PROCEEDINGS
OF
THE
IRE
three
power
inputs;
20,
5,
and
1
mw
peak.
The
fine
structure,
particularly
evident
in
the
20-mw
curve,
is
related
to
the
standing
wave
ratio
of
the
microwave
line.
At
points
of
poorer
matching
(i.e.,
at
3000
and
3400
Mc),
the
incident
power
upon
the
detector
is
diminished,
with
a
consequent
lowering
of
the
amounit
of
light
quenching.
THE
FUTURE
OF
THE
PLASMA
DETECTOR
The
plasma
microwave
detector,
as
it
exists
today,
does
not
rival
the
crystal
rectifier
as
an
envelope
detec-
tor.
A
standard
crystal
rectifier
can
detect
signals
with
strengths
in
the
order
of
10-8
watts.
In
the
present
state
of
development,
the
plasma
detector
under
optimum
conditions
can
respond
to
about
10-6
watts
of
inicident
eniergy.
A
crystal
semiconductor
used
as
a
mixer
can
de-
tect
microwave
signals
as
small
as
10-13
watts.
The
plasma
microwave
detector
has
not
been
investigated
for
any
mixing
properties.
There
are,
however,
several
approaches
available
to
improve
the
present
minimum
detectable
signal
level.
An
obvious
nmethod
of
increasing
the
plasma
detector
sensitivity
is
to
employ
a
dc
magnetic
field
so
as
to
cause
the
plasma
electrons
to
execute
cyclotron
motion.
In
this
condition,
the
electrons
are
more
efficient
absorbers
of
imicrowave
energy
at
particular
microwave
frequencies,
and
will
produce
miore
profound
quenching
of
light
out-
put.
The
relationship
of
magnetic
field
to
applied
micro-
wave
frequency
muay
be
related
simply
by
B=0.357f,
where
B
is
the
magnietic
field
in
Gauss
and
f
is
the
ap-
plied
mnicrowave
frequency
in
MV1c
per
second.
Thus,
to
produce
maximum
signial
enhancement
at
3000
Mc,
a
1070-Gauss
imiagnetic
field
would
be
employed.
Such
operation
will
narrow
the
banidwidth
of
the
device.
Practical
difficulties
miay
preveint
full
uitilization
of
the
advanitages
expected
from
operation
at
cyclotron
resoniance.
These
difficulties
concerni
the
comnpromiiise
necessary
in
optitmiumn
gas
pressure
to
satisfy
the
conl-
flicting
requirements
of
m-ninimlizing
pressuring
broadlen-
ing
effects
on
cyclotroni
resonance,
miaintaining
a
stable
discharge,
and
minimizing
unwanted
electroni
loss
through
diffusioni.
The
miagnietic
field
required
for
cyclo-
troni
resonian-ce,
however,
yields
the
a(lvanitage
of
re-
straining
electron
diffusion.
Methods
to
enhance
or
multiply
the
incident
micro-
wave
signal
offer
other
senisitivity
increasing
tech-
niques.
The
use
of
"squeezed"
waveguide
sectionis,
resoniant
cavities,
and
similar
structures
effectively
multiplies
the
incident
power
density
upon
the
detector.
These
manipulations
also
narrow
the
bandwidth
of
operationi.
Finally,
it
should
be
remembered
that
we
can
meas-
ure
only
what
we
can
see.
The
present
method
of
dis-
play,
presentation,
and
observation
leaves
much
to
be
desired
as
far
as
determining
the
ultimate
sensitivity
of
this
device.
Interaction
of
a
Modulated
Electron
Beam
with
a
Plasma*
G.
D.
BOYDt,
MEMBER,
IRE,
R.
W.
GOULDt,
MEMBER,
IRE,
AND
L.
M.
FIELDII,
FELLOW,
IRE
Summary-The
results
of
a
theoretical
and
experimental
investi-
gation
of
the
high-frequency
interaction
of
an
electron
beam
with
a
plasma
are
reported.
An
electron
beam,
modulated
at
a
microwave
frequency,
passes
through
a
uniform
region
of
a
mercury
arc
dis-
charge
after
which
it
is
demodulated.
Exponentially
growing
wave
amplification
along
the
electron
beam
was
experimentally
observed
*
Received
by
the
IRE,
August
7,
1961.
