# Observation and Modeling of Optical Emission Patterns and Their Transitions in a Penning Discharge

Authors: C. C. Klepper; R. C. Hazelton; F. Barakat; M. D. Keitz; J. P. Verboncoeur
Journal: International Journal of Plasma Science and Engineering
 (2008)

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## Abstract

A Penning discharge tube has been used as the excitation source for optical
detection of gaseous species concentrations in a neutral gas. This type of diagnostic
has been primarily used in magnetic fusion energy experiments for the detection of minority
species in the effluent gas (e.g., for helium detection in a deuterium background).
Recent innovations (US Patent
no. 6351131, granted February 26, 2002) have allowed for extension of the operation range from<1 Pa to as high as 100 Pa and possibly beyond. This is done by dynamically varying the gauge magnetic
field and voltage to keep the optical signals nearly constant (or at least away from a nonlinear
dependence on the pressure). However, there are limitations to this approach, because the
Penning discharge can manifest itself in a number of modes, each exhibiting a different spatial
emission pattern. As a result, varying the discharge parameters can cause the gauge to
undergo transitions between these modes, disrupting any intended monotonic dependence
of the overall emission on the varied parameter and hence any predicable impact on the emission.
This paper discusses some of the modes observed experimentally using video imaging of
the discharge. It also presents a first successful application, a particle-in-cell (PIC) code, to
simulate these modes and a mode transition. The hope is that a good understanding of the
physics involved in the mode transitions may allow for methods of either avoiding or
suppressing such transitions. This would aid in broadening the use of this plasma-based sensor technology.


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## Body

## 1. Introduction

The species-selective Penning gauge (SPG) is a sensor
that uses the gaseous electric discharge inside a Penning gauge tube to excite
optical emission from the gaseous species. Analysis of the optical emission leads
to the detection of the species and a measure of their relative concentrations
(Figure1). As such, this sensor has been most extensively used in magnetic
fusion energy (MFE) experiments to measure the concentration of helium in the
mainly hydrogen and/or deuterium effluent of fusion devices
[1–3]. The ability of a particle
removal scheme to preferentially remove helium (the ash in a burning fusion
reactor) is an important design issue for pumped limiters and divertors.Figure 1
Schematic of the SPG concept. In the study of
spatial emission patterns, the optical fiber to spectrometer views were simply
replaced with a CCD camera—lens system able to access most of the emitting
plasma.One of the limitations of the SPG, as developed in the
MFE research community, has been the inability to handle pressures above about
1 Pa (~7 mTorr). In fact, significant nonlinear effects
in the dependence of line emission on partial pressure have been seen as the
total pressure approaches this limit. Above that, spatial mode transitions
would be observed in the optical emission pattern of the plasma discharge.
These effects have, in general, not been understood and they have been avoided
by keeping the total gas pressure in the gauge low by means of differential
pumping.A more recent diagnostic development innovation, which
combines feedback control of both the voltage and the magnetic field of the
gauge to keep the gauge current nearly constant, independent of the total
pressure (Figure2), has been shown to reduce nonlinearity with limited
success. For example, in cases with He minority concentration in a hydrogen (or
deuterium) working gas, the region of linearity could be extended by nearly an
order of magnitude [4]. However, transitions between what would appear to be
different plasma discharge modes (i.e., the above-mentioned emission pattern
transitions) have complicated the further development of this diagnostic. The
work described in this paper was driven by an interest in the development of
physical and computational models that might predict the optical emission
pattern, based on the discharge parameters, as well as the transitions between
patterns. One could envision a “smart” feedback control system, which
automatically “steers” the operation of the gauge clear of the transition
points or boundaries on the IV-plane. Such a complex “expert system” would be
much easier built on a physical model than as a result of statistical studies.Figure 2
Schematic of feedback control concept for the SPG.Even though the magnetic confinement of electrons in a
Penning gauge allows for a higher degree of ionization than in a glow
discharge, the ionization is still much below 1% for pressures of interest (~0.1–100 mTorr, with the highest electron
densities not exceeding 1×1011cm−3). Therefore, neutrals and their interactions
with the plasma are very important. It was in part for this reason that the
particle-in-cell (PIC) code XOOPIC was chosen for this work. The code includes
a Monte-Carlo collision model for the neutrals. This paper includes a brief
description of XOOPIC and the way it was configured for the problem at hand.
Observations of the emission patterns using a video (CCD-type) camera in place
of the collection optics in Figure 1 are also presented. Finally, it is shown
that a transition from one pattern to another can be successfully modeled with
XOOPIC and, thus, this or a similar model can be a powerful tool in the further
development of this plasma-based sensor technology.


