PHYSICS OF PLASMAS 16, 092106 共2009兲
Generation of polarized shear Alfvén waves by a rotating magnetic
field source
A. Gigliotti,1 W. Gekelman,1 P. Pribyl,1 S. Vincena,1 A. Karavaev,2 X. Shao,2
A. Surjalal Sharma,2 and D. Papadopoulos2
1
Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1696, USA
Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742, USA
2
共Received 16 April 2009; accepted 19 August 2009; published online 16 September 2009兲
Experiments are performed in the Large Plasma Device at the University of California, Los Angeles
to study the propagation of field-aligned, polarized kinetic shear Alfvén waves radiated from a
rotating magnetic field source created via a novel phased orthogonal loop antenna. Both right and
left hand circular polarizations are generated at a wide range of frequencies from 0.21ⱕ ␻ / ⍀ci
⬍ 0.93. Propagation parallel to the background magnetic field near the Alfvén velocity is observed
along with a small parallel wave magnetic field component implying a shear mode. The
peak-to-peak magnitude of the wave magnetic field, 33 cm away from the antenna, is on the order
of 0.8% of the background field and drops off in the far field. The full width at half maximum of
the wave energy changes little over a distance of 2.5 parallel wavelengths while the exponential
decrease in wave energy as a function of distance can be attributed to collisional damping. Evidence
of electron heating and ionization is observed during the pulse. © 2009 American Institute of
Physics. 关doi:10.1063/1.3224030兴
I. INTRODUCTION
The shear Alfvén wave 共SAW兲 is found in a variety of
magnetized plasma environments. It has been artificially excited in a number of laboratory experiments1 and naturally
observed in a variety of astrophysical settings such as the
solar corona,2 near other planets such as Jupiter,3 and Earth’s
aurora.4 It is capable of transporting energy, accelerating particles, and mediating changes in the current structures of
plasmas. In fact, one may think of many low frequency current systems in a magnetoplasma as Alfvénic wave systems.
Shear waves were observed by the FAST,5 Cluster,6 and
Helios2 satellites and are now thought to play a major role in
charged particle acceleration in environments such as Earth’s
aurora,7,8 its bow shock,6 and the solar corona.2 Measurements of the incoming Poynting flux of shear waves toward
the auroral ionosphere by the Polar satellite indicate that they
alone may have enough energy to power certain types of
aurora.9
In this experiment, the study of these waves is motivated
by their possible application to the reduction of the energetic
particle flux in Earth’s inner radiation belt. Energetic protons
trapped at L ⬍ 2 are the greatest threat to microelectronics of
low Earth orbiting satellites as these particles will destroy
currently developed devices using a submicron feature size.
Large amplitude SAWs generated by a rotating magnetic
field 共RMF兲 source are a candidate for the remediation of
these energetic particles via nonadiabatic scattering by the
wave fields.10 Although a variety of shear waves have been
excited in the laboratory, a unique requirement in this effort
was the production of waves of fairly high amplitude with
arbitrary polarization.1 The following work encompasses
both the generation and a detailed characterization of these
1070-664X/2009/16共9兲/092106/8/$25.00
waves. A phased dual orthogonal loop antenna is used to
induce a RMF that couples to a polarization controlled, large
amplitude, SAW.
II. PROPERTIES OF SHEAR ALFVÉN WAVES
The SAW is an electromagnetic mode that exists in magnetized plasmas and propagates at frequencies below the ion
cyclotron frequency, ␻ ⬍ ⍀ci. To zeroth order, the wave
propagates parallel to the background magnetic field, B0, and
its magnetic field, B, is almost perpendicular to the background field while its electric field lies perpendicular to both
B0 and B.11–13 To first order, when k⬜ is included, there is a
small component of the wave’s electric field that lies along
the background field.13 It is this parallel component that
gives the SAW the ability to accelerate electrons and drive
field-aligned plasma currents. Perpendicular to B0, the currents of SAWs are carried by ions through their polarization
drift.14
It is well known that the SAW exists in two distinct
regimes, commonly known as the inertial and kinetic, which
are differentiated by the ratio of the electron thermal speed,
15
ve = 共2Te / me兲1/2, to the Alfvén speed, vA = B0 / 共4␲nimi兲1/2.