This
work
was
sup-
ported
by
the
Office
of
Naval
Research,
Contract
NONR
220(13).
t
Bell
Telephone
Labs.,
Inc.,
Murray
Hill,
N.
J.
t
California
Inst.
of
Tech.,
Pasadena,
Calif.
Tl
Microwave
Tube
Div.,
Hughes
Aircraft
Co.,
Culver
City,
Calif.
for
the
first
time
at
a
microwave
frequency
equal
to
the
plasma
fre-
quency.
Approximate
theories
of
the
effects
of
1)
plasma-electron
col-
lision
frequencies,
2)
plasma-electron
thermal
velocities
and
3)
finite
beam
diameter,
are
given.
In
a
second
experiment
the
interaction
between
a
modulated
electron
beam
and
a
slow
electrostatic
wave
on
a
plasma
column
has
been
studied.
A
strong
interaction
occurs
when
the
velocity
of
the
electron
beam
is
approximately
equal
to
the
velocity
of
the
wave
and
the
interaction
is
essentially
the
same
as
that
which
occurs
in
traveling-wave
amplifiers,
except
that
here
the
plasma
colum
replaces
the
usual
helical
slow-wave
circuit.
The
theory
predicting
rates
of
growth
is
presented
and
compared
with
the
experimental
results.
1906
December
Boyd,
Gould
and
Field:
Interaction
of
a
Modulated
Electron
Beam
with
a
Plasma
I.
INTRODUCTION
I
N
1929
Tonks
and
Langmuirl
reported
oni
experi-
ments
involving
electron-plasma
oscillations
and
defined
the
electron-plasma
oscillation
frequency
nloee(1
(,,
2
=
(1)
meO
where
e
is
the
magnitude
of
the
electronic
charge,
m
its
mass,
no
the
density
of
plasma
electrons
per
unit
volume,
and
C0
the
permittivity
of
free
space.
(MKS
units
are
used
throughout
this
paper.)
When
the
electron
thermal
velocities
are
small
com-
pared
to
the
velocity
of
waves
being
considered,
the
plasma
can
be
characterized
by
a
dielectric
constant
e
(cop2
-=
1-
-
)
(2)
Eo
(
-
r)
where
w
is
the
angular
signal
frequency
and
v
is
an
effec-
tive
collision
frequency
for
the
plasma
electrons.
For
the
experiments
described
in
this
paper
the
effect
of
the
massive
positive
ions
may
be
neglected.
In
1948
Haeff2
suggested
that
plasma
oscillations
excited
by
a
directed
beam
of
charged
particles
might
be
responsible
for
certain
types
of
RF
energy
received
from
the
sun,
and
he
discussed
the
mechanism
of
two-
stream
amplification.
Bohm
and
Gross3
have
given
a
more
extensive
discussion
of
the
interaction
of
an
elec-
troin
beam
and
a
thermal
plasma.
Complex
propagation
constants
were
found
for
waves
whose
frequency
is
ap-
proximately
equal
to
the
plasma
frequency
defined
in
(1).
The
significance
of
the
complex
propagation
con-
stant
is
that
small
disturbances
are
amplified
as
the
beam
drifts
through
the
plasma.
In
an
earlier
paper
Pierce4
had
noticed
a
similar
instability
when
an
elec-
tron
beam
passed
through
a
positive
ion
cloud
and
had
attempted
to
relate
this
to
positive
ion
oscillations
ob-
served
in
vacuum
tubes.
These
discoveries
have
stimu-
lated
a
very
great
amount
of
theoretical
study
of
in-
stabilities
in
plasmas
with
non-Maxwellian
velocity
dis-
tribution.
The
amplification
mechanism,
however,
is
es-
sentially
that
of
the
double-stream
amplifier
invenited
by
Haeff5
and
independently
by
Pierce
and
Hebenstreit.6
In
I
L.
Tonks
anid
I.
Langmuir,
"Oscillations
in
ionized
gases,"
Phys.
Rev.,
vol.
33,
pp.
195,
990;
1929.
2
A.
V.
Haeff,
"Space-charge
wave
amplification
effects,"
Phys.
Rev.,
vol.
74,
pp.
1532-1533;
1948.
Also,
"On
the
origin
of
solar
radio
noise,"
Phys.
Rev.,
vol.
75,
pp.
1546-1551;
1949.
3
D.
Bohm
and
E.