## 2. Experimental Setup

For this work, specially designed gauge tubes were
fabricated to give more flexibility and greater optical access of the
discharge. Separate electronics, including a KEPCO programmable current
amplifier and specially made circuitry, were used for the feedback control of
Figure2. As with most commercial Penning gauges, our tubes are designed with the cathode
at the same potential as the tube's envelope, which is typically the same as
the ground potential. The anode is then biased positive with respect to ground.
Unlike the “zero-profile” anodes found in commercial tubes (usually
consisting of a wire loop), our anode was designed to span most of the gap
between the cathode plates, leaving minimal (about 1.5 mm) air gaps to prevent
shorting to the cathode. Additionally, by using a rectangular cross-section
perpendicular to the electron-confining magnetic field, it was possible to
provide an opening in the anode for full visual access of the plasma and its
light emission, while keeping this opening away from the plasma. Figure 3 is
a 3D rendition of the anode electrode, which is fabricated from thin,
nonmagnetic stainless steel stock. The white dashed lines on one side of the
anode is a rough indication of a projection of the plasma region onto that
surface, intended to define the region of the intra-electrode space that
appeared to be occupied by the plasma discharge.Figure 3
Three-dimensional rendition of the anode electrode used in the present work.
The cathode is part of the vacuum envelope of the tube and has the form of
parallel plates in the region subtended by the anode. The latter is separated
from the cathode plates by a minimal (~1.5 mm) gap, except at the optical access end,
where the anode consists only of a thin brace providing structural stability.A CCD-type video camera was set up in place of the
spectroscopy collection optics of Figure1 and viewing in the same
direction. While recording current-versus-voltage (I-V) characteristic curves
for various gas pressures, the camera was used to document the emission
patterns and their transitions. Since the camera was not intensified, and it
was important to document even the faintest patterns, wavelength-selective
filters were not used. All visible light was collected (with typical CCD
spectral response).


### 2.1. Observations of Emission Patterns and Their Transitions

Mode transitions were found to be universal, in the
sense that they appeared in current-versus-voltage (I-V) characteristics for
any Penning tube geometry and at any working gas pressure. Figure4 shows a
typical I-V characteristic showing a number of mode transitions. The signal Imon is proportional to the current (output of a
noncalibrated current sensor). Descriptions of the types of spatial modes (or,
more precisely, distributions of the plasma emission), as observed visually,
are noted in the graph for some of the data points. These data are all at
1mTorr hydrogen with the current in the electromagnet fixed at 2A, which
produced a 737-Gauss magnetic field in the plasma discharge region of the
gauge. At a different magnetic field or pressure, this I-V characteristic can
be quite different.Figure 4
Current
versus voltage characteristic of the Penning gauge used in project.To test the ability of the XOOPIC model to simulate
the occurrence of transitions between spatial modes of the Penning discharge, a
number of cases were run, in which only the voltage of the gauge was varied,
while the background pressure and the magnetic field were kept constant. In one
set of such studies, hydrogen was used as the working gas at low pressure,
because a substantial transition had been observed and well documented for this
case. Figure5 shows CCD images of the Penning discharge on two sides of a spatial
mode transition as the voltage is changed from 1048 V (left image) to 1534V
(right image) at fixed magnetic field in 2 mTorr (~0.3 Pa) H2 discharge. One very clearly sees in these
images the change from plasma that is donut-like in shape to a plasma that is
highly concentrated near the center of the tube (in both cases, the plasma is
centered vertically with respect to the cathode plates, which are near the top
and bottom edges of the images). Figure 6 shows plots of the plasma emission
light intensity distribution from the CCD images of Figure 5 as a function
of R and Z.
Note that these data represent integrated emission profiles along the view of
the camera, which is similar to the view of the spectroscopy collection optics
of Figure 1.Figure 5
CCD images of
the Penning discharge showing the spatial mode transition as the voltage is
changed from 1048 V (left image) to 1534 V (right image) at fixed magnetic field,
737 Gauss, and in 2 mTorrH2.Figure 6
Plots of the
plasma emission light intensity distribution from the CCD images of Figure4
as a function of R and Z.


