A Study of the Motion of High-Energy Electrons
in a Helium Hollow Cathode Discharge
Z. D o n k ó
Research Institute for Solid State Physics of the Hungarian Academy of Sciences, Budapest, Hungary
Z. Naturforsch. 48a, 4 5 7 - 4 6 4 (1993); received November 23, 1992
The motion of high-energy electrons was studied in a helium hollow cathode discharge using
Monte Carlo simulation. The calculations were carried out in the pressure range of 2 - 1 0 mbar. The
length of the cathode dark space (CDS) was determined by simulation in an iterative way using
experimental voltage-current density characteristics of the discharge. At the lowest helium pressure
(2 mbar) the concentration of high-energy electrons was found to be the same at the CDS-negative
glow boundary and at the midplane of the discharge while at 8 mbars it was found to be by
1 - 2 orders of magnitude smaller. The results of our calculations support the existence of "oscillating" electrons. The probability of 1, 2 and 3 transfers through the negative glow (NG) for primary
electrons was found to be 37%, 11 % and 2%, respectively, at 2 mbar pressure. The spatial distribution of ionizations and the angular distribution of electron velocity at the C D S - N G boundary were
also investigated. The pressure dependence of the current balance at the cathode was obtained, and
the results indicate that with decreasing pressure other secondary emission processes than ion impact
become important in the maintenance of the discharge.
Key words: Hollow cathode discharge, Electron energy distribution, Monte Carlo simulation,
Oscillating electrons, Current balance.
1. Introduction
T h e properties of (cold cathode) hollow c a t h o d e
(HC) glow discharges have been examined for a long
time [ 1 - 7 ] . The m a i n uses of this type of discharges
are h o l l o w c a t h o d e light sources [8, 9] a n d gas lasers
[10-13].
T h e hollow c a t h o d e effect occurs when for example
the s e p a r a t i o n of t w o parallel plane c a t h o d e s is decreased f r o m a large distance a n d the separate negative glows start to coalesce. If a fixed voltage is
applied, the discharge c u r r e n t m a y rise orders of m a g n i t u d e c o m p a r e d to the " n o r m a l " current in a single
p l a n e c a t h o d e discharge.
A c c o r d i n g to [14] three different p h e n o m e n a cont r i b u t e t o the hollow c a t h o d e effect:
- because of the c a t h o d e geometry p h o t o n s a n d
m e t a s t a b l e a t o m s can reach the c a t h o d e with a
higher probability a n d release m o r e electrons t h a n
in a n ordinary discharge,
- as p r o p o s e d by Güntherschulze [15], there may exist
so-called "pendelelectrons" which oscillate between
the o p p o s i t e c a t h o d e surfaces and increase the ionization a n d excitation rate [16],
Reprint requests to Z. Donkö, Research Institute for Solid
State Physics of the Hungarian Academy of Sciences, H-1525
Budapest 114, P.O. Box 49, Hungary.
- d u e to the increased c o n c e n t r a t i o n of excited a n d
charged species in the negative glow additional p r o cesses (the rates of which d e p e n d nonlinearly on the
concentrations) m a y b e c o m e significant a n d increase f u r t h e r the current at c o n s t a n t voltage.
T h e first experimental evidence of the existence of
oscillating electrons was given by H e l m [14] w h o observed electrons at the c a t h o d e emitted f r o m a p r o b e
o n the opposite side of a cylindrical hollow cathode.
T h o s e electrons emitted f r o m one of the c a t h o d e s
a n d reaching the " o p p o s i t e " c a t h o d e surface have the
same energy distribution as the p r i m a r y ones. These
slow electrons h a v e a great c h a n c e to get a b s o r b e d by
the c a t h o d e [17]. At low pressures this effect causes a
significant loss in the ionization rate a n d limits the
lowest possible o p e r a t i n g pressure of the H C discharge [14].
In o r d i n a r y plane c a t h o d e discharges the role of
ultraviolet (UV) p h o t o n s in the m a i n t e n a n c e of the
discharge was f o u n d to be relatively u n i m p o r t a n t [18].
