiaat theory. A mart ■• ItatMMrf «fpff«Mfi %• «a

use of a "oorkecrov" inject loo eyetes. A Iklr« «etlw« ebtc* ti oee

to apply becauae of ita greater fle&tbiliiy la tm taper! tr«oe««ree mmmmt

to tbe electrons by cyclotron beettflf la a eaell rf eoelly llwagk «ftlcft

the beaa peases before enterin« tbe plaaaa raflao. flue

extroaely difficult to resliae for our esyeriaaaisl eaadtiM

For convenience In our Initial studlea, a veraics ef «be lira«

finally been adopted.

The experlaental aet-up la aa aboaii to fif. 1. ttckl larpe «••l« be»e

been apacad ao as to give an aalat aagnetic field «alfam %m l>«tttff tbe«

0.54 over a region of five to als centiaetera ocaiered at tbe prefee Te

produce a rapidly varying ■agoetlc field cl*ae to the coibate. !«• •■■tl-

lary colla have been provided. Thea« cootrel tbe field la «be eleieitt

of the cathode, but do not dlaturb the uaiforatty of tbe field la like

region near the probe by oore than too or three perceot. f%a fielda dtoe

to the too coll ayataaa are cootrelloi by soparaie $mm aogplte« eo tfeat

the Inhooogenelty can be varied relative 1« UM bertlgr—d kmtQ&KB&m

field. The electros boaa la tajocted, through a potaoiial dlffecoase. al

an angle to the oagnetlc field. Tbe tyateo la «—tf K •• UMl tbe LanHT

radius of the electrons la large taa»irid to ta« diataace of tbe grid ttwm

the cathode. In thla »ay, J*» electroaa trevei l» «oaoeiiellf atreigb«

lines through the grid region, sad then atari rvMtting abawl Ibe «agoets«

field Unas In the oeah field region. Yhe treaeveree «••rgy, • # la 2 '

equal to «Vain 9 , «körn V te tbe potential drop of tne grid, as« tbe

angle, 0 , tbst tbe lajectton ayetno nah*« eitb «be aingoe««c field ka < *

Thus, in thla caae, V • «-/h , «here ^t • W t UM etevtmna «M« «Mn

injected lato a high oegncttr 'told ragio* «bicb e««« ee a mttm I« to-

croeae the traaavora« energy of tbe baas. Thla aye in» baa «be n#»obtdgM

that It «ill alloo us to vary Ibe tranevnrae aad longllndttnal a^eegi of

the bann by chaagiim the ratio of tbe field pvatfooni by UM Ibdf» e»tle

to tnst produced by UM anall colls

Th« theoretical prodictiooe tor this lygo «9 taoiaftllilf ladtcaia

that It otll getwrelly be abnotete. I.e. aigaela «nil trm ttmm avtoa,

and esteraal «atfolatton «til not bo rsBotrod to «biet« a«

•

This has been confirmed qualitatively by the previous experimental work

which it is hoped to refine quantitatively in these studies. For example,

in a PIG discharge Landauer' observed radiation out to about the 45th har-

monic, fitting the relation {(O/biJ = n to better than 2$. Bekefi and

Hooper observed strong cyclotron harmonic radiation from a beam generated

discharge in mercury-vapor. As here, they produced the necessary trans-

verse energy by magnetic field inhomogeneity. Ikegami and Crawford9 have

also made measurements of radiation near cyclotron harmonics for a beam-

generated mercury-vapor plasma in a magnetic field producec by Helmholtz

coils. The mechanism for producing transverse beam energy was again an

inhomogeneous magnetic field.

During the previous reporting period, we studied radiation from an

argon positive column discharge immersed in the inhomogeneous magnetic

field produced by the set-up shown in Fig. 5 of QR 5. Great difficulty

was experienced in interpreting the many peaks in the noise spectrum.

The work was continued into the present reporting period until the modi-

fications leading to the set-up of Fig. 7 were adopted. Making these has

taken up much of the remainder of the quarter, and only preliminary re-

sults are available with the new configuration. These will be extended

during the coming quarter, and will be reported on in the next QR.

■27-

IV. ELECTROMAGNETIC W.iVE AMPLIFICATION IN MAGNETOPLASMAS

In the absence of a static magnetic field, interaction of an elec-

tron beam with a plasma leads, only to electrostatic beam/plasma inter-

actions of the types described in Section II. When a static magnetic

field is present, there are additional possibilities of electromagnetic

wave interaction. That of special importance under the present contract

is the interaction with the right-hand polarized electromagnetic wave

known in ionosphere terminology as the "whistler" mode. It has been dem-

onstrated theoretically that under conditions where a beam with transverse

energy interacts with the plasma, wave growth in this mode should be pos-

sible^ and that experimental situations in which this dominates over the

electrostatic growth mechanisms occurring at the same time appear to be

realizable.

