Energy and Power Engineering, 2011, 3, 436-443
doi:10.4236/epe.2011.34054 Published Online September 2011 (http://www.SciRP.org/journal/epe)
Plasma Current Sheath Motion in Coaxial
Plasma Discharge
Tarek M. Allam, Hanaa A. El-Sayed, Hanaa M. Soliman
Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, AEA, Cairo, Egypt
Received December 29, 2010; revised February 10, 2011; accepted March 1, 2011
Abstract
In this paper experiments and theoretical treatments [1] on 1.5 KJ coaxial plasma discharge device have been
carried out to show, plasma current sheath, PCS, motion in coaxial plasma discharge by studying: the effect
of nitrogen gas pressure in the range from 1 to 2.2 Torr and the axial position of PCS along the coaxial elec-
trodes on the modification factor, actual drive parameter, PCS curvature and shape (thickness). Also the dy-
namics of PCS along the coaxial electrodes due to the combination effect of induced azimuthal and axial
magnetic fields induction has been detected experimentally by using a magnetic probe technique.
Keywords: Coaxial Discharge, Plasma Current Sheath, Drive Parameter
1. Introduction
Several studies [2-4] which are related to PCS formation
in coaxial plasma discharge device is accomplished by
two basic processes, 1) the formation of an axisymmetric
current sheath at the surface of the insulator end of the
coaxial electrodes breech, 2) axial acceleration of PCS
by the electromagnetic force (r
J
B

) along the annular
of inter electrode discharge region.
An extensive study has been done by several authors
in the field of axial PCS dynamics which depends on
several macroscopic parameters like the energy of ca-
pacitor bank, the discharge current, the charging voltage
and the curvature of the PCS [5-9]. Also a drive parame-
ter

p
Ia

, where Ip is the peak discharge current,
a is the inner electrode radius and ρ is the ambient gas
density, has been derived previously to a plasma focus
devices of different types [10-13]
This parameter determines the speed of the PCS in
both axial and radial phases and it has a constant value
for Mather type of different aspect ratios, gas pressures
and discharge current [11]. Also some authors confirmed
that the drive parameter has a remarkably constant value
of PF devices with a range of energies from a few KJ to
hundreds of KJ [14].
The goal of this paper extends to investigate the actual
drive parameter of coaxial plasma discharge device as a
function of PCS position during the axial rundown phase,
also the behavior and shape of PCS are presented under a
different discharge conditions.
This paper is contained the following sections, Section
2 describes the experimental setup, Section 3 presented
the results and discussion. A conclusion of this work is
presented in Section 4.
2. Experimental Arrangment
The coaxial plasma discharge device used in this work
has five main parts, 1) the coaxial discharge chamber, 2)
the energy storage system, 3) the electrical power supply,
4) the vacuum system and 5) the gas flow inlet system
[15,16].
A schematic diagram of the coaxial plasma discharge
device and its electrical circuit are shown in Figures 1(a)
and (b) respectively. The diameter of the inner and outer
coaxial stainless steel electrodes are 2a = 5 cm and 2b =
8.9 cm respectively. The inner electrode length is 13 cm
and the inner electrode-to-outer electrode is 47 cm. the
inner and outer electrodes are insulated from each other
by a tubular Perspex insulator of 1.5 cm length. The
outer electrode muzzle has facilities for a magnetic probe
tool.
The coaxial electrodes device capacitor bank is com-
posed of three capacitors with total capacitance 30 µf, 20
KV, in this work, energy stored in this bank is obtained
by charging it to 10 KV from a power supply. The ca-
pacitor bank transfers the energy of 1.5 KJ to coaxial
electrodes when switched through a spark gap switch
which in turn switched by a 10 KV triggering pulse. The
device is filled with nitrogen gas with pressure varying

T. M. ALLAM ET AL.437
(a)

(b)
Figure 1. (a) Coaxial plasma discharge device; (b) Electrical circuit of the coaxial plasma discharge device.
from 1 to 2.2 Torr.
The data of experimental works were taken from an
average of approximately from 5 to 7 shots for each gas
pressures and axial distances under consideration.
3. Results and Discussion
In the present work the experimental and theoretical re-
sults of PCS motion are carried out along the axial dis-
tance and at the annular space between the two coaxial
electrodes system, at radial distance, r = average of inner,
a and outer radius, b of coaxial electrodes = 3.475 cm.
Figure 2 shows the variation of the axial PCS velocity
measured by a magnetic probe technique, Va, with axial
distance along the annular space between the coaxial
electrodes and at r = 3.475 cm for different nitrogen gas
pressures. It can be seen from this figure that the sheath
velocity has their minimum value at the beginning of the
discharge and then it increases gradually in axial phase to
reach its maximum value nearly at the muzzle for all
values of gas pressure under consideration. This behavior
was attributed to the current density of plasma sheath,
the gas mass swept by PCS along the coaxial electrodes
and the mean free path. The theoretical axial velocity, Ua
calculated by using a snow-plough model [17] is given
by,

