PHYSICS OF PLASMAS 20, 012108 (2013)
Dynamics of exploding plasmas in a large magnetized plasma
C. Niemann,1,a) W. Gekelman,1 C. G. Constantin,1 E. T. Everson,1 D. B. Schaeffer,1
S. E. Clark,1 D. Winske,2 A. B. Zylstra,1,b) P. Pribyl,1 S. K. P. Tripathi,1 D. Larson,3
S. H. Glenzer,3 and A. S. Bondarenko1
1
Department of Physics and Astronomy, University of California Los Angeles, Los Angeles,
California 90095, USA
2
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
3
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
(Received 26 October 2012; accepted 17 December 2012; published online 11 January 2013)
The dynamics of an exploding laser-produced plasma in a large ambient magneto-plasma was
investigated with magnetic flux probes and Langmuir probes. Debris-ions expanding at superAlfvenic velocity (up to MA ¼ 1:5) expel the ambient magnetic field, creating a large (>20 cm)
diamagnetic cavity. We observe a field compression of up to B=B0 ¼ 1:5 as well as localized
electron heating at the edge of the bubble. Two-dimensional hybrid simulations reproduce these
measurements well and show that the majority of the ambient ions are energized by the magnetic
piston and swept outside the bubble volume. Nonlinear shear-Alfven waves (dB=B0 > 25%) are
radiated from the cavity with a coupling efficiency of 70% from magnetic energy in the bubble to
C 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4773911]
the wave. V
I. INTRODUCTION
Laboratory experiments on dense, laser-produced plasmas exploding at high velocity into a relatively tenuous,
magnetized medium are of interest to a number of space and
astrophysical phenomena, including planetary bow shocks,1
coronal mass ejections,2 supernova remnants,3 or man-made
explosions in the ionosphere.4 Many of these counter streaming plasmas have super-Alfvenic velocities and launch collisionless shock waves, where collective effects produce
plasma turbulence and dissipation scale lengths far shorter
than the ordinary collision mean-free-path.5 The subAlfvenic regime has been investigated in numerous laboratory experiments6–9 as well as in chemical releases in Earth’s
magnetosphere,10 providing important data for benchmarking multidimensional hybrid models.11,12 Super-Alfvenic
explosions, however, where the debris ions are stopped in
part by the ambient magnetized plasma,13 have not been well
documented with laboratory experiments.
The work described here employs a high-energy (25 J)
laser14 coupled to the large plasma device (LAPD)15 to produce
dense plasma clouds that explode rapidly into a magnetized, stationary background plasma at ni ¼ 1012 cm3 and Te ¼ 5 eV.
The ambient plasma is large enough (18 m 0.6 m ) to support Alfven waves and is initially several orders of magnitude
less dense than the debris cloud. Numerous experiments of this
type have been performed previously at the LAPD, using
smaller lasers with energies around 1 J but higher shot-rates.16–
20
Those experiments have investigated the plasma diamagnetism in the presence of the ambient plasma,9 discovered that
shear-Alfven waves16 and whistlers19 are emitted from the
laser-plasma plume, and have produced colliding laser-plasmas
with relevance to magnetic reconnection.18 The experiments
a)
Electronic address: cniemann@ucla.edu.
Current address: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
b)
1070-664X/2013/20(1)/012108/12/$30.00
described here employ a laser-pulse that contains two-orders of
magnitude higher energy at intensities three orders of magnitude
higher, and extend earlier work to the super-Alfvenic regime
with significantly stronger coupling between the laser and the
ambient plasma. While many of the effects observed here at
higher energy display similar behavior as those reported from
low-power experiments, their magnitude is generally much
higher, and some of the observed features are very different.