Comparatively little experimental work has been reported so far on

propagation of the whistler mode in laboratory plasmas, and none of this

seems to have been directed towards observation of wave growth due to

interaction with a gyrating electron stream. Such a demonstration forms

the primary object of this project. If growth in the whistler mode could

be demonstrated, and utilized, it would offer very attractive practical

features. In particular, coupling should be facilitated, since the ampli-

fication occurs in fm electromagnetic mode, i.e., without conversion to

an electrostatic mode.

The aims of the present project are as follows: First, to elucidate

the theory of the whistler-type instabilities ,.n the simplest geometry,

and then to extend this to more realistic physical conditions, and second

to demonstrate directly by experiment that growth can occur in this mode.

(A) Theoretical Stud a.

No new analyses or computations have been carried out during the

reporting period. However, in connection with his Ph.D. thesis prepara-

tion, J. A. Tataronis has gathered together details of all our work in

this area to date. These will be written up in report form during the

coming reporting period.

(B) Experimental Studies.

Studies of whistler propagation have continued in the small magnet

-28-

■etup during the quarter. The wavcltncth of the ehtttler eeve« ta Uto

plasma was measured using the follovlng techalque: The slgMl rsufIsi

between the two antennas «as coapared with a reference algasl wht^t MS

larger than the trsnamltted signal, so that the too would edi aad sub-

tract when in and out of phase. This compared signal was sailed wtta

an electronic circuit that converted the slgnsl occurrli* during a ttaa

interval less than 2 »sac long Into s voltage that was dlaplayod on the

Y-axis of a graphical recorder. The sanpllng circuit was swthronlaed

with the pulsed discharge, and adjusted to select specific densities

for experimentation. The separation of the too antennae waa warled and

plotted on the X-axis of the recorder. This technique prodiced Intor-

ferograms of the type presented in Fig. 8. The wavelength In the plaami

was obtained by measuring the distance between successive naxlma (or

minima) of the interferograms.

Results obtained from many interferograms are plotted in Fig, 0,

The points represent experimental roaults, while the lines sre obtained

from the infinite, cold, collisionless, whistler dispersion relation.

In normalized form, this is,

kc cu 2 2 -1/2 {ex /ti£)

i + P b; -(1--) CD v (ü ' b b -

(9)

Notice that the agreement is quite good for 'arge values of k corres-

ponding to short wavelengths in the plasma. At lower frequencies, coi-

responding to longer wavelengths, the agreement Is not as good. This

result is to be expected because of the finite size of the experimental

apparatus. It was found experimentally, that for wavelengths in the

plasmas greater then 3.75 cm (= half the plasma diameter), the finite

geometry effect; became important, and the infinite plasma dispersion

relation was no longer valid.

The variation of the wavelength in the plasma visible in Fig. 8 was

a result of density gradients in the z-direction resulting from the axial

probe. Figure 10 is a plot of the relative density along the axis as a

function of the distance from the axial probe at different times in the

afterglow.

-29-

/

"1VN9*S CGiilhSNVyi

■30-

-i8

1 rw

9

-

ti •

I1 11 ■

I. -

/ >

-31-

d e 0'

■t-

•a

0 i ■a

a

o

SIXV ONCnV AllSN3a 3AllV13ä

-32-

, •■ ■

Due to a variety of reasons.it was found to bu poeclbU to otttsta

experimental dispersion relations which agreed with thoory only «vwr •

limited range of parameters. At low plasma deiwiftlw», or at low MgMtlc

fields, the wavelength in the plasma was too long to b. Masurad accur-

ately with the probe system that was used. Tha effects of oonunlforM-

ties in the magnetic field became very important when the syste« was ad-

justed near cyclotron resonance. These effects Halted the experlMBtal

range of the parameter (cu/ü^) to O.k < (o)^) < 0.9 . Althoufh tha

maximum density obtainable with the reflex plasma source waa greater

than h X 10 ■ /cm , it was necessary for the minimum of plasma density

at the axis to disappear before experiments could be performed. Tbla

limited the maximum plasma density that could be used for experimentation

to less than 5 x 10 /cm5 . It is unlikely that the maximum plasma

density can be increased using this source because, at a plasma deaalty

of 4 x 10 /cm , the gas is nearly fully ionized in the pressure range

where the source operates (0.5 < p < 2 mTorr).