1
2
2
2
2
ln
4π1
p
aa
I
ba
Ub
a







 





(1)
A modification factor, cm
F
ff (where, fm is
some percent of mass was sweeping by PCS and c
f
is
some percent of bank current was driving the PCS) can
be estimated from ratio of the measured axial PCS veloc-
ity, Va and the theoretical axial velocity, Ua [17].
1.0 1.2 1.4 1.6 1.8 2.0 2.2
0
2
4
6
8
0246810 12
first half cycle
first peak
axial velocity*10
6
(cm/s)
distance (cm)
pressure (Torr)
Figure 2. Variation of axial sheath velocity with respect to
axial distance and gas pressure.

T. M. ALLAM ET AL. 438
a
a
V
FU  (2)
Figure 3(a)-(d) show the variation of modification
factor, F and the axial distance, Z (from breech to muzzle
of coaxial electrodes system) at different nitrogen gas
pressures 1, 1.4, 1.8, 2.2 torr. It can be seen from this
figure, that for all values of gas pressures the distribution
of F with Z has approximately the same behavior and at a
distances approach the coaxial muzzle, F increases sharply
to reach a maximum value.
Actual drive parameter, D is estimated by multiplying
F with drive parameter a
p
I

 ,
p
actual a
I
DF









(3)
In our case, Ip ≈ 54.5 KA, ρ = 1.48 × 10–3, 2.07 × 10–3,
2.66 × 10–3 and 3.26 × 10–3 kg/m3 at P = 1, 1.4, 1.8, 2.2
torr respectively and a = 2.5 cm.
Figures 4(a)-(d) show the variation of ln(D) with ax-
ial distance ln(Z) at different gas pressures, this figure
indicates that D is decreased from the breech to a dis-
tance approaches to approximately a mid-distance of
coaxial electrodes length with different rates as follows:
0.346
DZ


for Z varied from (1 to 4 cm) for P = 1
Torr.
0.38
DZ


for Z varied from (1 to 4 cm) for P = 1.4
Torr.
0.45
DZ


for Z varied from (1 to 4.7 cm) for P = 1.8
Torr.
0.557
DZ


for Z varied from (1 to 4 cm) for P = 2.2
Torr.
After this distance, D is increased in a different two
regions with different rates as follows:
0.52
DZ

for Z varied from (4 to 8 cm), and
3.06
DZ

for Z varied from (8 cm to ~ muzzle) for P =
1 Torr.
0.47
DZ

for Z varied from (4 to 8 cm), and 6.5
DZ

for Z varied from (8 cm to ~ muzzle) for P = 1.4 Torr.
0.45
DZ

for Z varied from (4.7 to 7 cm) and
4.44
DZ

for Z varied from (7 cm to ~ muzzle) for P =
1.8 Torr.
(a) (b)
(c) (d)
Figure 3. (a)-(d) Variation of modification factor, F, versus axial distance, Z.

T. M. ALLAM ET AL.439
(a) (b)
(c) (d)
Figure 4. (a)-(d) Variation of ln(actual drive parameter, D) versus ln(Z) at different gas pressures.
0.247
DZ
2.285
DZ
for Z varied from (4 to 7 cm), and
for Z varied from (7 cm to ~ muzzle) for P =
2.2 Torr.
The above results illustrate that the rate of decreasing
of D with Z is increased with increasing of gas pressure
at axial distance, Z from breech to ~4 cm, while at a
mid-distance from ~4 cm to ~8 cm, the rate of increasing
of D with Z is decreased with increasing of gas pressure,
finally at axial distance approaches to coaxial muzzle (8
cm to muzzle), the rate of increasing of D with Z as a
function of gas pressure has a maximum value at P = 1.4
torr.
In general D, for all values of gas pressure has a maxi-
mum value at a distance closes to coaxial electrodes
muzzle.
The PCS thickness, λ variations with axial distance, Z
as a function of gas pressures are estimated from a radial
PCS density Jr data,

2π
r
I
t
Jr

 , where I(t) is the dis-
charge current, taking


sin sin,
p
I
tI wt
61
.
2π0.2110 secw


 
Variation of ln(thickness of PCS, λ in arbitrary unit)
and ln(Z) is presented in Figures 5(a)-(d) at different gas
pressures. This figure reveals that, λ is increased from a
distance closes to coaxial breech until a distance ~8 cm,
then it decreased to reach a coaxial muzzle, with differ-
ent rates as follows:
2.1
Z
  (1.6→8 cm), 2.9
Z

 (8 cm to muzzle)
for P = 1 Torr.
2
Z
  (1.6→8 cm), 3
Z

 (8 cm to muzzle) for
P = 1.4 Torr.
1.166
Z   (1.6→8 cm), 5.5
Z

 (8 cm to muzzle)