P.
Gross,
"Theory
of
plasma
oscillations.
A.
Origin
of
medium-like
behavior,"
Phys.
Rev.,
vol.
75,
pp.
1851-1864;
1949.
Also,
"Theory
of
plasma
oscillations.
B.
Excitation
and
damp-
ing
of
oscillations,"
Phys.
Rev.,
vol.
75,
pp.
1864-1876;
1949.
Also,
"Effects
of
plasma
boundaries
in
plasma
oscillations,"
Phys.
Rev.,
vol.
79,
pp.
992-1001;
1950.
4
J.
R.
Pierce,
"Possible
fluctuations
in
electron
streams
due
to
ions,"
J.
Appl.
Phys.,
vol.
19,
pp.
231-236;
1948.
6
A.
V.
Haeff,
"The
electron-wave
tube,"
PROC.
IRE,
vol.
37,
pp.
4-10;
January,
1949.
6
J.
R.
Pierce
and
W.
B.
Hebenstreit,
"New
type
of
high-fre-
quency
amplifier,"
Bell
Sys.
Tech.
J.,
vol.
28,
pp.
33-51;
1949.
the
case
of
the
plasma,
one
group
of
charged
particles
is
stationary.
Several
experiments
have
been
performed
in
which
directed
electron
beams
are
passed
through
the
plasma
region
of
a
gas
discharge.
Looney
and
Brown's7
early
experiment
is
representative.
A
beam
of
high-einergy
electrons
(several
hundred
volts)
was
injected
into
the
plasma
of
a
dc
discharge
from
an
auxiliary
electron
guIl.
RF
signals
were
detected
by
a
small
wire
probe
placed
in
the
beam.
The
probe
was
movable
and
showed
the
existence
of
standing-wave
patterns
of
oscillatory
en-
ergy.
Nodes
of
the
pattern
coincided
with
electrodes
which
bound
the
plasma.
The
thickness
of
the
ioIn
sheaths
at
these
electrodes
determined
the
standing-
wave
pattern.
The
frequencies
of
oscillation
seemed
to
be
related
to
the
transit
time
effects
of
the
electrons
between
the
sheaths
and
did
not
appear
to
verify
the
theory
of
Bohm
and
Gross.3
Later
Gordon8
investigated
the
energy
exchange
mechanism
which
was
involved
and
showed
that
the
results
of
Looney
and
Brown
might
be
understood
in
terms
of
reflex
klystron
oscilla-
tioIns
due
to
the
electron
beam
being
reflected
by
the
sheaths.
He
found
that
the
radiatioin
detected
by
the
probe
was
due
to
the
fields
of
the
bunched
beam
and
not
primarily
due
to
plasma
oscillations.
Wehner9
had
previously
built
a
plasma
oscillator
using
this
klystron
bunching
principle.
Very
recently
Kofoid10
found
oscillations
very
similar
to
those
of
Looney
and
Brown
when
two
oppositely
directed
electron
beams
were
passed
through
the
plasma.
This
result
tends
to
support
Gordon's
con-
clusion.
The
dispersion
equation
for
small
amplitude
waves
in
a
system
consisting
of
a
beam
and
a
collisionless
plasma
has
beeni
derived
by
a
number
of
investigators.
C
o2
(cb,
2
1
=
+
co2
(W
-
TVb)2
(3)
where
,x,
is
the
plasma
frequency
of
the
plasma,
COb
iS
the
plasma
frequency
of
the
beam,
and
Vb
is
the
drift
veloc-
ity
of
the
beam.
A
number
of
simplifying
assumptions
have
been
made
in
obtaining
this
result:
1)
Only
small
sinusoidal
waves
have
beeni
considered.
2)
The
electric
vector
and
the
direction
of
propaga-
tion
of
waves
have
been
taken
parallel
to
the
di-
rection
of
the
beam
(longitudinal
waves).
3)
All
quantities
were
independent
of
the
coordinates
7
D.
H.
Looney
and
S.
C.
Brown,
"The
excitation
of
plasmiia
os-
cillations,"
Phys.
Rev.,
vol.
93,
pp.
965-969;
1954.
8
E.
I.
Gordon,
"Plasma
Oscillations,
Interactions
of
Electron
Beams
with
Gas
Discharge
Plasmas,"
Ph.D.
dissertation,
Mass.
