Full text of DOI:10.1051/epjap:2001183

Eur. Phys. J. AP 15, 199–206 (2001)
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
ꢀ
c EDP Sciences 2001
Loss of plasma scaling with magnetic field, pressure
and discharge current in a CUSP confined plasma
a
A. Anukaliani and V. Selvarajan
Department of Physics, Bharathiar University, Coimbatore, 641046, India
Received: 8 April 1999 / Revised: 22 January 2001 / Accepted: 12 March 2001
Abstract. The confinement properties of a low beta argon discharge plasma in a spindle cusp magnetic
field was investigated. Plasma was produced by ionisation collisions by the electrons which were produced
by thermionic emission of electrons. The central problem involved with plasma confinement by a cusped
magnetic field is the loss of particles along the flux lines. Electron and ion leak widths were studied in
the ring and point cusps and measured over a range of magnetic field strengths (B), neutral pressures (P)
d d
and discharge currents (I ). It was found that the leak width was reduced with increase in I and B. The
ion leak widths were found to be larger than the electron leak widths. The normalised effect of magnetic
field and pressure on ion and electron leak widths in cusps are reported, compared and discussed. The
dependence of electron and ion leak widths on plasma densities were also studied. At very low pressures,
high plasma densities and high magnetic field strengths, a quasineutrality condition was attained.
PACS. 52.55. Lf Field-reversed configurations, rotamaks, astrons, ion rings, magnetized target fusion, and
cusps
1
Introduction
derived a cusp loss width that satisfied their experimen-
tally obtained scaling loss. Mukherjee et al. [13] produced
a plasma by electron impact ionisation of nitrogen based
gas mixtures and measured its densities by confining it
in a single cusp magnetic field for the surface treatment
of metals (plasma nitriding). In 1998 Morishita et al. [14]
estimated the cusp leak width of Jaeri’s Kamboko source
Cusped magnetic fields are widely used in laboratory de-
vices due to their ability to confine large volume uniform
quiescent plasmas. Magnetic cusps are being investigated
for use in ion beam sources, plasma etching reactors, ion
implantation, plasma nitriding, etc. Kitsunezaki et al. [1],
Hershkowitz et al. [2] and Leung et al. [3] have reported
that the leakage half width scaled with the hybrid larmor
(
multi cusp negative ion source) and obtained a width of
about ten times the value evaluated by two times ion lar-
mor radius on the surface of cusp magnet.
1/2
radius (rire)
where ri and re are the ion and electron
In all the above applications the plasma leak is very
important since it governs the power and particle balance
of the confined plasma. The efficiency of cusp devices for
plasma confinement (surface treatment of metals) depends
on plasma losses from cusps. The present report is based
on the study of the production and confinement of plasma
using a cusped magnetic field configuration. Of particular
interest are the profiles of plasma escaping through the
flux lines, characterized by their full width at half max-
imum (FWHM) called the cusp leak width. The depen-
dence of electron and ion leak widths (in the ring and
point cusps) of the confined system was measured over a
range of magnetic fields, discharge currents and neutral
pressures.
larmor radii respectively. Haines [4] discussed their exper-
iments and held the ion acoustic instabilities and visco re-
sistive sheaths as possible explanation for the hybrid leak
widths. Hershkowitz et al. [5] and Fujita et al. [6] have re-
ported hybrid leak widths in a low beta plasma confined by
a permanent magnetic cusp. Kozima et al. [7] have studied
plasma instabilities excited around a line cusp magnetic
field and have also reported hybrid leak widths. However
leak widths of the order of ion larmor radius in a laser
produced high beta plasmas were reported by Kogoshi
et al. [8] and Pechacek et al. [9]. A theoretical attempt
was made by Knorr et al. [10] to calculate the width of an
escaping plasma in a picket fence and they reported hy-
brid leak widths. Knorr et al. [11] derived an expression for
cusp leak width by considering the electric field (originat-
ing from the charge separation) and showed that the effect
of scattering of ions from the cusp region by fast electrons 2 Experimental details
is important for the diffusion across the magnetic field.
In 1986 Bosch and Merlino [12] experimented on ring and The experimental apparatus consisted primarily of four
point cusp leak widths and made a model in which they systems:
a
e-mail: physics@as250.bharathi.ernet.in
(1) Plasma generation system;

200
The European Physical Journal Applied Physics
Fig. 1. Schematic diagram of plasma chamber.
A filament assembly was used for thermionic emission
of electrons. Tungsten filaments of 0.05 cm dia and 7 cm
length were mounted between two copper discs. The fila-
ment current was passed through a copper rod to one of
the discs from which it returned coaxially through the fil-
aments, to the other disc and a copper tube. The system
was also water cooled.