The purpose of this paper is two-fold. First, we characterize the dynamics of the exploding debris-cloud and its interaction with the ambient plasma and magnetic field, to
demonstrate its potential as a piston for launching collisionless
shocks.21 Initially, the kinetic energy density in the laserplasma exceeds the energy in the ambient field and the
dynamics of the plasma is only marginally affected by the
background. However, the highly conducting laser-plasma
supports currents and thus expels the external magnetic field,
creating a diamagnetic cavity with the excluded field piling up
at its edge.22 We observe diamagnetic bubbles, an order of
magnitude larger and deeper than those in previous lowpower experiments, with expansion velocities five times
faster. Laminar electric fields at the bubble edge decelerate
the debris and accelerate the ambient ions3 so that the cavity
acts as a magnetic piston upon the background plasma. In the
experiments, super-Alfvenic pistons with Alfvenic Mach
numbers MA ¼ vpiston =vA up to 1.5 were produced and maintained for a considerable fraction of an ion-inertial length and
ion-gyroperiod. Two-dimensional hybrid simulations reproduce the features observed in the experiment and show a significant momentum transfer from the debris to the ambient
plasma. The simulations suggest that, at these low-Mach numbers, coupling from the debris ions to the ambient plasma is
dominated by laminar electric fields, rather than azimuthal
fields responsible for Larmor coupling in stronger shocks.
Experiments are currently limited by the low ambient plasma
density and consequently large scale-lengths (c=xpi ) that
20, 012108-1
C 2013 American Institute of Physics
V
012108-2
Niemann et al.
exceed the piston size by a factor of about two. Although a
super-Alfvenic pulse is observed to separate from the piston
and propagate through the ambient plasma, it does not currently have enough space and time to steepen into a fullblown collisionless shock. Future experiments will take
advantage of a new plasma source23 supporting higher ambient densities (factor 10 or more) and a new kilojoule-class
laser24 supporting larger pistons (factor 5). The measurements
and hybrid simulations presented here strongly suggest that
collisionless shocks with relevance to magnetized shocks in
the heliosphere can be launched in the LAPD with the
improved ambient plasma parameters.
Second, we give a detailed description of the lowfrequency current-systems that emerge from these large
laser-plasma cavities and compare their properties to those
found in previous experiments performed at lower laserenergies. While the underlying physics is similar, the
amplitude and spatial extend of the shear-waves and the
coupling efficiency from the bubble to the waves are significantly higher. Specifically, the larger, deeper, and
faster cavities in the experiments described here launch
nonlinear shear Alfven waves with record amplitudes of
dB=B > 25% and coupling efficiencies in excess of 70%
from the diamagnetic cavity to the waves. The overall
energy in these flux-ropes is two-orders of magnitude
higher than those found in previous experiments. The generation of such intense waves by laser-produced plasmas
provides a unique experimental platform to study nonlinear processes associated with these wave modes not currently accessible with antennas.25,26 Nonlinear Alfven
waves can interact with the surrounding plasma or with
other waves, giving rise to a number of nonlinear phenomena, including filamentation or wave amplitude modulations.27 Large amplitude Alfven waves can modify the
ambient plasma density through ponderomotive forces.28
Nonlinear Alfven waves are important in space and astrophysical plasmas,29 as well as in magnetic fusion devices.30 The energy cascade in wavenumber space in
magnetic turbulence in the solar wind, for example, is
believed to be mediated by nonlinear interactions among
Alfven waves.31 A high average power slab-laser system
will be available for future experiments in the LAPD32
and enable such measurements both at high laser pulse
energy (25 J) and high shot-rate (1 Hz), thus, supporting a
detailed characterization of nonlinear Alfven waves.
Highly nonlinear shear waves with amplitudes in excess
of dB=B ¼ 1 may also be excited with the new single-shot
kilojoule laser. The data presented here may serve as a
reference for such upcoming experiments.
The paper is structured as follows: Sec. II describes the
experimental setup and diagnostics. We then present measurements of the bubble dynamics in Sec. III and compare
them to two-dimensional hybrid simulations. The most important findings on the coupling to shear-waves from earlier
low-power laser experiments are reviewed in Sec. IV A for
comparison. In Sec. IV B, we present detailed measurements
of shear-waves produced in high-power laser experiments
and how they relate to the bubble dynamics (Sec. IV C). Section V is a summary.