This series of experiments completes the prelimiaary whistler stud-

ies using the small magnet system. The experimental apparatus used in

the small system is currently being transferred to the large magnet, and

is nearly ready to begin. A diagram of the experimental apparatus la

given in Fig. 11. The experimental arrangement is similar to that uaad

in the small magnet system. The principal differences are: (i) the

axial probe is not inserted through the cathode of the pulsed reflex

source, and (ii) the radial antonna is moveable, so that measurements

of the radial variations of the waves can also be made. As mentioned

in the last report,the magnetic field is uniform to 0.25 percent and has

a maximum value of 7.7 kilogauss.

The initial experiments performed on the large magnet system in

which the plasma is created by an intense rf source have not been suc-

cessful due to an unexpected complication. The dc power supply for the

magnet h ', as its controlling elements, three high-power thyristors

which are phase-controlled. The intense rf pulses cause the thyristors

to trigger at unpredictable times,resulting in a loss of control of the

large magnet. It does not seem feasible to shield the magnet power

-35-

I i ;

i I I 0

I

!

-5fc.

if —f-tmir tmm ti«) ISIMM rf rUHti—. Cmmm^mmtlf, it

I «*•! !*• p«a««« IMfl«B MM «MM »• W^lgni U tto M«

«••. All« MftM- ^««M WHM «kr» toUf tavwti^t«4

tori«t i»« c«M«i f«Mrt«r# »tatfy «f «M«tt«r «•*• pr»pu»u— «til

•• «iMirw taM »ilk ir«—>w tmm%3 mm to t«jMtto tat* • pl»tm

toll to iMMll^iito « t.W «Mil »«Mt «yat«. Ito mt*4 mmm • fmr-

•ll«l I^MIIM m**»m%m, «to to* to« xm^tw* «, toM «to tolto.,.11

A PMMto« «t*to*««l«ff« «f I«« wUMtf !• UMI !»• |«J«clto k«M it forw«

I« • »««IM «f «Mfe ri*U( »ag lajMito mi« • r««iM «r »trw« fft«.

«M*lag • <r«Mf«v *rf parallel mm%$ Ist« ir««*v«rM MM>tl, «to • rtow ,>** •* »•• «VM* MCII«! «f la« «MW», tin« poist t* mtir ««Mitoraii«*

-35-

■MI mt i»« «•tail« «f mm pr9*nm Im tiw MMI«

«Mil vttk !• UM rmX0vmm% tum*mtu*l mm t^inwini

C«<U«M ll-IV. tHMTMUl. tte PMCTM I« M Mft«M

(t) »M» »U«M ««pllflMUM «••% UMMWM ■^■llBUl —

IkMrvtiMl «w% vtll «MUMM «a iM^tiMfan mm

laiavitiina rir«i f*r taw • • o «MM OM» fa» u*

• • 1 mmm. it i« ••!uip«««« tMm mm mmmmmmtm

m tto —im-*tt nmmm <mmtrm%m m tm «til »• «».

»i*i«« «Mrur( Mi tiMf twtter .IMIM «tit k« «»«• U • wr« flwtfeu —ti——tf pn,,,! ^„^

|lt| tS««lr»«««iic (Mw •«pt|flc«fl«i !• «««•(««I««»« ••

raawt« es t*« ••i** •»•ctrw «*• «•

«••• «MIMUM tf imumm vtui UWM-

♦•r.« -Mp «ill M «.«• |S OM MtatMg -, n ,

ft«)« cMfi««r«iM« MMTIM« I« Utt* Mfwi, HIM

•ilk • *im M i««*tifri«i UM mnmm rr«|«MciM

•• tm »mmtm, mm *IM M» üB «f **f ifyi^ im

mmmf fMauuilv^y r«r • «•IM-IMMIIM MM I»I«C-

MtMt «ttk • Mt« *U«M.

(ill) tlMtrHigaiiic MM MpttftcaiiM i» M«MiM>««Ma —

mt tttm r«l***»t «i«^«r«i«i r«UiMM «111

■ MMIcAlty. A ^«riievlsr petm M r«c«lv«

• IMBIIM I« UW ca^Mtttlen of grOTttt rat«« «I i n j 11

lag M«« »mmUtfit* proc—mm la tM Mitt).. frMMMy

rMf«. ^r«PM*tloe MMwr««»at« «ni b» «IMMM la tM

l-b«ttd «rat«« prvparatorr to tatrMucla« m «laetroa MM

•tl» traMvara« «Mrgy to aaclt« »aw grootb.

