PHYSICS OF PLASMAS 18, 123501 (2011)
Wave and transport studies utilizing dense plasma filaments generated
with a lanthanum hexaboride cathode
B. Van Compernolle,a) W. Gekelman, P. Pribyl, and C. M. Cooper
Department of Physics, University of California, Los Angeles, 1000 Veteran Ave., Suite 15-70,
Los Angeles, California 90095, USA
(Received 30 March 2011; accepted 1 November 2011; published online 27 December 2011)
A portable lanthanum hexaboride (LaB6) cathode has been developed for use in the LArge Plasma
Device (LAPD) at UCLA. The LaB6 cathode can be used as a tool for many different studies in
experimental plasma physics. To date, the cathode has been used as a source of a plasma with a hot
dense core for transport studies and diagnostics development, as a source of gradient driven modes,
as a source of shear Alfvén waves, and as a source of interacting current channels in reconnection
experiments. The LaB6 cathode is capable of higher discharge current densities than the main
barium oxide coated LAPD cathode and is therefore able to produce plasmas of higher densities
and higher electron temperatures. The 8.25 cm diameter cathode can be introduced into the LAPD
at different axial locations without the need to break vacuum. The cathode can be scaled up or
C 2011 American Institute
down for use as a portable secondary plasma source in other machines. V
of Physics. [doi:10.1063/1.3671909]
I. INTRODUCTION
There is a need in certain classes of experiments to
make dense plasma filaments or high current density channels in a magnetoplasma. Dense plasma filaments facilitate
transport studies of plasmas with a hot dense core and introduce density and temperature gradients which set the stage
for studies of gradient driven modes. High current density
channels can directly excite waves in plasmas or enable
reconnection experiments by studying the interaction of multiple adjacent current channels. Both types of experiments
can be accomplished by the introduction of a cathode with
high emissivity. Current channels are studied in the space
between cathode and anode, while dense plasma filaments
are obtained in the quiescent plasma streaming out of the
cathode–anode region.
Lafferty1 in 1951 first reported on the use of lanthanum
hexaboride (LaB6) as a potent electron emitter. It boasts a
low work function of 2.67 eV and supports large emission
current densities (>10 A=cm2). LaB6 is a crystalline material
which is obtained by press sintering LaB6 powder and can be
easily machined to the desired form. LaB6 has been used in
a variety of instruments, such as electron beams, plasma
sources, Hall thrusters, scanning electron microscopes, and
hollow cathodes.2–6
LaB6 offers several advantages over conventional BaO
coated cathodes. It supports higher emission current densities, is more robust in terms of ion bombardment and can
therefore operate at higher discharge voltages, and is less
prone to poisoning by impurities.7,8 If there is an inadvertent
air leak, the LaB6 cathode can recover after vacuum is reestablished. Poisoning in this paper is not an issue since the
LaB6 cathode is used in conjunction with a larger BaO
coated nickel cathode, and impurities are kept to a minimum
a)
Electronic mail: bvcomper@gmail.com.
1070-664X/2011/18(12)/123501/10/$30.00
in the vacuum vessel in order to prolong the lifetime of the
larger cathode.
The difficulty with LaB6 lies in the higher operating
temperatures (>1600 C), more than 800 C higher than
operating temperatures of BaO coated cathodes. Higher heating power as well as more heat shielding is needed to
improve heating efficiency and to protect components of the
vacuum vessel. More care also needs to be put to prevent
large stresses due to uneven thermal expansion. The high
operating temperatures also limit the materials which can be
used in the cathode assembly. Stable materials at high temperatures such as carbon, molybdenum, and tantalum are
used in this design.
The LaB6 cathode is designed for operation in the LArge
Plasma Device (LAPD, http://plasma.physics.ucla.edu/
bapsf)9,10 at the Basic Plasma Science Facility (BaPSF) at
UCLA. The LAPD is a 21 m long cylindrical device. The
plasma is created through collisional ionization of a neutral
fill gas by an energetic electron beam. The electron beam is
produced through a pulsed discharge between a barium oxide
coated cathode, heated to 750 C, and a 70% transparent
wire mesh anode. Electromagnets provide a uniform axial
magnetic field. The cylindrical plasma column is 18 m long
and has a 60 cm diameter. The machine discharges 24 h a
day at 1 Hz, with typical discharge lengths of 15 ms.
The LAPD is readily diagnosable with 450 ports and
probe access every 32 cm along the machine. Probes are
inserted in the machine through ball valves11 which allow
for 3D movement. Probes are mounted on an external probe
drive system and can be moved to any (x,y) position with sub
millimeter accuracy. The data acquisition system is fully
automated and programmable, and controls the digitizers
and the probe drive system. Typically, the probe moves
through a series of user defined (x,y) positions at fixed z. At
each position, data from several plasma shots is acquired and
stored, before moving to the next position on the (x,y) grid.