An accelerating potential of 70 to 80 V was applied be-
tween the filaments and the walls of the chamber. The fil-
aments were made negative and the walls were grounded.
A current of 14 A was passed through each filament and
made to emit electrons thermionically. The electrons were
accelerated which produced a plasma through ionisation
of argon gas in the chamber.
Fig. 2. Magnetic field strength versus position on the z axis
with the maximum current of 250 A passing through the coils.
Two water cooled coils are located inside the chamber,
with their planes parallel to each other, separated by a
distance of 20 cm and perpendicular to the symmetry axis.
Each coil is made up of five layers of five turns each of
6 mm copper tubing enclosed in an insulating sleeve. Inner
and outer diameters of the magnetic coils are 16 cm and
(
2) vacuum system;
3) magnetic field system;
4) diagnostics.
(
(
2
5 cm respectively. By passing currents ranging from 50 A
to 250 A in opposite directions in the coils, the required
spindle cusp magnetic fields were produced. At a current
of 250 A, the maximum field in the centre of the ring cusp
was 160 G while the maximum field in the centre of the
point cusp was 300 G. The magnetic field configuration
for the maximum current is shown in Figure 2.
The plasma chamber is presented schematically in
Figure 1. It consists of a cylindrical vacuum chamber (wa-
ter cooled) made of SS 304, 5 mm thick, 700 mm in length
and 500 mm in diameter. The chamber has ports for feed
throughs and viewing. The chamber was pumped down to
−5
a pressure of 2 × 10 mb and was filled with argon. Ar-
gon pressure was then reduced to the required operating
pressures. The pressures were measured using pirani and
penning gauges. The chamber was water cooled through
tubes on its lateral surface.
The major diagnostic tool used in this investigation is
a cylindrical Langmuir probe, a tungsten wire of 0.05 cm
dia and 0.45 cm length. The probes are capable of linear
movement using Wilson feed throughs.

A. Anukaliani and V. Selvarajan: Scaling of plasma losses
201
−4
Fig. 3. Ion saturation current profile taken with a Langmuir probe across the point cusp (z = 14 cm, P = 5 × 10
mb,
I
d
= 500 mA).
3
Methodology
ion saturation current to the probe. Therefore the profile
in Figure 3 can be interpreted as plots of relative density
−5
Initially, air was pumped down to 10 mb and the cham- versus radial position. On the symmetry axis the current
ber was flushed with argon gas two to three times. Argon is maximum and decreases symmetrically on either side
was filled to the required operating pressure and plasma of it. The width of the profile at half maximum, i.e. the
was produced through collision of thermionically emitted Full Width at Half Maximum (FWHM), is called the leak
electrons with argon atoms.
width and characterises plasma losses through the point
Langmuir probes were introduced into the chamber at cusp.
the ring and point cusps using Wilson feed throughs. A
bipolar power supply was used to bias the probe. The I-V
4
.2 Leak widths as a function of magnetic field
characteristics of the probe were studied by keeping the
probes at different radial and axial positions. Using the
data on the linear portion (in the electron retardation re-
gion) of the characteristics the ln Ie (electron current) vs.
Vp (probe potential) were plotted and the electron tem-
perature of the plasma was calculated.
The ion current profile in the point cusp at different mag-
netic field strengths are illustrated in Figure 3. It is seen
that higher the strength of the magnetic field lower is the
probe current at all positions and the profiles (peaks) be-
come narrower as the strength of the magnetic field in-
creases. Thus an increase of applied magnetic field reduces
the plasma diffusing along the field lines. The scaling of
the point cusp leak width with magnetic field for differ-
ent pressures is shown in Figure 4. The variation of leak
width ranges from 6.4 cm at 60 G to 1.6 cm at 300 G at
Electron temperature and plasma density were in the
1
0
12
−3
range of 3 to 4.5 eV and 10 to 10 cm respectively.
The probe was kept at different locations across the
point cusp with its length perpendicular to the sym-
metry axis. At each point, the maximum probe current
(
ion/electron) at the given pressure and magnetic field was
−4
a pressure of 5 × 10 mb and a discharge current (Id) of
measured. The current is a measure of the charge density
at the point. The probe current was plotted against the
probe position. The experiment was repeated at different
selected pressures, magnetic fields and discharge currents
and across the ring cusp.
5
00 mA.
Theoretically, the leak width in a cusp configuration
could be given as [15]
ꢀ2
ꢁ1/2
DR
d =
(1)
Cs
4
Results and discussion
where
D is the effective diffusion coefficient.
R is the coil radius.