The inertial regime is characterized by ve ⬍ vA whereas the
kinetic is characterized by ve ⬎ vA. This experiment was conducted in the kinetic regime. In this limit, the dispersion
relation for the shear mode, including finite frequency effects, can be written as
␻/k储 = vA冑1 − 共␻/⍀ci兲2 + 共k⬜␳s兲2 ,
共1兲
where ␳s = cs / ⍀ci is the ion sound gyroradius, cs = 共Te / mi兲1/2
is the sound speed, ⍀ci = 共qiB0兲 / 共mic兲 is the ion cyclotron
frequency, Te is the electron temperature, and ⬜ and 储 denote
the components perpendicular and parallel to the background
magnetic field, B0, respectively.13 In general, the cross-field
16, 092106-1
© 2009 American Institute of Physics
092106-2
Phys. Plasmas 16, 092106 共2009兲
Gigliotti et al.
1600 cm
Cathode
Anode
Orthogonal Ring Antenna
Plasma
#1
z
50 cm
100 cm
x
B0
#2
Discharge Switch
Probe
1800 cm
FIG. 1. Schematic of experimental setup. The LAPD chamber and reproducible, quiescent, plasma column are shown. The orthogonal ring antenna
is aligned so the rotation axis of the induced magnetic field at the center of
the antenna is parallel to the direction of the background solenoidal field,
B0. The data are collected through the use of probes that can be placed at
various locations along z. This is not drawn to scale.
propagation of the SAW is much slower than parallel phase
speed v␾储 = ␻ / k储.15–17 As a result, the wave remains largely
localized to a fixed set of field lines.
III. EXPERIMENTAL ARRANGEMENT
The following experiment was conducted on the Large
Plasma Device 共LAPD兲 at the University of California,
Los Angeles 共see Fig. 1兲. The device is composed of an 18 m
long, 1 m diameter, stainless steel cylindrical vacuum chamber that is surrounded by 56 pancake electromagnets placed
at 32 cm intervals creating a uniform, ␦B0 / B0 ⬇ 1%, solenoidal magnetic field along the length of the device. In order to
provide access to the plasma column, there are 488 ports
evenly distributed down the length of the device. Of those,
424 are 15 cm diameter circular ports equipped with windows, gate valves, and various diagnostics. The remaining 64
are rectangular ports that allow for the insertion of larger
scale objects, such as our antenna, into the plasma column.
At 32 cm intervals, along the entire length of the machine, 65
of the circular ports are equipped with ball joints and gate
valves which allow for the insertion and two-dimensional
movement of diagnostic probes at many z locations.18
The LAPD creates a highly reproducible, highly magnetized, quiescent dc discharge plasma. The discharge occurs
between a heated barium-oxide coated nickel cathode and a
molybdenum mesh anode with a 52 cm separation. As a result, the remaining 16 m of the plasma column carries no net
current. The machine is backfilled with He at a pressure of
approximately 1 ⫻ 10−4 Torr and pulsed at 1 Hz. With the
background magnetic field, B0, held fixed at 1 kG, a 4.5 kA
discharge is run for 12 ms to produce a plasma column
17 m long and 50 cm in diameter with a density of
共2.3⫾ 0.3兲 ⫻ 1012 cm−3 共calibrated using a microwave interferometer兲, an electron temperature, Te, of 6 ⫾ 1 eV 共measured from a swept Langmuir probe兲, and an ion temperature, Ti, of 1 ⫾ 0.5 eV. For a wave driven at ␻ = 0.54 ⍀ci,
with a characteristic ␭⬜ = 9 cm determined by the antenna
size, the kinetic dispersion relation gives a parallel Alfvén
FIG. 2. 共Color online兲 Photographic image of the RMF antenna. Each coil
has three turns of enameled solid copper wire covered in epoxy to prevent
electrical contact with plasma. Coil 1 has a diameter of 9 cm and coil 2 has
a diameter of 8 cm.
wavelength of 317 cm. For these conditions, the axial length
of the device contains approximately five parallel Alfvén
wavelengths.