18, 123501-1
C 2011 American Institute of Physics
V
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Van Compernolle et al.
Phys. Plasmas 18, 123501 (2011)
FIG. 1. Cartoon of the experimental setup, not to
scale. The main LAPD cathode-anode operates at
1 Hz, with 15 ms pulses. When the LAPD plasma
reaches steady state, the LaB6 cathode-anode is
pulsed on. Probe access through ball valves at
multiple z locations allows for three dimensional
probing of the plasma.
Since the LAPD plasma is highly reproducible, an ensemble
measurement of the plasma parameters can thus be obtained
in a 2D plane at fixed z location.
Fig. 1 is a schematic of the machine and the experimental setup. The LAPD BaO coated cathode and the LaB6 cathode and their respective anodes are on opposite ends of the
machine. Each has its own pulsing supply. Discharge parameters for the LAPD cathode are 50–80 V at 2–5 kA (1.2
A=cm2). The LaB6 cathode operates at 30–400 V and up to
600 A (11 A=cm2), limited by the pulsing power supply. The
LaB6 source is turned on once the LAPD plasma has reached
steady state. Fig. 2 shows a cutaway view of the machine
and the LaB6 cathode. The anode is out of view.
FIG. 2. (Color online) Cutaway view, drawn to scale, of a section of the
LAPD with the LaB6 cathode inserted in the machine. The LaB6 cathode
produces an 8.25 cm diameter plasma embedded in the 60 cm diameter
LAPD plasma. Access to the machine is available every 32 cm axially and
every 45 poloidally, through circular or rectangular ports. Electromagnets
around the machine, drawn in yellow, provide the axial magnetic field. The
anode is 1.92 m away from the cathode and is out of the frame of the
picture.
The paper is organized as follows. Section II discusses
the requirements and the design of the LaB6 cathode. Section
III covers the performance of the cathode, the plasma profiles and shows how it is utilized in experiments.
II. DESIGN
The initial use of the LaB6 cathode design was for transport studies of plasmas with a hot dense core. The goal is to
produce a magnetized plasma column, several ion gyro radii
across, of high density and high temperature, embedded in a
much larger plasma column of lower density and lower temperature. The main LAPD cathode9,10 produces a 60 cm diameter plasma column of uniform density and temperature.
Typically densities are in the range of 2 1012 cm3 and
electron temperatures are on the order of 5 eV. In order to
perform transport studies, it was envisioned that the hot
dense core would need electron densities and electron temperatures of at least a factor of 2 greater.
LAPD operation requires that the LaB6 cathode be easily introduced into the LAPD without disturbing the background plasma production and without breaking vacuum.
Any experimental apparatus needs to be easily introduced
and removed through one of the valves, the largest of which
measures 35.25 cm high and 11.4 cm wide.
The design constraints of the LaB6 cathode are therefore
twofold. First, the cathode needs to be able to produce magnetized plasmas, larger than 10 ion gyro radii across, with
densities on the order of 1013 cm3, and temperatures on the
order of 10 eV. Second, in order to introduce the cathode
while the machine is in use, the assembly needs to fit through
one of the rectangular valves.
The ion gyro radius for a helium plasma with an ion
temperature of 1 eV is 2 mm in a 1000 G magnetic field. The
plasma produced by the 8.25 cm diameter LaB6 cathode is
therefore many ion gyro radii across (>40 qi), while still
small compared to the 60 cm diameter background plasma.
This makes the cathode adequate to study transport phenomena associated with plasma with a hot dense core.
123501-3
Wave and transport studies utilizing dense plasma filaments
Phys. Plasmas 18, 123501 (2011)
FIG. 3. (Color online) Overview of the cathode assembly. The outer dimensions of the assembly measure 12.25 in. 10.5 in. 2.56 in. (31.1 cm 26.7
cm 6.5 cm). The whole assembly is supported by
three 1 in. (2.54 cm) stainless tubes which connect
to the outside of the machine through three vacuum
feedthroughs (not shown). A stainless frame connected to the three tubes by means of three pairs of
brackets holds the heater assembly and the 8.25 cm
LaB6 cathode. The heater connections are shielded
from the plasma by a pair of carbon plates. Not
shown in the picture are additional heat shields
which surround the whole cathode assembly and are
attached to the stainless frame.
The cathode design itself is in large part based on the
design of a larger LaB6 cathode in use in the Enormous Toroidal Plasma Device (ETPD)12 at UCLA. A general overview
of the new cathode is depicted in Fig. 3. The outer dimensions
of the assembly measure 12.25 in. 10.5 in. 2.56 in.
(31.1 cm 26.7 cm 6.5 cm). The cathode assembly is
supported by a stainless steel frame, which attaches to three 1
in. OD stainless steel tubes by means of brackets. The stainless tubes are supported at the machine wall by three vacuum
feedthroughs with differentially pumped sliding seals. Copper
rods, insulated from the stainless tubes with boron nitride
spacers, provide the heater current (DC) and the discharge
current (pulsed). The heater connections are shielded from the
plasma by a pair of carbon plates.