### 2.2. XOOPIC and Its Application to the Penning Gauge

Before discussing numerical simulation, it is
interesting to note that theoretical work on the operation of the Penning gauge
is very limited in the literature. However, the physics of the Penning
discharge is akin to that of the magnetron discharge. The same crossed electric
field/magnetic field-induced “magnetron motion” confines the electrons and
enhances the ionization within the desired region. A significant amount of work
on the physics of the magnetron discharge can be found in the literature in the
1960s and 1970s, driven by the combined commercial interest in magnetrons for
microwave power generation and for sputter deposition of thin films
[5–7]. Especially driven by the
great potential for applications in thin film deposition for the
microelectronics industry, a surge of experimental activity in the study of
magnetron plasmas appears in the 1980s [8–10]. This then led to theoretical interpretation based on
numerical modeling of these experimental results, with most of the work done in
the 1990s, [e.g., [11, 12]]. Although the significant difference in the geometry
makes it difficult to extrapolate results from the magnetron to the Penning, a
good intuition can be developed from the existing work. This intuition led to
the development of the feedback control process mentioned in the introduction.
As mentioned, however, the appearance of spatial mode transitions limited the
success of the feedback process and this motivated the investigation of XOOPIC
as a possible modeling tool to help get beyond intuition in the further
development of the sensor.XOOPIC [13] is a two-dimensional particle-in-cell
(PIC) code that operates in x-y and r-z coordinates. It is capable of simulating the
electrostatic limit, as well as the fully electromagnetic Maxwell equations.
XOOPIC can simulate interaction of charged particles with a background gas
using a Monte-Carlo collision (MCC) model. The code can model fully
relativistic particles, general magnetic fields, and a wide variety of boundary
conditions for both particles and fields. It includes the capability to model
arbitrary configurations of boundaries, including internal boundaries, each
with general properties such as secondary emission or time-dependent voltage,
and each capable of measuring particle statistics such as impact energy and
angle in addition to currents.The Penning gauge geometry was set up for XOOPIC as
shown in Figure7. The code allows for planar or cylindrical geometry.
Naturally, a cylindrical geometry is chosen for the Penning tube. The magnetic
field can be entered either as a uniform constant field or as an input file
containing a distribution over the grid used in the calculation. The small
physical size of the gauge allowed for a conveniently small grid. The grid is
selected carefully so the Debye length (λD), is larger, on average, than the grid
spacing (average electron energies are in the range of 100–200 eV), while
maintaining enough particles per cell for good statistics while still retaining
practical run times on a PC.Figure 7
Penning gauge
tube geometry and grid setup for the XOOPIC code.The code was run on a 1 GHz Pentium PC running Linux.
With a typical plasma density of mid-109cm−3,
the total number of “particles” was still in the mid-105 range. Here “particles” actually refer to
the “super-particles” used in PIC codes to represent a large group of actual
plasma ions or electrons. A simulation typically takes 2-3 days to run on the
PC.