A computer controlled data acquisition system is used to
collect volumetric data. Computer controlled digitizers and
mechanical probe drives are used to acquire planar data sets,
transverse to the background field, at various axial positions
along the length of the device. In the plane transverse to the
background field, the probe drive positioning system is accurate to 0.5 mm, while in the axial direction along the field,
it is accurate to 1 cm. Probes are moved to a prespecified
position within the plane, the discharge plasma is created, the
orthogonal ring antenna is pulsed, and temporally resolved
data are collected at that location. This process is repeated at
each location. For this experiment, eight planes, each covering 1681 spatial locations, were collected spanning an axial
distance of 8 m along the device over the course of approximately 135 000 discharges.
IV. WAVE LAUNCHING
A. Orthogonal ring antenna
SAWs are launched using a RMF source realized using a
phased, orthogonal loop antenna 共Fig. 2兲. The antenna is
composed of two coils, each with three turns of 0.25 cm
diameter solid copper wire. The horizontal coil 共coil 2兲 has a
diameter of roughly 8 cm while the vertical coil 共coil 1兲 has
a diameter of 9 cm. These coils are driven by a pair of high
power resonant LRC circuits, set 90° out of phase with respect to each other. The antenna is carefully aligned such that
the axis of rotation of its induced magnetic field at the center
of the antenna is parallel to B0 共Fig. 1兲. In this experiment,
the antenna was pulsed for 100 ␮s, 10 ms into a 12 ms long
plasma discharge.
092106-3
Generation of polarized shear Alfvén waves…
Variable Capacitance
C. Diagnostics: Wave detection
High Power Amplifier Array
Line Resistance
50 Ω
50 Ω
50 Ω
Inductive Coil
50 Ω
50 Ω
Phys. Plasmas 16, 092106 共2009兲
50 Ω
Line Resistance
Variable Capacitance
FIG. 3. Schematic of the high power LRC driver used for each coil. Various
high voltage capacitors were used to tune the circuit to a wide range of
frequencies from 0.21ⱕ ␻ / ⍀ci ⬍ 0.93. In the experiment, two drivers locked
90° out of phase were used, one driver per coil.
The primary diagnostic used in this experiment is a
three-axis magnetic pickup coil. This probe features differentially wound loops that eliminate electrostatic pickup when
used in conjunction with a differential amplifier. The loops
are wound around a 1 mm cube with ten turns each. The
cube is mounted within a glass tube and attached to a thin
ceramic tube extending from the end of a stainless steel
probe shaft. The probe used in this experiment was calibrated
using a network analyzer and differential amplifiers with a
gain of 1 and 50 ⍀ output impedance were used.
Additional data come from a double-sided Langmuir
probe used to take ion saturation current measurements before and during the pulse where Isat ⬃ ne共Te兲1/2. A 56 GHz
microwave interferometer was used to acquire absolute line
averaged density measurements and a photodiode sensitive
to visible wavelengths was used to measure line integrated
light intensity across the center of the plasma column.
B. High power LRC driver
The LRC circuit utilizes the inductance of the antenna
and the inherent resistance of the lines while relying on high
frequency rf drivers developed in house to supply the circulating power 共Fig. 3兲. Combinations of high voltage capacitors allow for flexible tuning of the system. Together, these
components produce a phase locked, sinusoidal current wave
packet with peak-to-peak current of 1200 A and voltages
across the capacitors of 2000 V.