Inst.
Tech.,
Cambridge;
1957.
9
G.
Wehner,
"Plasma
oscillator,"
J.
Appl.
Phys.,
vol.
21,
pp.
62-63;
1950.
10
M.
J.
Kofoid,
"Experimental
two-beam
excitation
of
electron
oscillations
in
a
plasma
without
sheaths,"
Phys.
Rev.
Lett.,
vol.
4,
pp.
556-557;
1960.
1961
1907
PROCEEDINGS
OF
THE
IRE
perpendicular
to
the
direction
of
the
beam
and
the
effective
beam
boundaries
were
nieglected;
i.e.,
the
problem
was
considered
one-dimeinsional.
4)
Thermal
velocities
and
collisionis
of
the
plasma
electronis
were
nieglected.
5)
The
plasma
anid
the
beam
were
assumed
spatially
uniform.
One
may
interpret
this
dispersioni
relationi
as
giving
either
the
propagation
conistant
y
of
waves
whose
fre-
quenicy
is
o,
or
the
frequency
of
oscillation
of
disturb-
anices
whose
wave
niumber
is
y.
It
is
the
former
initer-
pretation
which
we
employ
in
this
paper.
In
the
absence
of
a
seconldary
electroin
beam
or
al-
terniative
feedback
path,
we
expected
the
system
of
ani
electron
beam
iinteractinig
with
a
plasma
over
a
finiite
lenigth
to
be
iniherenitly
stable;
that
is,
we
did
iiot
expect
spontanieous
oscillationis."1
Oni.
the.
other
hanid,
small
perturbationis
in
currenit
(shot
nioise)
or
velocity
of
the
incominig
electroni
beam
or
fluctuations
arisinig
in
the
plasma
would
increase
in
amplitude
along
the
electroni
beam.
In
the
first'2
of
the
two
experiments
described
below
(Fig.
1)
we
deliberately
introduced
a
modulationi
of
the
electroni
beam
at
a
microwave
frequency
and
ob-
served
the
amount
by
which
this
modulationi
was
in-
creased
after
havitig
passed
through
the
plasma.
This
experiment
verified
some
of
the
early
predictionis.
Kharcheniko,
et
al.,'3
examinied
the
modulation
of
the
beam
as
it
emerge(i
from
the
plasma
wheni
nio
micro-
wave
modulationi
had
beeni
applied
initially.
They
founid
a
nioise
modulationi
whose
frequency
spectrum
was
sharply
peakecl
at
the
plasma
frequency,
presum-
ably
due
to
the
selective
amplification
of
wide
band
fluctuation
noise.
Finally,
Bogdanov,'4
and
very
recently,
Allen
and
Kino,'5
repeated
our
first
experiment
with
a
longitudinal
magnietic
field
and
observed
several
in-
teresting
new
effects.
Durinig
the
course
of
the
firstexperiment
it
was
shown
'6
that
a
cylindrical
plasma
column
was
capable
of
sup-
porting
electrostatic
waves
whose
velocity
could
be
made
slow
compared
with
the
velocity
of
light.
This
"P
p.
A.
Sturrock,
"Excitation
of
plasma
oscillationis,"
Phys.
Rev.,
vol.
117,
pp.
1426--1429;
1960.
12
G.
D.
Boyd,
L.
M.
Field,
and
R.
W.
Gould,
"Excitation
of
plasma
oscillations
and
growing
plasma
waves,"
Phys.
Rev.,
vol.
109,
pp.
1393-1394;
1958.
(This
article
contains
a
preliminary
accounlit
of
the
first
experiment
described
here.)
13
I.
F.
Kharchenko,
et
al.,
"Experimental
and
theoretical
inves-
tigation
of
the
interaction
of
an
electron
beam
with
a
plasma,"
Proc.
Conf.
on
Ion
Phenomena
in
Gases,
Uppsala,
Sweden,
vol.
11,
pp.
671-680;
1959.
14
E.
V.
Bogdanov,
V.
J.
Kislov,
and
Z.
S.
Tchernov,
"Interaction
between
an
electron
stream
and
a
plasma,"
Proc.
Symp.
on
Milli-
meter
Waves,
Polytechnic
Inst.
of
Brooklyn,
N.
Y.,
vol.
9,
pp.
57-71;
April,
1959.
11
M.
A.