Fig. 4 shows the inner parts of the cathode assembly in
more detail. A carbon heating element is positioned 0.95 cm
behind the carbon plate holding the LaB6 cathode. The heating element is snaked, with arms 0.8 cm wide and 0.32 cm
thick. The distance between the arms is 0.32 cm. The element is slightly oversized compared to the LaB6 disk and
FIG. 4. (Color online) Inner parts of cathode assembly. A snaked carbon
element heats the LaB6 disk. The heating element sits 1.27 cm above the
LaB6 disk and has a larger diameter to ensure uniform heating. It is surrounded on all sides by heat shields. The discharge voltage connects directly
to the carbon frame holding the LaB6 disk. The heating circuit and discharge
circuit are electrically isolated from each other and from the supporting
frame and machine walls.
covers a 10.2 cm diameter area to ensure uniform heating.
Power is supplied through the two outer copper rods. The
rods are attached to molybdenum brackets which in turn bolt
to a block of carbon onto which the heating element is
attached. The discharge current comes in through the third
copper rod, which makes direct electrical contact with the
carbon frame holding the LaB6 disk. The discharge voltage
is electrically isolated from the heating element. Both the
heating circuit and the discharge circuit are electrically isolated from the supporting frame and from the machine walls.
In this sense, the cathode and remote anode can float electrically with respect to anything else in the machine. Insulation
is provided by alumina and boron nitride standoffs. The discharge power supply is based on the supply for the main
LAPD cathode13 but is limited to 450 V and 600 A.
The heating element is surrounded on all sides by a
carbon box, which acts as a primary heat shield. A series of
carbon and tantalum plates serves as heat shields in the back.
Additional heat shields surrounding the whole cathode assembly attach to the stainless frame (not shown in Fig. 3). These
consist of 0.5 mm thick molybdenum sheet. These heat
shields together with the primary heat shields (carbon box
around the heating element) improve the heating efficiency
and protect the LAPD machine walls from radiated heat.
The LaB6 disk14 is sandwiched between two carbon
plates, shown in Fig. 5. The front frame has an 8.25 cm diameter opening, with a 9.53 cm diameter groove in the back.
The groove is 0.33 cm high, 0.01 cm higher than the thickness of the LaB6 disk. The 8.9 cm diameter LaB6 disk lies in
the groove and is kept in place by tantalum cylinders. These
were made by hand, out of 0.01 cm thick tantalum sheet.
0.3 cm wide tantalum strips were cut and rolled into cylinders 0.3 cm high and 0.3 cm diameter. The tantalum cylinders keep the LaB6 disk in place, provide some spring
action, and establish a good electrical contact between the
carbon frame and the LaB6 disk. The 8.25 cm diameter opening of the front frame is the effective LaB6 emitter diameter.
The back frame has a 7.6 cm diameter opening and exposes
the LaB6 disk directly to the radiation from the heating
element.
The anode measures 25 cm by 28 cm and is made out of
70% transparent molybdenum mesh supported by a steel
frame. The anode is inserted in the machine through a
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Van Compernolle et al.
FIG. 5. (Color online) The LaB6 disk is sandwiched between two carbon
plates. Tantalum cylinders hold the LaB6 in place, provide some spring
action, and ensure good electrical contact between the carbon frame and
the LaB6.
rectangular valve. The anode is inserted Dz ¼ 1.92 m away
from the cathode, which is the spacing between two rectangular ports on the LAPD (the anode-cathode spacing can be
varied depending on experimental requirements). Plasma
parameters are measured past the cathode and anode in the
current free quiescent plasma region. Section III F describes
experiments in which the anode-cathode spacing is 10.86 m
and the plasma is probed in between the anode and cathode.
III. RESULTS
A. Cathode operation
Prior to insertion in the machine, the cathode assembly is
pumped down in a plenum attached to the LAPD and heated
with 150 W for several days. This evaporates and pumps out
as much water as possible before opening a valve to the
machine. LAPD operation requires the water level in the
machine to be kept low to prolong the lifetime of the LAPD
BaO coated cathode ðPH2 O < 5 107 TorrÞ. Once the LaB6
cathode is in the machine, it is further heated up slowly, over
the course of more than 10 h, to keep the water level in the
machine under control. The LaB6 discharge is started once the
cathode reaches emission temperatures. The cathode is left
pulsing overnight to equilibrate before use in experiments.
The discharge current can rise by 50% or more overnight as
impurities in the LaB6 disk outgas and are pumped away.