O n the o t h e r h a n d , in H C discharges the high i m p o r tance of p h o t o e l e c t r o n s emitted by the c a t h o d e d u e to
U V r a d i a t i o n f r o m the discharge has been experimentally d e m o n s t r a t e d [19, 20].
M u c h w o r k h a s been devoted to the study of the
c a t h o d e region of glow discharges in o r d i n a r y plane
a n d hollow c a t h o d e geometries [ 3 - 7 , 2 1 - 2 9 ] . This
0932-0784 / 93 / 0100-469 $ 01.30/0. - Please order a reprint rather than making your own copy.
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458
Z. Donkö • Electron Motion in a Hollow Cathode Discharge
p a p e r reports on o u r investigations o n hollow c a t h o d e
(HC) discharges aiming to get detailed i n f o r m a t i o n on
the m o t i o n of electrons. O u r calculations were based
on M o n t e C a r l o simulation. T h e length of the c a t h o d e
dark space (CDS) was obtained using measured
voltage-current density characteristics of the discharge.
T h e electron energy distribution f u n c t i o n ( E E D F ) at
the CDS-negative glow ( N G ) b o u n d a r y a n d at the
midplane of the discharge was calculated at different
pressures. The probability of multiple transfers
t h r o u g h the N G for p r i m a r y electrons was determined
in order to see whether there exist "oscillating" electrons in the discharge. T h e spatial distribution of ionizations, the angular distribution of electrons at the
C D S - N G b o u n d a r y were also investigated as well, as
the pressure dependence of the current b a l a n c e at the
cathode. In the calculations we used a fixed c a t h o d e
separation L = 1 cm a n d carried o u t calculations in
the p = 2 to 10 m b a r pressure range.
2. The Model of the Discharge
The discharge geometry a n d the
b u t i o n considered in the m o d e l are
The c a t h o d e s of the discharge (CI
shaped having a radius R a n d they
electric field distris h o w n in F i g u r e 1.
a n d C2) are r o u n d
are placed parallel
E(x)
-EoH
Fig. 1. The hollow cathode discharge geometry used in the
calculations and the specified E(x) electric field distribution.
(CI and C2: cathodes, A: anode, L: the distance between the
cathodes, R: radius of the cathodes, dashed region: negative
glow, d: the length of the CDS).
to each other at a distance L. T h e a n o d e (A) is placed
a r o u n d the negative glow region at L / 2 distance f r o m
the cathodes. In the model the 2 R > L case is c o n sidered, i.e. edge effects are ignored.
T h e m o t i o n of electrons in the H C was described by
M o n t e C a r l o simulation.
T h e electric field distribution (see Fig. 1) is specified
a priori based on experimental investigations [1]. In
the C D S a linearly decreasing electric field distribution was applied. T h e electric field at the C D S - N G
b o u n d a r y was supposed to be 5 eV/cm. This small
residual field does not modify the results of the calculation significantly but the zero field position must be
excluded f r o m the C D S because of the applied M o n t e
C a r l o p r o c e d u r e [22], The negative glow was s u p posed to be free of electric field [1],
Recent experimental investigations pointed out t h a t
the n u m b e r of ions entering the C D S f r o m the N G is
small c o m p a r e d to the n u m b e r of those created in the
C D S [30, 24]. In the model we a s s u m e that no ions
enter the C D S f r o m the N G .
T h e elementary collision processes considered in
the m o d e l are anisotrope elastic electron scattering,
electronic excitation, a n d electron i m p a c t ionization.
2.1. The Method
of the
Simulation
In the algorithm of simulation the electrons are
released one by one f r o m one of the c a t h o d e s (CI, see
Figure 1). T h e m o t i o n of the emitted electrons a n d all
a d d i t i o n a l electrons created in ionizing collisions are
traced by the C D S a n d N G M o n t e C a r l o procedures.