Cs is the ion acoustic speed.
The results are illustrated in Figures 3 to 8 and Tables 1
to 4.
In the above formula, it is assumed that plasma es-
capes from the cusps at the ion acoustic speed while diffus-
ing across the magnetic field due to collisions. In general,
4
.1 Cusp leak width
The maximum ion current to the probe as a function of the diffusion coefficient D will be determined by electron
position of the probe across the point cusp is shown in neutral particle collisions (classical diffusion) and non clas-
Figure 3. The positive ion density is proportional to the sical diffusion (Bohm diffusion) [15] and if we assume that

202
The European Physical Journal Applied Physics
d
Fig. 4. Ion leak width in the point cusp versus B at four neutral pressures (z = 14 cm, I = 500 mA).
−4
Fig. 5. Ion saturation current profile taken with a Langmuir probe across the ring cusp (r = 19 cm, P = 5 × 10
= 500 mA).
mb,
I
d
4
these processes are linearly additive, we may write
2.6 cm at 160 G (P = 5×10− mb and Id = 500 mA) and
the variation is approximately linear beyond B = 70 G
D = Dc + DB
(2)
(3)
(
Fig. 6) for all the pressures studied. The variation of ion
ꢀ
ꢁ
2
ce
r
Ti
ckTe
and electron leak widths in the ring and point cusps for
D =
1 +
+
−4
different discharge currents at P = 5 × 10 mb is given
τc
Te
eB
in Table 1.
where Dc and DB are the classical and Bohm diffusion
coefficients and τc is the electron neutral collisional relax-
ation time.
The normalised reduction in leak width (reduction
The probe current profiles of ions in the ring cusp re- per unit increase of magnetic field) in the point cusp
−4
gion (at P = 5 × 10 mb) and the corresponding leak (B = 60 to 300 G) and ring cusp (B = 40 to 160 G) for
width variation as a function of magnetic field and for dif- Id = 500 mA, are given in Table 2. The normalised reduc-
ferent pressures are shown in Figures 5 and 6 respectively. tion in leak width with increase in B is faster at the ring
From the profile of Figure 5, it is seen that leakage profiles cusp than at the point cusp. The results for electrons are
tended to have shoulders i.e., regions in which the den- qualitatively similar to those of ions. The normalised re-
sity remained nearly constant or increased slightly as the duction in leak width at ring and point cusps for the same
probe was moved from the centre of the cusp. Typically range of magnetic field (B = 60 to 160 G) are shown in
the ring cusp ion leak width varies from 7.2 cm at 40 G to Figures 7a and 7b.

A. Anukaliani and V. Selvarajan: Scaling of plasma losses
203
Fig. 6. Ion leak width in the ring cusp versus B at four neutral pressures (r = 19 cm, I
d
= 500 mA).
in the ring and point cusps (P = 5 × 10− mb).
4
Table 1. Variation of electron and ion leak widths with I
d
Discharge
current
(mA)
Point cusp leak width (cm)
I
d
Ions
115 175 240 300 60
Electrons
B (Gauss)→ 60
115 175 240 300
200
350
500
8.2 5.8
7.2 4.8
6.4 4.2
4.6
3.8
3.0
3.4
2.4
1.8
3.0
2.2
1.6
5.4 3.4
5.8 3.4
6.2 3.8
2.2
2.6
2.6
1.4
1.6
1.8
1.2
1.4
1.6
Ring cusp leak width (cm)
Electrons
100 130 160
Ions
B (Gauss)→ 40
70
100 130 160 40
70
200
350
500
9.0 6.0
7.8 5.4
7.2 4.2
5.4
4.8
3.6
4.4
3.4
3.0
4.0
3.0
2.6
4.0 2.8
4.8 3.6
5.6 4.0
2.4
2.8
3.4
1.4
1.8
2.4
1.2
1.6
2.0
d
Table 2. Reduction in leak width (normalised) I = 500 mA.
P (mb)
Point cusp leak width
Ring cusp leak width
B = 60−300 G B = 40−160 G
Ions (%) Electrons (%) Ions (%) Electrons (%)
−
−
−
−
4
5
8
1
5
× 10
× 10
× 10
× 10
0.020
0.022
0.029
0.033
0.026
0.024
0.020
0.019
0.038
0.045
0.060
0.065
0.030
0.035
0.043
0.047
4
3
3
4
.3 Leak widths as a function of pressure
500 mA, the increase in leak width for ions at ring cusp,
4
−
when the pressure is increased from 5 × 10 mb to 5 ×
−
3
1
1
0
mb is 102.78% at B = 40 G and 161.54% at B =
The scaling of the ion leak width in the ring cusp with
pressure for different magnetic field strengths is shown in
Figure 8. It is seen that at the neutral pressure of 5 ×
60 G and at the point cusp it is 96.88% and 187.5% at
B = 60 G and B = 300 G respectively.