The cathode is typically operated for two weeks at a
time, an experimental cycle time on the LAPD. After that,
the cathode is slowly cooled, removed from the machine,
and partly disassembled. The LaB6 disk is inspected for
cracks. Cracks can occur due to fast or uneven cooling of the
cathode assembly. The heating power to the cathode is
brought down over the course of 3 to 5 h, allowing for a
slow cool-down. Bringing down the heating power too rapidly, in this case in less than an hour, typically results in a
cracked LaB6 disk due to thermal stresses. The LaB6 disk is
also checked for large carbon buildup on the backside, which
can occur because the back is exposed directly to the carbon
heating element. If the backside of the LaB6 disk is coated
Phys. Plasmas 18, 123501 (2011)
unevenly with carbon, then the excess carbon is removed
with sandpaper. During disassembly, the thickness of the
arms of the carbon heating elements is measured to check for
carbon evaporation. If any thinning is observed, the heating
element is replaced to prevent a failure during the next experimental run. Under normal operating conditions, a heating
element lasts several months without substantial carbon
evaporation. After inspection, the cathode is reassembled. In
general no parts need to be replaced. All carbon pieces and
tantalum and molybdenum bolts and nuts can be reused.
Fig. 6 shows the LaB6 cathode inserted from the top of
the LAPD. The plasma from the 8.25 cm diameter LaB6
cathode is embedded in a 60 cm background plasma produced by the main LAPD cathode located at the far end of
the picture. The anode was inserted through a rectangular
port, 1.92 m away from the cathode. The picture shows a
580 A, 400 V helium discharge in a 900 G magnetic field.
The helium fill pressure was 104 Torr. The anode in the picture is a 17 cm diameter wire mesh anode. Other experiments
used a 25 cm by 28 cm rectangular wire mesh anode.
B. Plasma profiles
Density and temperature profiles with the LaB6 cathode
operating in the background plasma were obtained for a
range of discharge voltages and magnetic fields. The profiles
were measured by sweeping the voltage on a planar Langmuir probe, located at z ¼ 7.03 m. The LaB6 cathode and anode are located 3.2 m and 1.28 m from the probe,
respectively (cathode at z ¼ 3.83 m and anode at z ¼ 5.75 m).
The LAPD was filled with helium gas at a pressure of
4 105 Torr. The LAPD cathode was pulsing a 2.8 kA discharge current with a 55 V discharge voltage. The background plasma is left to equilibrate for 7 ms before the LaB6
cathode is switched on. For these experiments, the background plasma is at steady state at 1.25 1012 cm3 electron
density and 4.5 eV electron temperature. The profiles shown
below are the steady state density and temperature profiles
after the LaB6 cathode has been switched on.
Figs. 7 and 8 show the density and temperature profiles
at different discharge powers. The magnetic field was uniformly set to 700 G. The different discharge powers were
obtained by varying the discharge voltage applied between
FIG. 6. (Color online) Picture of a helium discharge of the LaB6 cathode in
the LAPD, viewed from behind, with several probes inserted into the
machine from the left. The magnetic field is 900 G, helium fill pressure is
104 Torr, and the discharge current is 580 A with a 400 V discharge
voltage.
123501-5
Wave and transport studies utilizing dense plasma filaments
Phys. Plasmas 18, 123501 (2011)
FIG. 7. (Color online) Density profiles at fixed magnetic field of 700 G for
different discharge powers. Raising discharge power steadily increases
plasma density. The “wings” are the background LAPD plasma. The shaded
area indicates the extent of the LaB6 cathode.
FIG. 9. (Color online) Density profiles at fixed discharge voltages of 150 V,
and nearly fixed discharge power, for different magnetic fields. Higher fields
improve radial confinement resulting in increased densities and steeper
density profiles. The shaded area indicates the extent of the LaB6 cathode.
the cathode and anode, from 25 V to 150 V in 25 V increments. The profiles are taken on a radial cut through the center of the LaB6 plasma. The LaB6 cathode produces a fairly
flat temperature profile on the field lines connected to the
LaB6 cathode and a sharply peaked density profile. The electron temperature profile is mainly set by parallel losses at the
end of the machine. The parallel electron thermal conductivity is larger than the perpendicular electron thermal conductivity by a factor of x2ce s2e ’ 106 .15,16 Even though the radial
temperature gradient (cm scale) is much steeper than the parallel temperature gradient (m scale), the radial electron heat
flux is still orders of magnitude smaller than the parallel
electron heat flux due to the large difference in thermal conductivities. Radial losses are therefore minimal. The temperature on a field line is then set by the power input on that
field line. Field lines in contact with the LAPD cathode only
show a uniform temperature of about 4.5 eV. Field lines in
contact with both cathodes (shaded area in Fig. 8) exhibit
a fairly uniform elevated temperature. A strong electron
temperature gradient exists between these two regions,
giving evidence that radial losses are minimal. Radial density losses, however, are not negligible compared to parallel
losses, resulting in a peaked density profile, which extends
well into the background LAPD plasma (Fig. 7).