T h e C D S M o n t e C a r l o procedure is based on the
w o r k of Boeuf a n d M a r o d e [22], the N G M o n t e C a r l o
p r o c e d u r e is simpler because the N G is supposed to be
free of electric field. In these p r o c e d u r e s the distance
between successive collisions of electrons is determined by r a n d o m numbers. T h e accelerating effect of
the electric field (in the CDS) a n d the energy dependence of collision cross sections are taken into account.
In the C D S simulation procedure the null-collision
m e t h o d is applied to speed-up the c o m p u t a t i o n [31,22].
T h e electrons are traced until they leave the C D S o r
their kinetic energy falls below the ionization p o t e n tial of helium ( £ ; = 24.56 eV) in the N G . T h e low energy electrons are t r a p p e d in the negative glow and d o
not c o n t r i b u t e to direct electron i m p a c t ionization.
T h e y m a y participate in excitation, cumulative ionization processes (not considered in the model) and carry
the current to the anode.
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459 Z. Donkö • Electron Motion in a Hollow Cathode Discharge
A l t h o u g h the electric field is o n e dimensional, the
electrons m o v e in a three dimensional space. T h e state
of a n electron in the p h a s e space is characterized by its
p o s i t i o n (x), energy (e) a n d cosine (p) of the angle 6
m e a s u r e d between the x-axis a n d the electron's velocity vector (as in [22]).
T h e cross sections of the considered elementary
processes are t a k e n f r o m [32] a n d [33]. In the case of
elastic scattering the scattering angle is determined
r a n d o m l y considering the form of the differential cross
section of the process used by Boeuf a n d M a r o d e [22].
T h e scattering after excitation is assumed to be
isotropic, the scattering angle is chosen randomly, as
well as the energy loss of the electron. In the ionization
process the scattered a n d ejected electrons share the
r e m a i n i n g kinetic energy a n d the directions of their
velocity vectors are assumed to be c o p l a n a r a n d perp e n d i c u l a r [22].
T h e electrons are emitted f r o m the c a t h o d e with a n
initial energy r a n d o m l y distributed between zero a n d
( £ ; — 2 £ 0 ) e V , w h e r e £ , a n d E0 are the ionization
p o t e n t i a l of H e a n d the work function of the c a t h o d e
material, respectively [34].
In the simulation the electrons m a y be a b s o r b e d by
or reflected f r o m a n y of the two cathodes, the reflection coefficient was t a k e n to be 0.2 [17].
In the simulation only the half of the H C discharge
is considered. Because of the symmetry, whenever an
electron crosses the m i d p l a n e of the H C , a n o t h e r elect r o n is s u p p o s e d t o arrive f r o m the other side with the
s a m e energy a n d oppositely directed velocity.
While tracing the electrons the electron energy dist r i b u t i o n f u n c t i o n ( E E D F ) builds u p at given positions in the discharge region [22]. Also the fluxes of
electrons a n d H e + ions per emitted electron are obtained in the C D S . These quantities already m a k e it
possible to calculate the current density as it is s h o w n
in s o m e detail in the following.
where e is the electronic charge, n the H e concentration, M the H e + ion m a s s a n d crs the cross section of
the H e + -I- H e -* H e + H e + symmetric charge transfer
process [24], T h e cross section <xs depends, however,
on the e = M(v+)2/2 kinetic energy of the ion as [35-37]
<xs = kl - k2 • l n ( a ) ,
where kt a n d k2 can be considered to be c o n s t a n t s
within the ion velocity r a n g e of interest a n d are k n o w n
f r o m experimental investigations [37]. T h e average
ion velocity v+ is calculated by the iterative solution of
(1) a n d (2).
F r o m the M C simulation we o b t a i n the fluxes of
electrons a n d H e + ions per emitted electron: F~(x)
a n d F + ( x ) . T h e current density consist of electron a n d
ion c u r r e n t densities a n d j=j~{x) + j+(x) holds in the
stationary case. M o r e o v e r we can define 0 ( x ) as
of the Discharge
F+(x) +
=
2e
nnM
E(x)
<rc
(3)
F~(x)
Since the positive space charge (created by H e + ions)
is d o m i n a n t in the C D S the Poisson e q u a t i o n m a y be
written:
dEjx)
1
—:— = —
dx
£n
(4)
r M ,
where q+ is the positive space charge
Q+(x)=j+(x)/v+(x).