V. EXPERIMENTAL RESULTS
The RMF source is found to drive large amplitude, fieldaligned kinetic SAWs with arbitrary polarization. It is large
amplitude in the sense that the peak-to-peak magnitude of
the wave magnetic field is approximately a 1% distortion of
the background field, and this displacement is close to the
t = 4 s
FIG. 4. 共Color兲 A portion of the three-dimensional volumetric data set consisting of 13 448 spatial locations is plotted at an early time in the pulse, ␶
= 4 ␮s. The wave is launched from an antenna 33 cm to the lower left of the first plane. The magnetic field vectors are shown within a 2 m long section of
the LAPD. For orientation purposes, an idealized cross section of the LAPD is drawn: magnets are purple, the vacuum vessel is gray, and access ports are
shown with semitransparent and reflective glass.
092106-4
Phys. Plasmas 16, 092106 共2009兲
Gigliotti et al.
Average Phase Velocity versus Frequency
vphase / vA
Bx (Gauss)
Position (x,y,z) = (0.0, 0.0, 96.9) cm
Time (μs)
Position (x,y,z) = (0.0, 0.0, 96.9) cm
f / fci
By (Gauss)
FIG. 6. Plot of the average parallel phase velocity of the driven wave measured for various ratios of the drive frequency 共f兲 to the ion cyclotron
frequency 共f ci兲. The solid curve is the theoretical parallel shear Alfvén phase
velocity, given by Eq. 共1兲.
Time (μs)
Bz (Gauss)
Position (x,y,z) = (0.0, 0.0, 96.9) cm
Current (Amps)
Current in Coil #1 and Coil #2
Time (μs)
FIG. 5. Plots of Bx, By, and Bz in the center of the plasma column, 96.9 cm
away from the RMF antenna. Indicative of the shear mode, the direction of
the waves magnetic field is predominantly perpendicular to B0, with a small
Bz component. Note that the origin of our coordinate system is located at the
back end of the orthogonal ring antenna on the side opposite the cathode
共Fig. 1兲.
“cone” angle of spread of the wave.17 At large enough amplitudes this could lead to wave current filamentation.19 A
wide range of frequencies can be launched 共0.21ⱕ ␻ / ⍀ci
⬍ 0.93 in the present investigation兲 in both left and right
hand circular polarizations. A volumetric data set, 8 m along
the machine’s axis and 35 cm square in the transverse plane,
is acquired with a left hand circularly polarized SAW at
roughly half the cyclotron frequency, ␻ = 0.54 ⍀ci. Although
the study of the antenna’s near-field characteristics is of general interest, the primary focus of this publication is on the
far-field radiation pattern of the propagating SAW driven by
the RMF source 共Fig. 4兲.
The observed magnetic wave field generated by the
RMF antenna lies primarily perpendicular to B0, with
Bx ⬇ By Ⰶ Bz 共see Fig. 5兲, which is consistent with the theoretical polarization of the kinetic SAW radiated from a
source of small transverse size.15
The shear wave dispersion relation 关Eq. 共1兲兴 is verified
for the radiated waves by varying the background magnetic
field while holding both the driver frequency and background plasma density fixed. The results 共shown in Fig. 6兲
are in reasonable agreement with the prediction of Eq. 共1兲,
Current in Coil #1 (Amps)
Alfvén Wave Field Components
By (Gauss)
Time (μs)
Current in Coil #2 (Amps)
Antenna Current
Bx (Gauss)
FIG. 7. Above is a plot of the current on each coil of the RMF antenna. Coil
1 is oriented with its normal parallel to x and coil 2 is oriented with its
normal parallel to y. Also included are two hodograms, running from
␶ = 关0 , 48兴 ␮s, illustrating the left hand circular polarization of both the coil
currents and the wave magnetic field components. In this case, magnetic
field data are taken from the center of the wave pattern, 96.9 cm away from
the antenna.