A similar profile scan was done with the discharge voltage
kept fixed at 150 V, and the background magnetic field was
varied between 500 G and 900 G. Figs. 9 and 10 show the electron density and electron temperature profiles, respectively. The
electron temperature profiles show no dependence on the background magnetic field. Again, the electron temperature is set
mainly by parallel heat losses to the end of the machine. The
parallel thermal conductivity has no magnetic field dependence,
hence the profiles of Fig. 10. The electron density profiles of
Fig. 9 do have a slight dependence on magnetic field. Radial
density losses are higher at lower fields, resulting in lower peak
densities, and larger radial density decay lengths. Radial density
transport in the LAPD and LAPD like plasmas is dominated by
Bohm diffusion.17 Therefore, the radial density diffusivity
FIG. 8. (Color online) Electron temperature profiles at fixed magnetic field
of 700 G for different discharge voltages. Electron temperature increases
above the 4.5 eV background temperature with discharge power, as
expected. The shaded area indicates the extent of the LaB6 cathode.
FIG. 10. (Color online) Electron temperature profiles at fixed discharge
voltage of 150 V, and nearly fixed discharge power, for different magnetic
fields. Profiles are almost identical for all magnetic fields. Electron temperature profiles are mainly determined by axial heat losses, governed by jjj
which has no magnetic field dependence. The shaded area indicates the
extent of the LaB6 cathode.
123501-6
Van Compernolle et al.
scales as Dr DB 6:25e6 ðT=BÞ. For Te ’ 6 eV and
B ¼ 900 G, one finds Dr ’ 4e4 cm2 =s. The radial flux rate is
on the order of DB n=L? ’ 2:5e16 cm2 =s, with L? ’ 5 cm
the perpendicular gradient scale length and n ’ 3e12 cm3 .
The total number of particles lost radially is estimated as
DB n=L? 2pRLaB6 L ’ 7e20 s1 , where RLaB6 is the radius
of the LaB6 plasma and L is its length. This can be compared to
the number of particles lost per second at the end of the
machine. Particles flow out the end at the sound speed at a particle flux rate of ncs ’ 3e18 cm2 /s. The total number of particles lost at the end of the machine is ncs pR2LaB6 ’ 2e20 s1 .
Radial and parallel particle losses are therefore comparable,
and changing the magnetic field, and thus changing the radial
diffusivity, has an appreciable effect on the overall peak density
and on the radial profiles of Figure 9.
C. High power operation
In Sec. III B, the LaB6 cathode was operating at low discharge currents, approximately 1–2 A=cm2. In this section,
results are shown for operation at higher discharge powers.
The magnetic field was set to 1 kG and the machine pressure
was raised to 104 Torr, whereas typical LAPD operating
pressures are in the range of 1–3 105 Torr. The LAPD
cathode operated at 2.2 kA, 45 V. The LaB6 cathode was
switched on after the LAPD cathode had been on for 7 ms
and the plasma had reached steady state. The discharge voltage between LaB6 cathode-anode was varied from 0 V to
400 V in steps of 20 V. The steady state discharge current
from the new cathode is seen to increase almost linearly with
the applied discharge voltage in Fig. 11. The highest discharge current measured was 580 A, which corresponds to a
current density of 11 A=cm2, assuming a uniform current
density across the LaB6 disk. Under these conditions, the
discharge power due to the LaB6 cathode is larger than the
discharge power due to the entire LAPD cathode. The maximum discharge current was limited by a transistor rated for
600 A in the pulsing power supply. With a higher power
transistor, the discharge current could forseeably be raised
further.
FIG. 11. Discharge current versus discharge voltage at B0 ¼ 1 kG, helium
fill pressure of 104 Torr. Discharge current was limited by the 600 A transistor in the pulsing power supply.
Phys. Plasmas 18, 123501 (2011)
Measurements of the electron density and electron temperature were obtained by sweeping the voltage on a planar
Langmuir probe at z ¼ 7.03 m (cathode at z ¼ 3.83 m and anode at z ¼ 5.75 m), plotted in Fig. 12. Single point measurements were taken for each of the discharge voltages in
Fig. 11. The probe was positioned on the same field line as
the center of the LaB6 cathode. At low discharge powers,
there is a fast increase of electron temperature with increasing discharge powers. This fast increase tapers off because
the electron heat losses increase quickly with increasing temperature. Electron heat is lost due to parallel heat conduction
to the end of the machine. The parallel electron heat conductivity jek is proportional to Te5=2 , and it takes progressively
more discharge power to further heat the plasma. The electron density is observed to increase close to linearly with
applied discharge power. Densities of the order of 1013 cm3
are routinely reached.