Using the b o u n d a r y c o n d i t i o n t h a t the electric field at
the C D S - N G b o u n d a r y is, E(x = d)^0
the electric
field distribution in the C D S is o b t a i n e d by integration of (4):
E(x) = - - ]
e
+
£o d
( Z ) d t = - - j
eo
J
f
^
(5)
dx,
(6)
v •(Ö
F u r t h e r m o r e the discharge voltage is:
f
J
E(x) dx =
1
Q
j
Parameters
O u r p r i m a r y a i m is to be able to calculate the current density f r o m the given voltage a n d the results of
the simulation.
T h e v+(x) average velocity of H e + ions in the C D S
is given by
v+(x)
F+(x)
j+(x)
V =
2.2. Calculation
(2)
(1)
f r o m which the discharge current density j can be
calculated.
This calculation is s t r a i g h t f o r w a r d if d, the length of
the C D S is k n o w n (e.g. f r o m experiments). W h e n d is
only a p p r o x i m a t e l y k n o w n a n d the j(V) characteristics of the discharge are measured, d m a y be determined in a n iterative way. T h e simulation is carried
out using the same voltage a n d pressure values as in
the experiment, a n d d is a d j u s t e d in the consecutive
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Z. Donkö • Electron Motion in a Hollow Cathode Discharge
165
0.30
4. Results and Discussion
E
0.25
JJ
C
oO
o
0.20
0.15
-C
ö)
c
Q)
0.10
145
10
Pressure [mbar]
Fig. 2. The measured V(p) characteristics of the discharge
( + ) at constant j = 1 m A / c m 2 and the length of the C D S (•)
as a function of p.
runs to result in a c u r r e n t density in agreement with
the m e a s u r e d value. In o u r calculations the latter
m e t h o d was chosen.
3. Experimental
Because of the lack of experimental d a t a on d in
hollow c a t h o d e discharges a n experiment was carried
out to obtain the voltage-current density [V(jj] c h a r acteristics of the discharge. In order to keep the gas
relatively cool the V[j) characteristics of the discharge
were recorded in pulsed o p e r a t i o n a n d using the averaging m o d e on a H P 54501 A digitizing oscilloscope.
The experimental discharge t u b e consisted of
48.5 m m diameter r o u n d faced electrodes placed
10 m m a p a r t serving as cathodes. T h e a n o d e was a
circle s h a p e d wire of a b o u t 52 m m d i a m e t e r placed at
half distance between the electrodes. T h e c a t h o d e
material was high purity a l u m i n i u m .
T h e measured discharge voltage (obtained f r o m the
V(j) curves) as a f u n c t i o n of H e pressure is s h o w n in
Fig. 2 at a c o n s t a n t current density of 1 m A / c m 2 .
Starting f r o m 10 m b a r pressure the voltage decreases
t o w a r d s lower pressures. It can be seen t h a t the lowest
voltage representing the best o p e r a t i n g c o n d i t i o n s for
the H C discharge occurs at p = 4 m b a r . At even lower
pressures the voltage increases rapidly. T h e pressure
dependence of the length of the C D S (calculated in the
iterative m a n n e r explained in 2.2) is also plotted in
Figure 2.
In the following, results obtained f r o m the calculations are presented.
In Figs. 3 a n d 4 the E E D F is shown at 2 a n d 8 m b a r
pressures at x = d ( C D S - N G b o u n d a r y ) a n d at x = L / 2
(midplane of the discharge). T h e peak in the E E D F at
the highest electron energies represents the b e a m electrons. T h e shape of these peaks is identical to the
initial energy distribution of primary electrons. Figure 3 indicates that the density of b e a m electrons at
the C D S - N G b o u n d a r y at 8 m b a r pressure is by one
order of m a g n i t u d e smaller t h a n that at 2 m b a r . At the
m i d p l a n e of the discharge this ratio is a b o u t 1/100. It
can also be noticed that the b e a m electron density at
x = d a n d at x = L/2 is a b o u t the same at 2 m b a r .