092106-5
Phys. Plasmas 16, 092106 共2009兲
Generation of polarized shear Alfvén waves…
t = 40.0 μs
t = 41.2 μs
t = 42.4 μs
x Position (cm)
y Position (cm)
y Position (cm)
y Position (cm)
Left Hand:
x Position (cm)
x Position (cm)
x Position (cm)
y Position (cm)
y Position (cm)
y Position (cm)
Right Hand:
x Position (cm)
x Position (cm)
x Position (cm)
y Position (cm)
y Position (cm)
y Position (cm)
Single Coil:
x Position (cm)
x Position (cm)
FIG. 8. Above is a series of wave magnetic vector fields for left hand, right hand, and linear polarizations at three time steps separated by a quarter period.
The wave polarization was controlled by changing the polarization of the magnetic field induced by the RMF antenna. These planes are 384.5 cm or
approximately 1.2 parallel wavelengths, away from the RMF antenna.
using a perpendicular wavelength of the 9 cm antenna size.
The phase velocity of the wave is measured using the time
delay of phase fronts between two probes axially separated
by 127 cm. The measurement is temporally within the
middle of the wave pulse and at the spatial center of the
wave pattern. An average value of two phase fronts in the
middle of the pulse for both the x and y components of the
wave field are taken for each value of f / f ci. The error
bars reflect the uncertainty in measuring the time delay of
the phase fronts. The wave propagates along B0 with a
092106-6
Phys. Plasmas 16, 092106 共2009兲
Gigliotti et al.
J
J
y
x
z, B0
t = 4.6 μs
FIG. 9. 共Color兲 Isosurfaces of current density at ␶ = 4.6 ␮s. The surfaces begin 33 cm to the right of the antenna and end approximately 8 m away. Two
rotating, counterpropagating helical current channels can be seen flowing in the z direction along B0. As time advances the currents rotate in a left-handed
sense. The outer isosurface represents a current density of 0.25 A / cm2 and the inner surface a current density of 0.5 A / cm2, whereas red denotes current flow
in the positive z direction and blue in the negative z direction. Magnetic field vectors are also shown 共enhanced online兲. 关URL:
http://dx.doi.org/10.1063/1.3224030.1兴
parallel phase velocity close to the theoretically predicted
values for the kinetic SAW. In all cases, the parallel Alfvén
phase velocity vA is below the electron thermal velocity,
vTe = 1.45⫻ 108 cm/ s.
It was observed that the polarization of the SAW produced depends directly on the polarization of the RMF
source. For this experiment, the current in the antenna was
configured such that the magnetic field rotated in a left hand
sense with the vertical coil 90° out of phase with the horizontal coil 共Fig. 7兲. The wave generated by this rotating field
was observed to be left hand circularly polarized.
Similarly, if the phase relationship between the two coils
is reversed such that the RMF rotates in the right hand sense,
a right hand circularly polarized shear wave is excited. In
both the left and right hand cases, at half the ion cyclotron
frequency, the resulting wave patterns are near identical with
the only difference being that they rotate in the opposite
sense 共Fig. 8兲. If only a single coil is driven, a linearly polarized shear wave is excited. In this case, the wave magnetic
field oscillates in a single direction resulting in a wave pattern similar to the left and right hand cases, but with the
addition of a central null every half period and without rotation, as exemplified in the lower third portion of Fig. 8.
The wave current is calculated from the curl of the magnetic vector field, Jជ = ⵜ ⫻ Bជ / ␮0. This reveals the presence of
two well-defined, helically rotating wave current channels,
propagating in the z direction, parallel to B0 共Fig. 9兲. These
parallel currents are again indicative of a shear mode.
The wave generated by the RMF antenna has a maximum measured amplitude of approximately 4 G, 33 cm away
from the antenna, which translates into a ratio of the wave
field magnitude, B, to the background field magnitude, B0, of
B / B0 ⬇ 0.4%. An estimate of the magnetic energy of the
wave within the 35⫻ 35⫻ 767 cm3 volume of the collected
data set yields 1.7 mJ. In comparison, there is approximately
1 J of energy in the LAPD plasma contained in that same
volume.