Fig. 13 shows the electron density and electron temperature profiles of a LaB6 discharge at 220 A discharge current
and 280 V discharge voltage. The machine parameters were
B0 ¼ 500 G and a helium fill pressure of 9 105 Torr. The
LAPD cathode operated at 3.5 kA, 55 V and creates a uniform plasma of 2 1012 cm3 electron density plasma and
4 eV electron temperature before the LaB6 cathode is turned
on. Fig. 13 shows the profiles in steady state with this LaB6
discharge. The density in the core goes up by a factor of 5
and the electron temperature increased by a factor of 2.5.
The increase in electron temperature is mainly confined to
the field lines in contact with the LaB6 cathode, since parallel
heat transport dominates. The electron density also peaks
mostly on the same field lines but has wide wings which
extend well into the background plasma.
Transport studies investigating the formation of the electron density and temperature profile of plasmas with a hot
dense core will be reported elsewhere. The high density
plasma from the LaB6 cathode has already been used in laser
plasma experiments18,19 and will be used as a target plasma
for the development of a Thomson scattering diagnostic for
the LAPD.20
FIG. 12. (Color online) Dependence of peak electron density and electron
temperature versus discharge power of the LaB6 cathode. Discharge voltage
varied from 0 V to 240 V in 20 V steps.
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Wave and transport studies utilizing dense plasma filaments
FIG. 13. (Color online) Electron density and electron temperature profiles
for a 280 V, 220 A discharge, at B0 ¼ 500 G, helium fill pressure of
9 105 Torr. The shaded area indicates the extent of the LaB6 cathode.
D. Source of large scale gradient driven modes
Plasmas with large temperature and density gradients
were used to drive gradient driven modes, such as drift
Alfvén waves, unstable. To maximize the gradients, the
LaB6 cathode is switched on during the afterglow of
the LAPD plasma. Once the BaO discharge is switched off,
the background electron temperature decays on a time scale
of 100 ls, and the density decays on the time scale of ms.
The LaB6 cathode is switched on 2 ms into the afterglow.
The LAPD plasma at that time is uniformly cold at 0.5 eV
and the density is on the order of 1012 cm3. A moderate
LaB6 discharge of 75 V and 100 A creates strong electron
temperature gradients on field lines at the edge of the LaB6
disk, and more gentle density gradients which extend well
into the background plasma. Profiles look similar to Fig. 13,
but the gradients are steeper.
Ion saturation measurements in the edge of the hot dense
core plasma show strong oscillations while the LaB6 cathode
is on (upper panel Fig. 14). These are localized to the region
of strong gradients. Fluctuation amplitudes of dn=n ’ 100%
are observed. Correlation measurements were done to ana-
FIG. 14. Upper panel: ion saturation current in the edge of the hot core
show strong fluctuations while the LaB6 cathode is on (from t ¼ 0 ms to
t ¼ 15 ms, B0 ¼ 1000 G). Lower panel: cross spectrum of ion saturation current averaged over a region in space where large fluctuations were observed.
Several distinct low frequency gradient driven mode are present.
Phys. Plasmas 18, 123501 (2011)
lyze the mode structure of these fluctuations. A Langmuir
probe at z ¼ 8.63 m, scanning the whole cross section of the
plasma, is cross correlated with a fixed Langmuir probe at
z ¼ 8.95 m, which serves as a phase reference. The lower
panel of Fig. 14 shows the cross spectrum averaged over a
region in space where large fluctuations were observed. Distinct low frequency modes are present at f ¼ 1.4 kHz, 3.75
kHz, 5 kHz, and 8.25 kHz.
Cross correlation analysis brings out the mode structure.
The signals from both probes were digitally filtered around
each of the 4 frequency peaks and were then cross correlated
with each other. The four panels (a), (b), (c), and (d) in
Fig. 15 show the cross covariance for the signals filtered
at the 4 frequencies in Fig. 14(b), i.e., 1.4 kHz, 3.75 kHz,
5 kHz, and 8.25 kHz, respectively. The respective mode
numbers are m ¼ 3, m ¼ 4, m ¼ 1, and m ¼ 2. The lower frequency m ¼ 3 and m ¼ 4 modes extend from the edge of the
core plasma well into the background plasma column. The
higher frequency m ¼ 1 and m ¼ 2 modes reside right at the
edge of the core plasma. Similar cross correlation analysis
was done with a moving and a fixed magnetic field probe.
The m ¼ 1 and m ¼ 2 mode are present in the magnetic field
measurements, but the m ¼ 3 and m ¼ 4 mode have no magnetic field fluctuations associated with them. Therefore, both
electrostatic and electromagnetic gradient driven modes
have been observed. These modes have been recently studied
under a range of different conditions. A manuscript detailing
the results is in preparation.