### 2.3. PIC Modeling of Mode Transitions

As mentioned, Figure6 shows the intensity (mostly
emission from the hydrogen Balmer-alpha line at 6563 Å) distribution as a
function of radius and vertical position between the cathode plates. It is
interesting to display the data in this fashion, because then one can attempt
to compare with similar 3D plots of the electron density and other plasma
parameters, as one finds in the standard output of the XOOPIC run. Such plots
of the electron density are shown in Figure 8
for two extreme cases for the
voltage, at fixed magnetic field and low hydrogen pressure.Figure 8
Electron
density distributions computed in an XOOPIC simulation of the Penning
discharge. It shows a spatial mode transition as the voltage is changed from
800 V to 2500 V at a fixed magnetic field of 0.4 kG in
1 mTorrH2.The assumption is that the light emission is
proportional to the electron density, since it is mainly the electrons in the
discharge that excite the atomic transitions, which in turn produce the
emission. However, the electron energy distribution function may also vary
spatially, and will strongly influence the excitation profile. Of course, other
factors, such as charge-exchange between neutral atoms and plasma ions can also
contribute to the distribution of the emission and cause it to be different
from that of the electron density (e.g., by resulting in deexcitation of atomic
states involved in the line emission process). Since the pixels of the CCD
camera are actually integrating the light along their line of sight in an
optically thin medium, the same operation is carried out numerically on the
density profiles of Figure8 to allow for direct comparison. The resulting
line-integrated densities, shown in Figure 9,
qualitatively show the same transition in the light emission pattern seen in the
CCD data of Figure 6.Figure 9
The same
simulations as in Figure8 but with the densities integrated along the lines
of sight of the CCD. This allows for direct comparison with the experimental
data of Figure 6 (assuming the plasma emission is proportional to the
density, which is not unreasonable when most emission comes from neutrals
excited by electrons).Clearly, the match is not perfect, nor expected to be
(since the density is not the only factor in the emission intensity, as
explained above, and the geometry of the Penning tube in the model only
approximates that of the actual tube used in the experiment). However, it is
clear from these results that the gross features of the light emission
distribution, which is what has been denoted as aspatial mode
in the preceding discussion, and the transition to different distributions or modes,
can in fact be simulated by a numerical code like XOOPIC.To make use of this new capability to simulate the
behavior of the Penning discharge, it is also necessary to understand what
specific processes in the simulation might cause the effects, such as the mode
transitions. This work has only now begun and a complete understanding will
require additional simulation runs. However, some ideas have arisen from trends
seen in the various standard output diagnostics of XOOPIC. These give a
direction to be pursued in the follow-on study.One potential effect to investigate in the mode
transition described here might be changes in the magnetic sheath. If we assume
the plasma is fairly conductive so that most of the voltage drop is radial,
then we expect a strong azimuthal motion due toE×B forces. For dense plasma, a thin layer might
shield most of the radial field, so that electrons in the inner radii see
little field and hence attain a temperature insufficient for ionization.It is noted that as the voltage in the simulation goes
from 800 to 2500 V, the Debye length (λDe) should double from 5 mm to nearly 1 cm if the
full voltage is available, according to λDe1/λDe2=n2V1/n1V2,
where n is the electron density. Similarly, the
(electron cyclotron motion) gyroradius (rce) should double from 2.5 mm to 5 mm, according
to rce1/rce2=V1/V2.
These numbers indicate that both the gyroradius and the Debye length are
comparable to the system size, so the changes in these parameters may be
significantly contributing to the observed modal changes.One of the standard diagnostic outputs of the
simulation code is the azimuthal velocity as a function of the radius.
Comparing the two cases in Figure10, it is found that the velocity
distribution shifts toward the smaller radii at the higher voltage. It is noted
that the magnitude of these velocities (peak values of 1.5×107 and 2.8×107 m/s, for low- and high-field cases, resp.) are
large compared to thermal velocities (for typical ≤~10eV thermal electrons, average velocities are ≤~0.1×107 m/s). These azimuthal velocities are caused by
the E×B drift and correspond to energies that can
contribute substantially to the excitation and ionization of neutral species.
Consequently, the plasma light emission profile is a convolution of the E×B rotation and the electron density. At the
lower voltage, the E×B rotation is clearly reduced in the central
region of the gauge. Since the magnetic field is specified in this model, and
there is no diamagnetic current in the electrostatic limit, this implies that
the radial electric field must be shielded at the small radii for the
low-voltage case. (By taking dne/dr at the steepest density gradient region of the
low-V case, where ne≈4×1015 m−3,
an upper limit for the diamagnetic current |c⋅B×∇p/B2|≈(ckT/B)⋅dne/dr can be obtained. It corresponds, after
dividing by e⋅ne,
to a velocity of about 1×105 m/s, which is two orders of magnitude below
the average E×B velocity. This indicates that the diamagnetic
effect can be safely ignored.) The shift of the peak density toward the axis of
symmetry of the gauge is consistent with a reduction of the screening of the
electric field at the higher voltage, and therefore with the increased
azimuthal motion at the smaller radii.Figure 10
Change in
azimuthal velocity (vΦ,
radial phase space) in the transition of Figure 8.It is also noted that relative lifetime (or residence
time in the Penning trap) of the electrons and ions can determine the
penetration (or thickness) of the sheath, and consequently the fields. (It is
noted that even the sign of the field can change as the electron-ion balance is
changed.) The evidence indicates that the low-voltage case has losses high
enough that it does not form the typical diffusive profile (Bessel function), but
is instead hollow, possibly indicating a lower or localized ionization rate or
reduced diffusion. Since the primary source of light emission is likely to be
excited by energetic electrons produced by theE×B drift, then the modeled changes in the
azimuthal velocity distribution are consistent with this picture.