Allen
and
G.
S.
Kino,
"Interaction
of
an
electroni
beam
with
a
fully
ionized
plasma,"
Phys.
Rev.
Lett.,
vol.
6,
pp.
163-165;
1961.
16
A.
W.
Trivelpiece,
"Slow
Wave
Propagation
in
Plasnma
Wave-
guides,"
Ph.D.
dissertation,
Calif.
Inst.
Tech.,
Pasadena;
1958.
Also,
A.
WV.
Trivelpiece
and
R.
W.
Gould,
"Space
charge
waves
in
cylindrical
plasma
columnes,"
J.
Appl.
Phys.,
vol.
30,
pp.
1784-
1793;
1959.
Also,
"Electro-mechanical
modes
in
plasma
waveguides,"
Proc.
IEE,
vol.
105,
pt.
B,
pp.
516-519;
1958.
suggested
the
second
experiment'7
(lescribe(1
below
(Fig.
4)
in
which
traveling-wave
interactioni
occurred
between
such
a
slow
wave
anid
ani
electroni
beam
nwhich
passed
down
the
axis
of
the
plasma
at
a
velocity
about
equal
to
the
wave
velocity.
I
1.
INTERACTION
AT
PLASMA
RESONANCE
The
first
experiment
utilized
devices
of
the
type
shown
in
Fig.
1.
An
electron
beam
was
modlulated
by
a
short
helix,
passed
along
the
axis
of
the
plasma
columnii,
an(l
then
upon
emerging
was
demodulated
bv
a
seconcd
helix.
The
plasma
density
could
be
varied
by
chlanging
the
arc
current,
and
strong
amplificationi
was
foullni
to
occur'2
only
when
the
plasma
frequenicy
was
very
close
to
the
modulation
frequency.
ARC
INPUT
COLLECTOR
OUTPUT
WAVEGUIDE
WAVEGUIDE
FOCUSING1
CYLINDER-
ELECTRON
/
GUN
MODULATION
l
BEAM
\
HELIX
COLLECTOR
1
1
,
m
---r-
(---)---~~~~~~~~~~~~M------
---D--,--------
-
----
ANTENNAWI
X
DEMODULATtON
ANTENNAVJ
HELI
X
1
PLASMA
INTERACTION
REGION
ARC
CATHODE
"
1*
s;,
I
t /
4
-
MERCURY
WELL
Fig.
1-Helix
modtulationi
experiuiienit.
A.
The
Effect
of
Thermal
Velocities
of
the
Plasma
Elec-
trons-
One-Dimensional
Theory
Bohm
and
Gross3
have
derived
the
dispersion
equa-
tioIn,
includinig
the
effect
of
the
thermal
distribution
of
velocities
of
the
plasma
electronis,
for
a
broad
electron
beam
passinig
through
a
stationary
plasma.
The
effect
of
short-range
collisionis
of
the
plasma
electrons
may
also
be
in-cluded
in
ani
approximate
manniier
through
the
initroductioni
of
a
velocity-inidepenidenit
collisioni
frequenlcy18
v.
Ve
nlow
give
a
discussioni
of
the
solutions
of
this
equationi
for
the
coniditionis
of
our
first
experi-
menit.
All
waves
were
cassumed
to
have
exponienitial
spatial
and
time
dependenice
ei(wt
l-,
where
y=/-ia
was
the
complex
propagation
constant
anid
a
aind
f
were
both
real.
A
beam
plasma
frequency
was
defined
in
terms
of
the
beam
electron
density
nb
by
Wb2
=
nbe2/mEo.
The
thermal
distributioni
of
velocities
of
the
electron
beam
about
their
meani
velocity
Vb
was
neglected
sinice
their
17
G.
D.
Boyd
and
R.
W.
Gould,
"'Travellinig
wave
interaction
ill
plasmas,"
J.
Nuclear
Energy,
vol.
2,
pt.
C,
pp.
88-89;
1961.
(This
article
contains
a
preliminary
accouint
of
the
seconid
experiment
de-
scribed
here.)
18
R.
W.
Gould,
"Plasma
Oscillations
and
Radio
Noise
from
the
Disturbed
Sun,"
Calif.
Inst.
of
Tech.,
Pasadena,
Calif.,
Tech.
Rept.
4,
Contract
NONR
220
(13);
September,
1955.
1908
December