E. Source of shear Alfvén waves
Shear Alfvén waves can be launched with the LaB6 cathode by applying a pulse train in the Alfvén wave frequency
range to bias the cathode instead of a single pulse. The LaB6
cathode then serves not as a source of ionization but as a
source of modulated parallel electron current. The emission
current of the cathode can couple to the parallel wave current
of the shear Alfvén wave and thus radiate shear waves. An
example is shown in Fig. 16. The machine operated at
2.7 105 Torr at a magnetic field of 800 G and a
2 1012 cm3 density. The pulsing power supply of the LaB6
cathode was triggered with a pulse train, shown in the middle
panel of Fig. 16. The trigger consists of 20 pulses at 189 kHz
with a 50% duty cycle. The applied frequency of 189 kHz
corresponds to f=fci ¼ 62% which is in the typical frequency
range of shear Alfvén waves observed in the LAPD.
The measured frequency spectrum of the Bx component,
Dz ¼ 415 cm away from the cathode, at x ¼ 8.6 cm,
y ¼ 3.5 cm is shown in the upper panel of Fig. 16. A sharp
peak is present at the launched frequency of 189 kHz. Below
30 kHz some low frequency modes exist, which are gradient
driven modes as in Sec. III D. The Bx data sampled at
x ¼ 8.6 cm, y ¼ 3.5 cm was band pass frequency filtered at
189 kHz and is displayed in the lower panel of Fig. 16. A
pulse train of 20 oscillations is followed by smaller oscillations. These smaller oscillations are most likely due to waves
reflected from the end of the machine. The perpendicular
magnetic field components of the wave are larger than the
parallel components by a factor of 7. Based on the frequency
123501-8
Van Compernolle et al.
Phys. Plasmas 18, 123501 (2011)
FIG. 15. (Color) Cross covariance of the
ion saturation currents of a moving Langmuir probe and a fixed Langmuir probe
Dz ¼ 32 cm away, both measuring ion saturation current. Both electrostatic and electromagnetic gradient driven modes are present
with mode numbers ranging from m ¼ 1 to
m ¼ 4 and higher. The black dotted line
indicates the edge of the LaB6 cathode. (a)
f ¼ 1.4 kHz, (b) f ¼ 3.75 kHz, (c) f ¼ 5 kHz,
and (d) f ¼ 8.25 kHz.
of the wave (f < fci) and on the large perpendicular magnetic
field component, the wave can be identified as a shear Alfvén
wave. The parallel phase speed of the wave can be estimated
from the dispersion relation for the kinetic ðvA < ve Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 q2 with
shear Alfvén wave,21 x=kk ¼ vA 1 x2 =X2i þ k?
s
qs ¼ cs=Xi. For our plasma parameters, we calculate
qs ’ 0:5 cm, k? ¼ 16 cm, and vA ¼ 6.2 107 cm=s. The estimated parallel phase speed is x=kk ’ 5 107 cm=s. The distance from the probe to the end of the machine was 894 cm;
therefore, the reflected wave will reach the probe after
Dt ¼ 2 894=vA ’ 36ls. The oscillations in Fig. 16 persist
for about 40–50 ls, in fairly good agreement with the estimated Dt. This strengthens the argument that those smaller
oscillations are indeed due to reflected waves, and therefore
the wave is a propagating wave.
The estimate for k? of 16 cm can be obtained from the
transverse wave profile shown in Fig. 17. The azimuthal
component of the magnetic field B/ is shown in a (x,y) plane
at 4 different times. Each picture advances in time by a quarter wave period. The distance between a maximum and a
minimum is about 8 cm, therefore k? ¼ 16 cm. The perpendicular wave length is set by the diameter of the LaB6 source
(¼8.25 cm). Phase fronts are moving radially outwards, consistent with the kinetic Alfvén wave dispersion. The phase
patterns of Fig. 17 show that the LaB6 cathode can produce a
clean single mode Alfvén wave. Amplitudes are in the range
of hundreds of mG. The authors are confident that Alfvén
waves in the range of several Gauss can be launched in
future experiments, as the data shown here was done at low
discharge currents. This brings the wave in a regime where
electron heating and plasma modification due to Alfvén
waves become important.
F. Source of interacting current channels
for reconnection studies
FIG. 16. Top panel: amplitude spectrum of magnetic field fluctuations at
x ¼ 8.6 cm, y ¼ 3.5 cm, Dz ¼ 415 cm away from the cathode. Middle
panel: input trigger to pulsing power supply, train of 20 pulses at 189 kHz
and 50% duty cycle. Lower panel: Alfvén wave magnetic field fluctuations
at x ¼ 8.6 cm, y ¼ 3.5 cm, Dz ¼ 415 cm, filtered at 189 kHz. Wave is still
present after the 20 input pulses, due to wave reflection at the end of the
machine.
The LaB6 cathode has been used in a series of reconnection experiments (see also Refs. 22 and 23). The reconnection studies revolve around the dynamics of interacting
current channels. Both the case of 3 cylindrical current channels and the case of 2 parallel current sheets have been studied. To this purpose, the LaB6 cathode is masked off with a
carbon plate.