C o n t r a r y to this, the b e a m electron density decreases
by a b o u t an order of m a g n i t u d e f r o m the b o u n d a r y to
the middle of the discharge at 8 m b a r pressure.
The p r i m a r y electrons emitted f r o m the c a t h o d e are
accelerated in the C D S a n d m a y cross the negative
glow once or several times. Figure 5 shows the pressure dependence of the probability that a primary elect r o n crosses the N G once, twice a n d three times. It can
be seen in Fig. 5 that at the lowest pressure (2 m b a r )
a b o u t 3 7 % of the primary electrons emitted f r o m the
"left" c a t h o d e fly into the opposite ("right") C D S ,
« 1 1 % comes back to the "left" C D S a n d « 2 %
crosses the N G once more. The probabilities of the
given n u m b e r s of transfers fall closely exponentially as
the pressure increases. It is noted that at the " o p t i m a l
pressure" (at the lowest operating voltage) only ~ 9 %
of the p r i m a r y electrons cross the N G a n d the p r o b ability of multiple transfers is rather small.
T h e a n g u l a r distribution of the electron's m o t i o n at
a given x = x 0 plane can be visualized by storing the e
a n d p values for each electron crossing the x = x 0
plane a n d plotting the stored values as d o t s o n the
(e, p) phase plane. Also the axial vx a n d radial vR c o m p o n e n t s of the velocity instead of e a n d p m a y be
used. (v x a n d vR are related to the s a n d p variables
as vx = v • p a n d t'R = ±v ]/1 — p2, where v = ] / 2 e / m ,
m being the mass of the electron. It is n o t e d t h a t the
velocity space is spherically symmetric a r o u n d the
x axis (i.e. all radial directions are equivalent). T h e
sign of vx indicates the direction of the electron's
velocity: the dots on the half plane ^ > 0 c o r r e s p o n d
to electrons moving from the C D S to the N G a n d on
the half plane vx < 0 to those moving f r o m the N G
t o w a r d s the C D S . In Figs. 6 and 7 the a n g u l a r distri-
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461 Z. Donkö • Electron Motion in a Hollow Cathode Discharge
CDS-NG BOUNDARY
2
mbar
0.01
8 mbar
0.001
0.0001
50
100
150
200
£ [ e V]
Fig. 3. The EEDF at the CDS-NG boundary (x = d) of the
hollow cathode discharge at 2 and 8 mbar pressures.
b a c k w a r d flux of electrons i n t o the C D S f r o m the N G .
This flux consist of electrons which are b a c k s c a t t e r e d
from the N G , created in the N G in a n ionization
process or came t h r o u g h the N G f r o m the o p p o s i t e
C D S . At 8 m b a r the n u m b e r of electrons t h a t cross the
N G is m a r g i n a l (see Figure 5). T h e result of this can be
clearly seen in the p h a s e plane plot of Fig. 7: the n u m ber of b a c k w a r d m o v i n g high energy electrons is very
small.
1000
m
=
D
100
q3
^
10
<4—
Pressure [mbar]
Fig. 5. The probability of k = 1, 2 and 3 transfers of primary
electrons through the negative glow as a function of gas
pressure.
1
0.1
0
50
100
150
200
£ [eV]
Fig. 4. The EEDF at the midplane of the hollow cathode
discharge (x = L/2) at 2 and 8 mbar pressure. (The increased
noise of the EEDF at 8 mbar occurs because of the small
number of electrons reaching the midplane of the discharge
at this pressure.)