T. M. ALLAM ET AL. 440
(a) (b)
(c) (d)
Figure 5. (a)-(d) The relation between ln(λ) and ln(Z) at different gas pressures.
for P = 1.8 Torr.
0.85
Z
  (1.6→8 cm), (8 cm to muzzle)
for P = 2.2 Torr.
5.44
Z 


These results clear that, the rate of increasing of λ with
Z is decreased with increasing of gas pressure from a
distance closes to coaxial breech until Z = 8 cm, and at a
distances varied from 8 cm to muzzle; the rate of de-
creasing of λ with Z is increased with increasing of most
values of gas pressures and it has a maximum value at P
= 1.8 torr. Previous results indicate that, a decrease in
thickness of PCS after a propagating an axial distance of
8 cm, is clearly reflected the mass loss effects [17].
Inclination angle θ of PCS with Z-axis along the co-
axial electrodes can be detected from the determination
of axial distance traveled by PCS at a distance closes to
inner surface of outer electrode and at radial distance r =
3.475 cm during the same time. Variation of inclination
angle θ of PCS with Z-axis along the coaxial electrodes
and at different values of gas pressure is cleared in Fig-
ures 6(a)-(d). It can be seen from this figure that θ is
damped with two regions, the first one from the breech
until a distance Z ~ 4 cm and the second from Z ~ 4 cm
to muzzle with different rates as follows:
0.19
Z 

 (0.5 to 4 cm) and (4 cm to
muzzle) for P = 1 Torr.
0.7
Z 


0.185
Z 

 (0.55 to 4 cm) and (4 cm to
muzzle) for P = 1.4 Torr.
0.773
Z 


0.22
Z 

 (0.75 to 4 cm) and (4 cm to
0.68
Z 



T. M. ALLAM ET AL.441
(a) (b)
(c) (d)
Figure 6. (a)-(d) Variation of ln(θ) with ln(Z) at different gas pressures.
muzzle) for P = 1.8 Torr.
0.2
Z 

 (0.55 to 4 cm) and (4 cm to
muzzle) for P = 2.2 Torr.
0.58
Z 


The above data show that, the rate of decreasing of
angle θ with Z has approximately the same values for all
gas pressures under consideration from the breech to Z =
4 cm, while at axial distance from 4 cm to muzzle, the
rate of decreasing of θ with axial distance Z has a maxi-
mum value at P = 1.4 torr i.e. at this pressure the para-
bolic PCS profile is more canted than other gas pressure
values under consideration, also this behavior could be
owing to the fact that the magnetic pressure B2/2µ [3] has
a peak value at this gas pressure value.
Variation of the ratio of induced axial and azimuthal
magnetic fields Bz and Bθ respectively, with the axial
distance, Z is shown in Figures 7(a)-(d) for different gas
pressures. In general this figure demonstrated that
z
BB

varies between 0.75 and 4.5, hence the magnetic
helicity plays a role in the PCS motion which must be
taken into account.
4. Conclusions
Experimental and theoretical results showed that a rapid
increase of modification factor, cm
F
ff with axial
distances, Z approach to coaxil electrodes muzzle for all a

T. M. ALLAM ET AL. 442
(a) (b)
(c) (d)
Figure 7. (a)-(d) Ratio of Bz/Bθ versus axial distance Z.
nitrogen gas pressures under consideration, this behavior
suggests that, the current and mass shedding effect which
taking place during the PCS motion along the coaxial
electrodes is significant along this distance.
Results of actual drive parameter, D or speed parame-
ter, inclination angle, θ and thickness, λ of PCS distribu-
tion with axial distance along the coaxial electrodes, Z at
different gas pressures demonstrated that, each of these
parameters has two or three different regions with dif-
ferent rates, specially at a distance closes to coaxial
muzzle. Results of axial distribution of D, θ, λ demon-
strated that, these distributions affect by two important
parameters namely the current shedding, Fc and mass
losses, Fm. The peak value of rate of change of the above
parameters with axial distance, Z is detected approxi-
mately at the gas pressure of 1.4 torr. A general view of
PCS motion along the coaxial electrodes at different gas
pressures is illustrated from the axial distribution of the
ratio z
BB

, it showed that, the PCS has a helical
structure along the coaxial electrodes. At a distance be-
yond the coaxial muzzle (from 8 cm ~ muzzle) and at P
= 1.4 torr, the PCS moves with approximately less heli-
cal motion than other gas pressures under consideration,
i.e. the axial force Jr × Bθ affecting on PCS motion is
greater than the azimuthal force Jr × Bz.
From the obtained results, one can conclude that, the
proper PCS motion is found at approximately P = 1.4
torr filling nitrogen gas pressure.
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