. .

i.

*tif. •. *.. iMitt««« tm rt**««

tM»«r»ii9 ftiMltri. C«iif«r«i«

► !■• I« ■»

». ». A. •rtl, •. A., i. tp^i. pn,.. ^||

CüSk).

■•

.•., i. BMl«r to. H. c^, • ,

•r« 0., «at liipii. I. 0.. Ap^t. pay.. Leiter« ^ lyy (1964).

». tiMVMi. t. ,^ .r*»lurtf r. 1. "^w. V||th jn,, „..,,„„, Conf.r-

rkiarauM m l<Mii«*a «MM, migi ... Yuto#i.»».f Augu..

IC. Btll. T. f., ««d iHMMt, 0., Piyt. Mv. j^^, 1:<X) (i^).

•37-

ICA-noRS, LKTURES, REPORTS AXD CONFER^f iS

Contract Dk-2B-0k^-AMC-0y)kl{E)

I Juo« - 31 August, 1967

1. Qmrtmrly Rvport No. ^ (l March - ^1 May 1967)

l.P.R. 1(0 (June 196?).

2. Dlaaant, P., "inverse Velocity Space Spectra and Kinetic Equations'

l.P.R. 175 (June 1967).

Am. J. Phys. (to be published)

3» Dlament, P., "integral Equations for Inhomogeneous Magnetoplasma

Waves"

l.P.R. 17U (June 1967).

k. Crnwford, >'. W., and Tataronis, J. A., "Some Studies of Whistler

Mode Amplification"

[= l.P.R. 151 (April 1967)].

* 8th International Conference on Phenomena in Ionized

Gases, Vienna, Austria, August 1967.

(To be published in the Proceedings).

Dr. J. Carter (Fort Monmouth) visited the Laboratory on July 20, 1967,

lor discussion of the work.

-58-

UNCLASSIFIED Secufily ClassifiriUion

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Stanford liniversity Stanford, California

2«. REPORT SECURITY eu»»IIFIC« TION

UNCLASSIFIED 2b. CROUP

NA i «t riiin T n t L t

FAST WAVE BEAM-PLASMA INTERACTIONS

4 DESCRIPTIVE NOTES fTVpr o/ri-por( nm/ iiic/ut/ve d«(e«;

Sixth Quarterly Report (1 June - 31 Auf.ust 1967) s AU rnoRlsl (Firm name, miildlo inlliml, ISMI mime)

STAFF

Wt ^ OR T D A 1 E

September 1967 M1HAC1 OR CiHANT NO

DA 28-043-AMC-02041(E) h. PROJECT NO

7900.21.2A3.40.01.50.410.5

7«. TOTAL NO Ol- PAGES

2S. Tli. NO or RE rs

»a. ORIGINATOR'S REPORT NUMBEHIS)

SU-IPR 201

JX

9l>. OTHER REPORT NOIS) (Any olhet numdor» ihi.l muy fc.' Hmalant Ihlt report) "

ECOM-02041-10

This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of CG, USAECOM, Attn: AMSEL-KL-TG, Ft. Monmouth, N.J. 07703

Jl'PlEMINTARV NOTES

It AHhTRACT

12. SPONSORING Ml LI1AHV ACIIVirf

U.S. Army Elactronlcs Command Ft. Monmouth, N.J. 07703 - AMSEL-KL-TG

This report describes a program of work on beam/plasma Interaction. Both electrostatic and electromagnetic wave amplifying mechanisms are under investiga- tion. For the former, studies in the absence of a stat'c magnetic field are directed towards verifying the theory for the cases of finite beam/infinite plasma, and beam/surface wave amplification, when transverse modulation is applied. Two distinctly different lines are being followed for interactions in the presence of a static magnetic field: Electrostatic cyclotron harmonic wave interaction is being examined, both theoretically and experimentally, and the potentialities of electromagnetic wave growth in the "whistler"! mode are being investigated.

r I

DD ,'°B.".,1473 UNCLASSIFIED MCUntV ('liii.sifiidtiun

UNCLASSIFIED Security CUitsifirution

KEY WORD!

BEAM/PLASMA FAST WAVE INTERACTION PLASMA COUPLING TRANSVERSE INTERACTION MICROWAVE AMPLIFICATION HIGH POWER

imi-ssimLL Svcurii' ( lasKiflcatiun

. .