b u t i o n is p l o t t e d at the C D S - N G b o u n d a r y (x = d) at
pressures of 2 a n d 8 m b a r . It c a n be seen in Figs. 6
a n d 7 t h a t the electrons enter the N G in a quite wide
r a n g e of angles. T h e d o t s on the vx < 0 half plane in
Fig. 6 indicate t h a t at 2 m b a r there is a significant
In the H C discharge the electrons starting f r o m
b o t h c a t h o d e s c o n t r i b u t e to the ionization in the negative glow a n d even in the " o p p o s i t e " c a t h o d e d a r k
space. Figure 8 shows the source f u n c t i o n 9 n + ( x ) / 9 r of
H e + ions at p = 4 m b a r pressure. T h e total source
function is the sum of t w o functions c o r r e s p o n d i n g to
the electrons (and electron avalanches) starting f r o m
the "left" a n d "right" cathodes. T h e total source function exhibits a characteristic b e h a v i o u r as the o p e r a t ing pressure is changed. This d e p e n d e n c e is plotted in
Figure 9.
T h e current balance at the c a t h o d e is defined as the
ratio of the ion to the electron current density j + / j ~ . I n
plane c a t h o d e discharges in helium den H a r t o g et al.
have f o u n d a typical value « 3.3 for the current balance [24]. It was n o t e d by t h e m t h a t this value does
not imply a secondary emission coefficient of « 0.3 for
ion impact since o t h e r electron emission processes
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462
Z. Donkö • Electron Motion in a Hollow Cathode Discharge
9 -
p = 2 mbar
6 -
*
y
r
; " i \
(/)
n
i
3 -
E
u
<o
o
o
o
-3
-
c
- 6
"Ö
-
_9
-9
-6
-3
vx
0
[106
3
6
9
x [cm]
m/s]
Fig. 6. Distribution of the velocity of high-energy electrons
crossing the C D S - N G boundary (x = d) plotted on the
(vx, vR) phase plane at p — 2 mbar.
9 -
Fig. 8. The spatial distribution of the source function of H e +
ions at p = 4 mbar pressure. The arrows (-* and <-) indicate
the source functions corresponding to electron avalanches
started from the "left" and "right" cathodes, respectively.
I indicates the total source function.
p = 8 mbar
6
ni(0
E
o
(0
o
c
- 6
"Ö
-
-9
-9
-6
-3
vy
9
[106
m/s]
Fig. 7. Distribution of the velocity of high-energy electrons
crossing the C D S - N G boundary (x = d) plotted on the
(vx,
phase plane at p = 8 mbar.
x [cm]
Fig. 9. The spatial distribution of the total source function of
He + ions at p = 2, 4 and 8 mbar pressure.
t h a n i o n i m p a c t m a y a l s o t a k e p a r t in t h e m a i n t e -
discharge, the obtained current balance values are
n a n c e of t h e d i s c h a r g e . T h e r e s u l t s f o r t h e c u r r e n t
close t o 3. W i t h d e c r e a s i n g p r e s s u r e (i.e. t o w a r d s t h e
b a l a n c e of t h e p r e s e n t M o n t e C a r l o s i m u l a t i o n s a r e
h o l l o w c a t h o d e o p e r a t i o n m o d e ) j+/j~
s h o w n in F i g u r e 10. A t h i g h e r p r e s s u r e s , w h e r e t h e
nificantly. T h i s i n d i c a t e s e v e n w i t h o u t t h e k n o w l e d g e
d i s c h a r g e b e h a v e s m o r e like a p l a n e single c a t h o d e
of t h e a c t u a l e l e c t r o n e m i s s i o n coefficients of t h e dif-
d e c r e a s e s sig-
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463 Z. Donkö • Electron Motion in a Hollow Cathode Discharge
4
T h e c o m p a r i s o n of the electron energy distribution
functions ( E E D F ) at the C D S - N G b o u n d a r y a n d at
the m i d p l a n e of the discharge showed t h a t there is a
strong pressure d e p e n d e n c e : T h e c o n c e n t r a t i o n of
high energy electrons
C
ß
(0
CO
+->
- is a b o u t the s a m e at the t w o positions at 2 m b a r ,
- at 8 m b a r pressure it is by 1 a n d 2 o r d e r s of magnit u d e smaller t h a n at 2 m b a r at the C D S - N G
b o u n d a r y a n d at the m i d p l a n e , respectively.