## 2.1. Observations of Emission Patterns and Their Transitions

Mode transitions were found to be universal, in the
sense that they appeared in current-versus-voltage (I-V) characteristics for
any Penning tube geometry and at any working gas pressure. Figure4 shows a
typical I-V characteristic showing a number of mode transitions. The signal Imon is proportional to the current (output of a
noncalibrated current sensor). Descriptions of the types of spatial modes (or,
more precisely, distributions of the plasma emission), as observed visually,
are noted in the graph for some of the data points. These data are all at
1mTorr hydrogen with the current in the electromagnet fixed at 2A, which
produced a 737-Gauss magnetic field in the plasma discharge region of the
gauge. At a different magnetic field or pressure, this I-V characteristic can
be quite different.Figure 4
Current
versus voltage characteristic of the Penning gauge used in project.To test the ability of the XOOPIC model to simulate
the occurrence of transitions between spatial modes of the Penning discharge, a
number of cases were run, in which only the voltage of the gauge was varied,
while the background pressure and the magnetic field were kept constant. In one
set of such studies, hydrogen was used as the working gas at low pressure,
because a substantial transition had been observed and well documented for this
case. Figure5 shows CCD images of the Penning discharge on two sides of a spatial
mode transition as the voltage is changed from 1048 V (left image) to 1534V
(right image) at fixed magnetic field in 2 mTorr (~0.3 Pa) H2 discharge. One very clearly sees in these
images the change from plasma that is donut-like in shape to a plasma that is
highly concentrated near the center of the tube (in both cases, the plasma is
centered vertically with respect to the cathode plates, which are near the top
and bottom edges of the images). Figure 6 shows plots of the plasma emission
light intensity distribution from the CCD images of Figure 5 as a function
of R and Z.
Note that these data represent integrated emission profiles along the view of
the camera, which is similar to the view of the spectroscopy collection optics
of Figure 1.Figure 5
CCD images of
the Penning discharge showing the spatial mode transition as the voltage is
changed from 1048 V (left image) to 1534 V (right image) at fixed magnetic field,
737 Gauss, and in 2 mTorrH2.Figure 6
Plots of the
plasma emission light intensity distribution from the CCD images of Figure4
as a function of R and Z.