−4
The scaling of leak width with pressure and magnetic
field can be explained using equation (1).
1
0
mb (Id = 500 mA) the ion leak width is 7.2 cm
for 40 G and 2.6 cm for 160 G and as the pressure is
−3
increased to 5 × 10 mb, the ion leak width increases to
At low pressures, the plasma neutral collisions are
1
4.6 cm for 40 G and to 6.8 cm for 160 G. The increase rare. This suggests that the leak width is not determined
in leak width with pressure is due to the diffusion caused by classical diffusion due to plasma neutral collisions.
by plasma neutral collisions. For a discharge current of Here the Bohm diffusion [15] dominates and therefore

204
The European Physical Journal Applied Physics
Fig. 7. Normalised reduction in leak width in the point and ring cusps for the same range of B (60–160 G).
equation (1) predicts a leak width given by:
diffuses outward from the filaments. This suggests that
the leak width is determined by neutral particle collisions
at high pressures. Therefore equation (1) predicts a leak
width given by [15]:
ꢂ2R
ꢀ
ck Te
ꢁꢃ
1/2
d =
for Ti ꢀ Te
(4)
Cs 16eB
ꢀ2
ꢀ
ꢁꢀ
1/2
ꢁꢁ
1/2
2
ce
R
r
Ti
!
d =
1 + T
for Ti ꢀ Te (7)
1
/4 1/4
Cs τc
e
mi Te
√
d ∝
d ∝
√
(5)
(6)
P
1/4
B
d ∝ mi (σTe)
(8)
(9)
ꢀ
ꢁ
B
1
√
√
·
P
d ∝
B
B
Hence at low pressures and high magnetic fields the leak where σ is the electron neutral collision cross section.
width does not depend on pressure but varies inversely
This suggests that for high neutral pressures, plasma
as the square root of the magnetic field (Fig. 8). There is neutral collisions are important in the field free region and
no change in leak width with increase in P at low P and the plasma diffused outward from the filaments.
high B values. In Table 3a, it is seen that at low pressures
At high P and low B values, for a given P the ratio
and high B values (240 and 300 G at point cusp and 130 of leak widths is equal to the inverse ratio of the mag-
and 160 G at ring cusp), the ratio of d values obtained netic fields (Eq. (9)). The experimental results are given
experimentally is approximately equal to the reciprocal of in Table 3b. It is seen that for a given P value, the ratio
the ratio of the square roots of the corresponding B values of leak widths is in good agreement with inverse ratio of
indicating good agreement with theory (Eq. (6)).
At sufficiently high pressures, plasma neutral collisions
magnetic fields both at point and ring cusps.
For the point cusp, at sufficiently high pressures, (Id =
are important in the field free region and the plasma 200 mA and P = 5 × 10− mb) and low magnetic field
3

A. Anukaliani and V. Selvarajan: Scaling of plasma losses
205
d
Fig. 8. Ion leak width in the ring cusp versus P for different values of B (I = 500 mA).
Table 3. (a) Comparison of ratio of leak widths obtained from theory and experiment Low P High B; (b) Comparison of ratio
of leak widths obtained from theory and experiment High P Low B.
Low P High B
I
d
(mA)
P (mb)
Point cusp (
B
2
/B
1
= 1.2)
Ring cusp ( = 1.1)
B
2
/B
1
B
1
= 240 G and B
2
= 300 G
B
1
= 130 G and B = 160 G
2
Ions
1.13
Electrons
1.16
Ions
1.11
Electrons
1.16
× 10−
4
5
2
00
50
00
−4
8
5
× 10
1.15
1.09
1.11
1.14
1.16
1.13
1.11
1.13
−4
× 10
3
5
−4
8
5
× 10
1.13
1.13
1.09
1.12
1.15
1.15
1.18
1.20
−4
× 10
× 10−
4
1.08
1.09
1.13
1.15
8
High P Low B
I
d
(mA)
P (mb)
Point cusp (B
2
/B
1
= 1.92)
Ring cusp (B
2
/B
1
= 1.75)
B
1
= 60 G and B
2
= 115 G
B
1
= 40 G and B
2
= 70 G
Ions
1.89
Electrons
1.92
Ions
1.76
Electrons
1.66
× 10−
3
5
200
350
500
−3
8
5
× 10
1.91
1.94
1.86
1.85
1.75
1.76
1.73
1.67
−3
× 10
−3
8
5
× 10
1.90
1.91
1.83
1.80
1.79
1.59
1.78
1.72
−3
× 10
× 10−
4
1.93
1.88
1.76
1.67
8
strengths (B = 60 G), the ion leak width (14.4 cm) is the point and ring cusps and the theoretical values are
nearly as large as the coil inner diameter (16 cm) as in illustrated in Table 4.