The wave pattern remains well collimated, exhibiting
very little cross-field propagation over the course of 8 m. The
measured full width at half maximum of the temporally and
spatially averaged magnetic energy density increases by approximately 15% over this interval 关Fig. 10共b兲兴. However,
examining the energy density versus distance along the magnetic axis of the machine, z, reveals that the energy density
decreases approximately 85% over this same distance of 8 m
关Fig. 10共c兲兴. This decay can be attributed to electron collision
damping. The dispersion relation for collisionally damped
kinetic Alfvén waves can be written as20
冋
␻2 − kz2VA2 1 −
册
␻2
2 2
+ 共 ␳ sk ⬜兲 2 + i ␻ k ⬜
␭e ␯e = 0,
⍀2i
共2兲
where ␭e = c / ␻ pe is the electron skin depth and ␯e is electron
collision frequency due to collisions with ions and neutrals.
The axial damping of the Alfvén wave due to electron
collisions can be derived from Eq. 共2兲 as follows: The wave
Phys. Plasmas 16, 092106 共2009兲
Generation of polarized shear Alfvén waves…
z = 192.8 cm
z = 384.5 cm
z = 704.0 cm
A
Current
Light
A
Time (ms)
x Position (cm)
Ion Saturation Current and Light Intensity
Ion Saturation Current
(A/cm2)
Full Width at Half Maximum
(cm)
FWHM of Average Magnetic Energy Density
B
Current
Light
B
Time (ms)
Distance from Antenna (cm)
Average Energy Desnsity
(ergs/cm3)
Average Magnetic Energy Density vs. Distance
kzr =
FIG. 10. 共a兲 Time averaged magnetic energy density plotted vs x coordinate
centered in the plane at y = 0 for three axial distances, z, from the RMF
source. The energy density is time averaged during the pulse from
␶ = 关40, 80兴 ␮s. 共b兲 Plot of the full width at half maximum of the spatially
and temporally averaged magnetic energy density of the wave vs the distance from the antenna. The energy density is spatially averaged along a
strip centered at x = 0 running from y = 关−3 , 3兴 cm. It is then time averaged
during the pulse from ␶ = 关40, 80兴 ␮s. 共c兲 Point plot of the measured time
averaged magnetic energy density vs the distance from the antenna, along a
line down the center of the wave pattern 共储B0兲. The energy density is averaged in time during the pulse from ␶ = 关40, 80兴 ␮s. The solid curve is an
exponential fit that gives a collisional damping length of 397.5 cm, which
agrees well with the theoretically predicted value of 410 cm.
frequency is set by the driver and therefore is real valued, a
spectrum of real-valued perpendicular wavenumbers k⬜ is
present as determined by the antenna geometry, and the parallel wavenumber is taken to be complex kz = kzr + iki, which
is self-consistently determined by the plasma dielectric.
Equation 共2兲 then yields
and
FIG. 11. Plots of the ion saturation current at the center of the wave pattern
and the visible light intensity line integrated across the center of the plasma
column, 198 cm away from the antenna. Both signals are digitally bandpass
filtered from 0 to 100 kHz. 共a兲 The 12 ms LAPD dc discharge is shown in its
entirety and a large spike in both signals is apparent during the antenna
pulse at ␶ = 0. 共b兲 This plot is an expansion in time of the above spikes. The
sharp initial rise in both cases can be attributed to electron heating and
subsequent ionization.
C
Distance from the Antenna (cm)
ki =
␻
VA
冑冉
冑1 + k⬜4 ␭4e ␯2e /␻2 − 1
2 1−
␻2
+ 共 ␳ sk ⬜兲 2
⍀2i
冊
Light Intensity (AU)
Ion Saturation Current and Light Intensity
Ion Saturation Current
(A/cm2)
Average Energy Desnsity
(ergs/cm3)
Average Magnetic Energy Density vs. x Position
Light Intensity (AU)
092106-7
2 2
␭ e ␯ e␻
k⬜
ki 2VA2
1
.