2
c
0)
=J
O
1
o
O
2
4
6
8
10
Pressure [mbar]
Fig. 10. The dependence of the current balance j+/j~
cathode of the discharge o n helium pressure.
at the
ferent processes t h a t o t h e r processes t h a n ion impact
b e c o m e m o r e i m p o r t a n t at lower pressures. This is
in a c c o r d a n c e with t h e observation t h a t in hollow
c a t h o d e discharges the e n h a n c e d U V r a d i a t i o n from
the N G contributes in a significant way to the mainten a n c e of the discharge.
As it was expected at low pressures m a n y electrons
cross the negative glow. At 2 m b a r the probability of
1, 2 a n d 3 transfers for p r i m a r y electron were f o u n d to
be 3 7 % , 1 1 % a n d 2 % , respectively. T h e decrease of
the transfer probabilities with increasing pressure is
close to exponential. These results s u p p o r t the possibility of multiple transfers of electrons t h r o u g h the
negative glow, i.e. the existence of oscillating electrons.
T h e a n g u l a r distribution of the electron velocity at
the C D S - N G b o u n d a r y was f o u n d to be r a t h e r wide.
T h e phase plane p o r t r a i t s at t h e C D S - N G b o u n d a r y
indicated the b a c k s c a t t e r i n g of electrons f r o m the N G ,
a n d also t h a t at low pressures there exists a significant
flux of high energy electrons f r o m the " o p p o s i t e " C D S .
T h e source f u n c t i o n c o r r e s p o n d i n g to electron impact ionization showed a characteristic pressure dependence.
T h e pressure d e p e n d e n c e of the current balance
(j+/j~) a t the c a t h o d e indicated t h a t with decreasing
pressure o t h e r secondary electron emission processes
t h a n ion i m p a c t b e c o m e m o r e i m p o r t a n t .
5. Conclusions
T h e m o t i o n of high energy (a > E t = 24.56 eV) elect r o n s in a helium h o l l o w c a t h o d e discharge has been
studied using M o n t e C a r l o simulation. T h e length of
the C D S in the plane parallel H C discharge was determined by applying the simulation in a n iterative way
a n d using experimentally measured current densityvoltage characteristics. T h e calculations were carried
out in the pressure r a n g e of 2 - 1 0 m b a r at j = 1 m A /
c m 2 . T h e low value of the current density justifies the
i g n o r a n c e of cumulative processes a n d t h e r m a l effects.
Acknowledgements
Discussions o n this w o r k with D r . M . Jänossy, Dr.
K. Rözsa, a n d D r . P. Mezei are greatfully acknowledged. I t h a n k D r . M . Jänossy for his advices a n d his
help in the p r e p a r a t i o n of the m a n u s c r i p t . T h a n k s are
also d u e to M r s . T. J. F o r g ä c s , M r . J. Töth, M r . E.
Särközi, a n d M r . Gy. C s ä s z a r for the c o n s t r u c t i o n of
the discharge t u b e a n d their help in the m e a s u r e m e n t s .
This w o r k was s u p p o r t e d by the H u n g a r i a n Science
F o u n d a t i o n O T K A G r a n t N o . F-4475.
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464
[1] P. F. Little and A. von Engel, Proc. Roy. Soc. London
A 224, 209 (1954).
[2] A. von Engel, Ionized Gases, Clarendon Press, Oxford
1965.
[3] Y. M. Kagan, J. Phys. D : Appl. Phys. 18, 1113 (1985).
[4] S. Hashiguchi and M. Hasikuni, Japanese J. Appl. Phys.
26, 271 (1987).
[5] S. Hashiguchi and M. Hasikuni, Japanese J. Appl. Phys.
27, 1010 (1988).
[6] S. Hashiguchi and M. Hasikuni, Japanese J. Appl. Phys.
27, 2007 (1988).
[7] S. Hashiguchi, I E E E Transactions on Plasma Science
19, 297 (1991).
[8] A. Walsh, Spectrochimica Acta 7, 108 (1955).