Table 1. For the same Id, P and B at the ring cusp, the
The experimental results are not in agreement with
ion leak width (17.2 cm) is nearly as large as the coil inner theory (Eq. (1)). At the point cusp the experimental and
separation (20.0 cm) and the escaping plasma is no longer theoretical values of leak widths differ approximately by
constrained by the magnetic field but presumably by the a factor of 3.5 and at ring cusp by a factor of 2 at low B
mechanical constraint of the magnetic coils.
and high P values. At high B and low P, the experimental
and theoretical values differ by a factor of 3 both at the
The leak width d has been calculated theoretically us- point cusp and the ring cusp.
ing equation (1) as a function of B (Id = 500 mA). The
The difference in the values of leak width obtained the-
experimental values of leak widths obtained for ions in oretically and experimentally is due to the approximations

206
The European Physical Journal Applied Physics
Table 4. Experimentally and theoretically calculated values of ion leak widths at the point and ring cusps.
3
Low B High P (I
Point cusp (B = 60 G)
Theoretical Experimental
.62 12.6
High B Low P (I
Point cusp (B = 300 G)
d
= 500 mA, P = 5 × 10− mb)
Ring cusp (B = 40 G)
Theoretical
6.66
Experimental
14.6
3
= 500 mA, P = 5 × 10− mb)
4
d
Ring cusp (B = 160 G)
Theoretical
.58
Experimental
1.6
Theoretical
0.79
Experimental
2.6
0
made in deriving the formula (Eq. (1)) for the leak width for ions at high Id and 70% for electrons at low Id and
and the uncertainty in the numerical factor 1/16 in the at the point cusp the same was 75% (B = 60 to 300 G)
−4
Bohm diffusion coefficient [12]. Bosch and Merlino [12] on for ions and 77.78% for electrons for P = 5 × 10 mb.
comparison found that the theoretical and their experi- The loss of plasma characterised by the leak width was
mental values in general differed by a factor of three.
found to be independent of pressure at low pressures and
−1/2
high magnetic fields and the leak width scaled as B
.
At low pressures, high magnetic fields and high discharge
currents the plasma was quasineutral. The study will be
of interest for producing large volume plasmas which will
be useful for basic studies and also for plasma processing.
4
.4 Leak width as a function of discharge current
The dependence of ring cusp electron and ion leak widths
−3
upon discharge currents (at P = 5 × 10
mb) is also
shown in Table 1. The plasma density was varied by chang-
ing the filament current (which changes the discharge cur-
rent) while all the other parameters were kept constant.
The authors acknowledge the award of Scheme No.
SP/INC/PP-21/91 by the Department of Science and Tech-
nology and one of the authors (AA) acknowledges the Senior
Research Fellowship awarded by the Council of Scientific and
Industrial Research, Government of India.
−4
It is seen that (at a pressure of 5 × 10
mb) as the
discharge current (plasma density is proportional to dis-
charge current) is increased from 200 mA to 500 mA, the
ion and electron leak widths become comparable and the
quasineutrality condition is satisfied. Also as the discharge
current is increased the ion leak width decreases but the
electron leak width increases. At relatively low discharge
currents, ionisation will be small. Hence together with pri-
mary electrons, it is likely that plasma will be non neu-
tral. Therefore the magnetic coil surfaces will acquire a
negative potential and it will act as an accelerator for
ions through the point and ring cusps. Also, the ion gyro-
radius will be much larger than the electron gyroradius.
Hence, leak width for ions is larger than that for electrons
at low discharge currents. As discharge current increases
the plasma will become less and less nonneutral. The coil
surfaces will acquire lesser negative potential thereby de-
creasing the acceleration on ions and increasing the flow
of electrons. Hence, at one stage the leak width of ions
and electrons will be comparable exhibiting quasineutral-
ity. Bosch and Merlino [12] explained the difference in leak
widths between ions and electrons at low and high plasma
densities on the basis of self consistent electrostatic fields
developed in the cusp region.
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2
3
4
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5
Conclusion
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An argon discharge plasma was produced and confined by
a cusped magnetic field configuration. Increase of mag-
1
netic field reduced the cusp leak width. The reduction was 15. N.A. Krall, A.W. Trivelpiece, Principles of Plasma Physics,
as good as 63.89% at the highest magnetic field to that at
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