In the case of the three cylindrical current channels, the
carbon plate has equidistant holes of 1 inch diameter, with 1.5
inch center to center spacing. This effectively reduces the
larger LaB6 disk to three electron emitters, which create 3 current channels between cathode and anode. The magnetic field
of three current channels has a X-point between any of two
channels. Magnetic reconnection can occur at one or more of
these X-points. In these experiments, the cathode and anode
are placed on opposite ends of the machine, Dz ¼ 10.86 m, in
123501-9
Wave and transport studies utilizing dense plasma filaments
Phys. Plasmas 18, 123501 (2011)
FIG. 17. (Color) Azimuthal magnetic field
component of Alfvén wave launched by pulsing
the LaB6 cathode on and off for 20 bursts at 189
kHz and 50% duty cycle. Panels (a) through (d)
show snapshots with time progressing by a quarter period from plot to plot (Dt ¼ 1.32 ls). The
black dotted line indicates the edge of the LaB6
cathode.
order to maximize the distance that the current channels can
interact. The experiments are also performed at low axial
magnetic field to ensure a strong interaction between the current channels by maximizing Bcurrent channels=B0.
Fig. 18 shows the axial current at four different axial
locations, at Dz ¼ 64 cm, Dz ¼ 256 cm, Dz ¼ 383 cm, and
Dz ¼ 639 cm, where Dz ¼ 0 cm is the location of the LaB6 cathode. Close to the LaB6 cathode, the three current channels can
clearly be identified. Peak current densities are on the order of
8 A=cm2. The parallel current in the channels exerts an attractive force, so that further away, the three current channels
merge. The current channels are not stationary in time. They
are observed to rotate counterclockwise in time in a right
handed fashion, i.e., in the electron gyration direction (B0
comes out of the plane). The radius of rotation increases with
increasing distance from the LaB6 cathode. Close to the cathode, at z ¼ 64 cm, the current channels are almost line tied to
the cathode. At the anode, however, they are not line tied, and
they can end at any point on the 25 cm by 28 cm anode.
In the experiment, data was acquired in 16 (x,y)-planes,
every Dz ¼ 64 cm, resulting in a 3D data set. Fig. 19 shows a
snapshot in 3D of the magnetic field lines. Field lines were
started on a circle of 1 cm radius around the center of each
current channel and are followed throughout the measurement
volume. Field lines with different colors emanate from different holes in the carbon mask. The field lines of a single current
channel both twist and writhe.24 The twist measures the torsion of a field line about the central axis of the current channel, and the writhe measures the twisting of the central axis of
the current channel. In this experiment, the twist is about 270
and the writhe is about 180 . The twist and writhe of the field
lines is left handed, consistent with Jz Bz < 0.25,26 More
complex analysis of the 3D data set has been done and will be
discussed in a future paper.27
FIG. 18. (Color) Axial current density calculated from Jz ¼ c=4pr B at (a) Dz ¼ 64 cm,
(b) Dz ¼ 256 cm, (c) Dz ¼ 383 cm, and (d)
Dz ¼ 639 cm. The labels help track the current
channels in the four planes. The current channels are line tied close to the cathode but attract
each other and merge far from the cathode. In
the picture, the background field points out of
the paper.
123501-10
Van Compernolle et al.
Phys. Plasmas 18, 123501 (2011)
performed at the Basic Plasma Science Facility at UCLA,
funded by NSF=DOE.
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2
FIG. 19. (Color) Field lines obtained from a volumetric measurement of the
magnetic field. The z-axis is compressed by a factor of 10. Field lines are
started on a circle of 1 cm radius around the center of each current channel.
Field lines with the same color emanate from the same hole in the carbon
mask. The field lines of an individual current channel twist in a left handed
fashion and the current channels themselves spiral around each other. The
current channels are line-tied at the LaB6 cathode but are seen to rotate further downstream in the electron gyration direction, i.e., right handed rotation
or clockwise in this figure.
IV. CONCLUSIONS
In conclusion, the design and operation of a portable LaB6
cathode has been reported in this paper. The cathode can be
scaled up or down for use as a portable secondary plasma
source in other machines. The cathode was shown to operate at
current densities of 11 A=cm2, limited by the pulsing power
supply. Higher operating current densities are feasible. The
LaB6 cathode can provide higher densities and temperatures
than the main LAPD cathode, i.e., densities upwards of 1013
cm3 and temperatures of 10 eV. The LaB6 cathode is an important new tool for the LAPD and has been used in a number
of different experiments. To date, it has been used as a source
of a plasma with a hot dense core for transport studies and diagnostics development, as a source of gradient driven modes, as a
source of shear Alfvén waves, and as a source of interacting
current channels in reconnection experiments. Other uses can
be envisioned and will be explored in the future.
ACKNOWLEDGMENTS
The authors wish to thank Zoltan Lucky and Marvin
Drandell for their technical help. The research was