## 2.2. XOOPIC and Its Application to the Penning Gauge

Before discussing numerical simulation, it is
interesting to note that theoretical work on the operation of the Penning gauge
is very limited in the literature. However, the physics of the Penning
discharge is akin to that of the magnetron discharge. The same crossed electric
field/magnetic field-induced “magnetron motion” confines the electrons and
enhances the ionization within the desired region. A significant amount of work
on the physics of the magnetron discharge can be found in the literature in the
1960s and 1970s, driven by the combined commercial interest in magnetrons for
microwave power generation and for sputter deposition of thin films
[5–7]. Especially driven by the
great potential for applications in thin film deposition for the
microelectronics industry, a surge of experimental activity in the study of
magnetron plasmas appears in the 1980s [8–10]. This then led to theoretical interpretation based on
numerical modeling of these experimental results, with most of the work done in
the 1990s, [e.g., [11, 12]]. Although the significant difference in the geometry
makes it difficult to extrapolate results from the magnetron to the Penning, a
good intuition can be developed from the existing work. This intuition led to
the development of the feedback control process mentioned in the introduction.
As mentioned, however, the appearance of spatial mode transitions limited the
success of the feedback process and this motivated the investigation of XOOPIC
as a possible modeling tool to help get beyond intuition in the further
development of the sensor.XOOPIC [13] is a two-dimensional particle-in-cell
(PIC) code that operates in x-y and r-z coordinates. It is capable of simulating the
electrostatic limit, as well as the fully electromagnetic Maxwell equations.
XOOPIC can simulate interaction of charged particles with a background gas
using a Monte-Carlo collision (MCC) model. The code can model fully
relativistic particles, general magnetic fields, and a wide variety of boundary
conditions for both particles and fields. It includes the capability to model
arbitrary configurations of boundaries, including internal boundaries, each
with general properties such as secondary emission or time-dependent voltage,
and each capable of measuring particle statistics such as impact energy and
angle in addition to currents.The Penning gauge geometry was set up for XOOPIC as
shown in Figure7. The code allows for planar or cylindrical geometry.
Naturally, a cylindrical geometry is chosen for the Penning tube. The magnetic
field can be entered either as a uniform constant field or as an input file
containing a distribution over the grid used in the calculation. The small
physical size of the gauge allowed for a conveniently small grid. The grid is
selected carefully so the Debye length (λD), is larger, on average, than the grid
spacing (average electron energies are in the range of 100–200 eV), while
maintaining enough particles per cell for good statistics while still retaining
practical run times on a PC.Figure 7
Penning gauge
tube geometry and grid setup for the XOOPIC code.The code was run on a 1 GHz Pentium PC running Linux.
With a typical plasma density of mid-109cm−3,
the total number of “particles” was still in the mid-105 range. Here “particles” actually refer to
the “super-particles” used in PIC codes to represent a large group of actual
plasma ions or electrons. A simulation typically takes 2-3 days to run on the
PC.