␻2
2
1 − 2 + 共 ␳ sk ⬜兲
⍀i
共4兲
The experimental parameters yield the electron-ion collision
frequency ␯ei = 5.2⫻ 106 s−1, which is much higher than the
electron-neutral collision frequency21 ␯en = 1.1⫻ 105 s−1 and
is therefore dominant. Using the antenna diameter
共⬃9 cm兲 as an approximation for ␭⬜, we get k⬜␭e = 0.24,
k⬜␳s = 0.35, and the decay length di = 1 / ki = 425 cm. The
solid line in Fig. 10共c兲 is the least-squares fit to an exponential decay of the data: A共z兲 = A0e−z/di with fitting parameters
A0 = 0.44 ergs/ cm3 and di = 398 cm, which is in good agreement with the theoretical value.
Measurements of both the line integrated visible light
intensity across the center of the wave pattern and the ion
saturation current at the center of the wave pattern show
sharp increases during the 100 ␮s antenna pulse 共Fig. 11兲.
This response can be attributed to electron heating and subsequent ionization.
VI. CONCLUSION
共3兲
It is demonstrated that SAWs of arbitrary polarization
can be launched using an orthogonal loop antenna. A key
motivation of the experiment was the possibility of injecting
SAWs in the inner radiation belt from one or more satellites.
092106-8
Phys. Plasmas 16, 092106 共2009兲
Gigliotti et al.
As discussed in Ref. 10, SAWs with frequency of the order
of 1–10 Hz interact resonantly with 30–100 MeV protons
and can enhance their precipitation rate. For space injection
and given the relatively low frequency it was suggested that
a rotating superconducting or permanent magnet could be
used to generate a RMF similar to the one that was generated
in the present experiment. The wave propagation is field
aligned with the full width at half maximum changing little
over 2.5 wavelengths of propagation. The drop in wave intensity as a function of distance from the antenna is exponential and can be explained by collisional damping. It is
difficult to produce high amplitude SAWs. For example the
vacuum magnetic field in the loop antenna is of order 350 G
on axis, however the largest near-field wave amplitudes were
from 8 G peak-to-peak falling off to 3 G peak-to-peak in a
axial distance of 8 m, approximately 2.5 parallel wavelengths. One reason for this is that the wave current is limited by the electron saturation current Iesat = nevtheA. If a current larger than Iesat was to flow through the plasma the
electrons would have to drift faster than their thermal speed
which would lead to a violent Buneman-type instability. The
diameter of the center of the current channel is on the order
of 2 cm. For the conditions described, the total electron saturation current is 30 A / cm2. Thus, a 2 cm diameter channel
produces, at most, a 13 G field. This is on the order of what
is observed. Larger wave fields would be observed if the
plasma density were ten times larger or if a nonthermal electron population carried the current as was the case in recent
laser target experiments.22 The wave power estimated from
S = VA共␦Bw2 / ␮0兲 ⬇ 4.5⫻ 104 W / m2, where ␦Bw is the measured wave field. From Fig. 10共a兲 the cross sectional diameter of the wave is 6.5 cm giving a radiated wave power of
about 188 W and energy of 19 mJ for a 100 ␮s wave burst
共the total energy in the plasma is 6.6 J兲. It is difficult to
estimate the radiation efficiency as the phase between the
voltage on the RMF antenna 共1000 V兲 and the current
共600 A兲 is not precisely known. At best it is in the order of
1%. In this experiment, the wave amplitude is large enough
to cause electron heating and fast electrons as evidenced in
measurements of visible light emitted from the plasma.
Ionization is also observed evidenced by the longer decay
time of the elevated ion saturation current when compared to
the visible line integrated light intensity. A discussion of
the electron, as well as ion heating, is the subject of a future
publication. The experiment demonstrated for the first
time the feasibility and control of RMFs using specialized
antennas.
ACKNOWLEDGMENTS
We acknowledge support by the ONR under MURI
Grant No. N000140710789. This work was done on the
LAPD at UCLA. The device is part of the Basic Plasma
Science Facility funded by the Department of Energy 共No.