[9] P. Apai and K. Rözsa, in: Proceedings of Pentagonale
Workshop on Elementary Processes in Clusters, Lasers,
and Plasmas (T. D. Märk and R. W. Schrittwieser, eds.),
Kiihtai, Austria 1991, p. 286.
[10] R. Solanki, E. L. Latush, D. C. Gerstenberger, W. M.
Fairbank, Jr., and G. J. Collins, Appl. Phys. Lett. 35, 317
(1979).
[11] K. Rözsa and M. Jänossy, in: Proceedings of the XVIth
International Conference on Phenomena in Ionized
Gases, Düsseldorf, invited papers (W. Bötticher, H.
Wenk, and E. Schulz-Gulde, eds.), 150 (1983).
[12] M. Jänossy, P. Mezei, P. Horväth, and L. Csillag, Opt.
Commun. 68, 58 (1988).
[13] P. Mezei, P. Apai, M. Jänossy, and K. Rözsa, Opt. Commun. 78, 259 (1991).
[14] H. Helm, Z. Naturforsch. 27 a, 1812 (1972).
[15] A. Güntherschulze, Z. Physik 19, 313 (1923).
[16] H. Helm, H. F. Howorka, and M. Pähl, Z. Naturforsch.
27 a, 1417 (1972).
[17] R. Kollath, Encylopedia of Physics, Vol. XXI, Springer,
Berlin 1956, p. 263.
[18] H. Helm, Beitr. Plasmaphysik 18, 233 (1979).
Z. Donkö • Electron Motion in a Hollow C a t h o d e Discharge
[19] T. Iijima, T. Arai, K. Nihira, and T. G o t o , in: Proceedings of the XVIIIth International Conference on Phenomena in Ionized Gases, Swansea, contributed papers
(W. T. Williams, ed.), Vol. 1, 66 (1987).
[20] R. M. Chaudhri, M. M. Chaudhri, F. Deba, and M. N.
Chaudhri, Int. J. Electronics 62, 679 (1987).
[21] Tran Ngoc An, E. Marode, and P. C. Johnson, J. Phys.
D: Appl. Phys. 10, 2317 (1977).
[22] J. P. Boeuf and E. Marode, J. Phys. D : Appl. Phys. 15,
2169 (1982).
[23] M. Ohuchi and T. Kubota, J. Phys. D : Appl. Phys. 16,
1705 (1983).
[24] E. A. Den Hartog, D. A. Doughty, and J. E. Lawler,
Phys. Rev. A 38, 2471 (1988).
[25] R. J. Carman, J. Phys. D : Appl. Phys. 22, 55 (1989).
[26] M. Yumoto, Y. Kuroda, and Y. Sakai, J. Phys. D: Appl.
Phys. 24, 1594 (1991).
[27] A. Date, K. Kitamori, Y. Sakai, and H. Tagashira,
J. Phys. D: Appl. Phys. 25, 442 (1992).
[28] M. Dalvie, S. Hamaguchi, and R. T. Farouki, Phys. Rev.
A 46, 1066 (1992).
[29] Z. Donkö and M. Jänossy, J. Phys. D : Appl. Phys. 25,
1323 (1992).
[30] D. A. Doughty, E. A. Den Hartog, and J. E. Lawler,
Phys. Rev. Lett. 58, 2668 (1987).
[31] H. R. Skullerud, J. Phys. D: Appl. Phys. 1, 1567 (1968).
[32] F. J. de Heer and R. H. J. Jansen, J. Phys. B: At. Mol.
Phys. 10, 3741 (1977).
[33] J. C. Nickel, K. Imre, D. F. Register, and S. Trajmar,
J. Phys. B: At. Mol. Phys. 18, 125 (1985).
[34] H. D. Hagstrum, Phys. Rev. 104, 317 (1956).
[35] O. B. Firsov, Zh. Eksp. Teor. Fiz. 21, 1001 (1951).
[36] S. Shinha and J. N. Bardsley, Phys. Rev. A 14, 104
(1976).
[37] D. Rapp and W. E. Francis, J. Chem. Phys. 37, 2631
(1962).
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