## 2.3. PIC Modeling of Mode Transitions

As mentioned, Figure6 shows the intensity (mostly
emission from the hydrogen Balmer-alpha line at 6563 Å) distribution as a
function of radius and vertical position between the cathode plates. It is
interesting to display the data in this fashion, because then one can attempt
to compare with similar 3D plots of the electron density and other plasma
parameters, as one finds in the standard output of the XOOPIC run. Such plots
of the electron density are shown in Figure 8
for two extreme cases for the
voltage, at fixed magnetic field and low hydrogen pressure.Figure 8
Electron
density distributions computed in an XOOPIC simulation of the Penning
discharge. It shows a spatial mode transition as the voltage is changed from
800 V to 2500 V at a fixed magnetic field of 0.4 kG in
1 mTorrH2.The assumption is that the light emission is
proportional to the electron density, since it is mainly the electrons in the
discharge that excite the atomic transitions, which in turn produce the
emission. However, the electron energy distribution function may also vary
spatially, and will strongly influence the excitation profile. Of course, other
factors, such as charge-exchange between neutral atoms and plasma ions can also
contribute to the distribution of the emission and cause it to be different
from that of the electron density (e.g., by resulting in deexcitation of atomic
states involved in the line emission process). Since the pixels of the CCD
camera are actually integrating the light along their line of sight in an
optically thin medium, the same operation is carried out numerically on the
density profiles of Figure8 to allow for direct comparison. The resulting
line-integrated densities, shown in Figure 9,
qualitatively show the same transition in the light emission pattern seen in the
CCD data of Figure 6.Figure 9
The same
simulations as in Figure8 but with the densities integrated along the lines
of sight of the CCD. This allows for direct comparison with the experimental
data of Figure 6 (assuming the plasma emission is proportional to the
density, which is not unreasonable when most emission comes from neutrals
excited by electrons).Clearly, the match is not perfect, nor expected to be
(since the density is not the only factor in the emission intensity, as
explained above, and the geometry of the Penning tube in the model only
approximates that of the actual tube used in the experiment). However, it is
clear from these results that the gross features of the light emission
distribution, which is what has been denoted as aspatial mode
in the preceding discussion, and the transition to different distributions or modes,
can in fact be simulated by a numerical code like XOOPIC.To make use of this new capability to simulate the
behavior of the Penning discharge, it is also necessary to understand what
specific processes in the simulation might cause the effects, such as the mode
transitions. This work has only now begun and a complete understanding will
require additional simulation runs. However, some ideas have arisen from trends
seen in the various standard output diagnostics of XOOPIC. These give a
direction to be pursued in the follow-on study.One potential effect to investigate in the mode
transition described here might be changes in the magnetic sheath. If we assume
the plasma is fairly conductive so that most of the voltage drop is radial,
then we expect a strong azimuthal motion due toE×B forces. For dense plasma, a thin layer might
shield most of the radial field, so that electrons in the inner radii see
little field and hence attain a temperature insufficient for ionization.It is noted that as the voltage in the simulation goes
from 800 to 2500 V, the Debye length (λDe) should double from 5 mm to nearly 1 cm if the
full voltage is available, according to λDe1/λDe2=n2V1/n1V2,
where n is the electron density. Similarly, the
(electron cyclotron motion) gyroradius (rce) should double from 2.5 mm to 5 mm, according
to rce1/rce2=V1/V2.
These numbers indicate that both the gyroradius and the Debye length are
comparable to the system size, so the changes in these parameters may be
significantly contributing to the observed modal changes.One of the standard diagnostic outputs of the
simulation code is the azimuthal velocity as a function of the radius.
Comparing the two cases in Figure10, it is found that the velocity
distribution shifts toward the smaller radii at the higher voltage. It is noted
that the magnitude of these velocities (peak values of 1.5×107 and 2.8×107 m/s, for low- and high-field cases, resp.) are
large compared to thermal velocities (for typical ≤~10eV thermal electrons, average velocities are ≤~0.1×107 m/s). These azimuthal velocities are caused by
the E×B drift and correspond to energies that can
contribute substantially to the excitation and ionization of neutral species.
Consequently, the plasma light emission profile is a convolution of the E×B rotation and the electron density. At the
lower voltage, the E×B rotation is clearly reduced in the central
region of the gauge. Since the magnetic field is specified in this model, and
there is no diamagnetic current in the electrostatic limit, this implies that
the radial electric field must be shielded at the small radii for the
low-voltage case. (By taking dne/dr at the steepest density gradient region of the
low-V case, where ne≈4×1015 m−3,
an upper limit for the diamagnetic current |c⋅B×∇p/B2|≈(ckT/B)⋅dne/dr can be obtained. It corresponds, after
dividing by e⋅ne,
to a velocity of about 1×105 m/s, which is two orders of magnitude below
the average E×B velocity. This indicates that the diamagnetic
effect can be safely ignored.) The shift of the peak density toward the axis of
symmetry of the gauge is consistent with a reduction of the screening of the
electric field at the higher voltage, and therefore with the increased
azimuthal motion at the smaller radii.Figure 10
Change in
azimuthal velocity (vΦ,
radial phase space) in the transition of Figure 8.It is also noted that relative lifetime (or residence
time in the Penning trap) of the electrons and ions can determine the
penetration (or thickness) of the sheath, and consequently the fields. (It is
noted that even the sign of the field can change as the electron-ion balance is
changed.) The evidence indicates that the low-voltage case has losses high
enough that it does not form the typical diffusive profile (Bessel function), but
is instead hollow, possibly indicating a lower or localized ionization rate or
reduced diffusion. Since the primary source of light emission is likely to be
excited by energetic electrons produced by theE×B drift, then the modeled changes in the
azimuthal velocity distribution are consistent with this picture.


## 3. Summary and Conclusions

Spatial mode transitions are manifested in drastic
changes in the plasma light emission pattern in the gauge tube. Such
transitions are deleterious to the operation of the gauge as a gas species
concentration sensor, especially over large gas pressure ranges. A plasma
simulation study using XOOPIC has shown that this code can indeed simulate, at
least qualitatively, the occurrence of such transitions. With a reasonably
working setup for the Penning discharge, the code can already be run on a
desktop PC with convergence times that are increasingly practical in an
industrial product development setting. It is therefore a potential tool for
improvement of the sensor for specific applications, which can include
greenhouse gas emission monitoring in plasma processing of semiconductors.



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*Source: 360964-2007-08-22.xml*