DE-FC02-07ER54918兲 and the National Science Foundation
共No. NSF-PHY-0531621兲. We would also like to thank Marvin Drandell, Zoltan Lucky, and Mio Nakamoto for their
technical assistance.
1
W. Gekelman, J. Geophys. Res. 104, 14417, doi:10.1029/98JA00161
共1999兲.
2
J. Hollweg, M. Bird, H. Volland, P. Edenhofer, C. Stelzried, and B. Seidel,
J. Geophys. Res. 87, 1, doi:10.1029/JA087iA01p00001 共1982兲.
3
I. de Pater and S. Brecht, Icarus 151, 1 共2001兲.
4
P. Louarn, J. E. Wahlund, T. Chust, H. de Feraudy, A. Roux, B. Holback,
P. O. Dovner, A. I. Eriksson, and G. Holmgren, Geophys. Res. Lett. 21,
1847, doi:10.1029/94GL00882 共1994兲.
5
C. Chaston, C. Carlson, W. Peria, R. Ergun, and J. McFadden, Geophys.
Res. Lett. 26, 647, doi:10.1029/1998GL900246 共1999兲.
6
O. Alexandrova, A. Mangeney, M. Maksimovic, C. Lacombe, N.
Cornilleau-Wehrlin, E. Lucek, P. Decreau, J. Bosqued, P. Travnicek, and
A. Fazakerley, J. Geophys. Res. 109, A05207, doi:10.1029/
2003JA010056 共2004兲.
7
C. Hui and C. Seyler, J. Geophys. Res. 97, 3953, doi:10.1029/91JA03101
共1992兲.
8
D. Hayward and J. Dungey, Planet. Space Sci. 31, 579 共1983兲.
9
J. Wygant, A. Keiling, C. Cattell, M. Johnson, R. Lysak, M. Temerin, F.
Mozer, C. Kletzing, J. Scudder, W. Peterson, C. Russell, G. Parks, M.
Brittnacher, G. Germany, and J. Spann, J. Geophys. Res. 105, 18675,
doi:10.1029/1999JA900500 共2000兲.
10
X. Shao, K. Papadopoulos, and A. S. Sharma, J. Geophys. Res. 114,
A07214, doi:10.1029/2009JA014066 共2009兲.
11
A. Hasegawa, J. Geophys. Res. 81, 5083, doi:10.1029/JA081i028p05083
共1976兲.
12
C. Goertz and R. Boswell, J. Geophys. Res. 84, 7239, doi:10.1029/
JA084iA12p07239 共1979兲.
13
W. Gekelman, S. Vincena, D. Leneman, and J. Maggs, J. Geophys. Res.
102, 7225, doi:10.1029/96JA03683 共1997兲.
14
N. Palmer, W. Gekelman, and S. Vincena, Phys. Plasmas 12, 072102
共2005兲.
15
G. Morales and J. Maggs, Phys. Plasmas 4, 4118 共1997兲.
16
G. Morales, R. Loritsch, and J. Maggs, Phys. Plasmas 1, 3765 共1994兲.
17
W. Gekelman, D. Leneman, J. Maggs, and S. Vincena, Phys. Plasmas 1,
3775 共1994兲.
18
D. Leneman and W. Gekelman, Rev. Sci. Instrum. 72, 3473 共2001兲.
19
T. Drozdenko and G. Morales, Phys. Plasmas 8, 3265 共2001兲.
20
J. Vranjes, D. Petrovic, S. Poedts, M. Kono, and V. M. Cadez, Planet.
Space Sci. 54, 641 共2006兲.
21
P. Baille, J.-S. Chang, A. Claude, R. M. Hobson, G. L. Ogram, and A. W.
Yau, J. Phys. B 14, 1485 共1981兲.
22
C. Constantin, W. Gekelman, P. Pribyl, E. Everson, D. Schaeffer, N.
Kugland, R. Presura, S. Neff, C. Plechaty, S. Vincena, A. Collette, S.
Tripathi, M. Villagran Muniz, and C. Niemann, Astrophys. Space Sci.
322, 155 共2009兲.