Phys. Plasmas 20, 012108 (2013)
II. EXPERIMENTAL SETUP
The experiments were performed with the Phoenix
Nd:glass-laser system14 and the LAPD.15 The LAPD creates
highly magnetized plasmas that are large enough (18 m
length, 60 cm diameter) to support Alfven waves. Plasmas
are typically produced at densities up to ni ¼ 2 1012 cm3 ,
electron temperatures around Te ¼ 5 eV, and ion temperatures around Ti ¼ 1 eV. The quiescent and current-free
plasma is created in helium or neon in a steady, axial magnetic field of 275–1800 G by pulsing a barium oxide coated
(BaO-Ni) cathode at one end of the machine negatively with
respect to an anode grid 30 cm away. A few ms after the discharge is initiated, the plasma reaches a steady state, and a
0.500 thick graphite-target embedded in the preformed plasma
is irradiated with a laser energy up to 25 J.
The high-energy laser system consists of a Q-switched
Nd:YAG oscillator (1064 nm, 10 mJ, 5 ns FWHM), 7 mm
Nd:YAG pre-amplifier, and four flashlamp-pumped Nd:silicate rod-amplifiers (25 mm double-pass, 32 mm, and 45 mm)
that boost the 10 mJ seed-pulse to an output energy of 30 J
(25 J in the P-polarized component). A 30 m long beamline
in air transports the 40 mm diameter beam from the laserlaboratory one story down to the LAPD. A combination of
quarter-waveplate and thin-film polarizers is used to optically isolate the laser-system from the target, preventing
laser damage due to backscatter and creating a circularly
polarized beam on target.
An aspheric f/6 doublet-lens inside the plasma vessel
creates a tight focus (50 lm FWHM) and peak intensities up
to 1013 W=cm2 at 20 J with an energy stability of 10%. The
on-target intensity could be changed during the experiments
by translating the focusing lens closer to the target by several
cm. The target normal was aligned exactly perpendicular to
the external field to direct the blow-off plume into a transverse direction. The flat target surface was offset 13 cm from
the axis of the LAPD, providing roughly 40 cm of ambient
plasma to interact with as the laser-plasma expands perpendicularly across the magnetic field (Fig. 1). After each shot,
the target was translated by a few mm to provide a fresh surface. In the following, all data will be expressed in LAPDcoordinates (see Fig. 1), where the external B-field points in
the positive z-direction, the laser blow-off propagates horizontally in negative x-direction, and the transverse field of
the shear-waves is typically measured where it is vertical (ydirection). Relative distances from the target along these
coordinates will be denoted as Dx, and Dy in transverse
direction, and Dz axially.
An array of ten magnetic flux probes (i.e., Bdot probes)33
was distributed along the machine at distances Dz up to 7 m
from the target to measure the magnetohydrodynamic (MHD)
response of the ambient plasma along the direction of the magnetic field. One additional probe was inserted from a port
opposing the target to investigate the dynamics of the diamagnetic cavity perpendicular to the external field. All probes could
be positioned at arbitrary transverse positions (x-axis) using
motorized probe-drives with sub-mm precision. The reproducibility of the ambient plasma, along with its 1 Hz repetition rate
and the high-shot rate of the laser system (5–10 shots/hour)
012108-3
Niemann et al.
FIG. 1. Schematic of the LAPD (a) and the laser-target configuration (b).
The graphite target is located at 5 m axially from the anode and x ¼ 13 cm
from the symmetry axis of the cylindrical vacuum vessel. An f/6 lens
inserted into the plasma focuses the beam onto the target surface (x ¼ 13 cm,
y ¼ 0, z ¼ 0) with an angle of incidence of 43 . The magnetohydrodynamic
response of the ambient plasma across and along the field is measured with
an array of magnetic flux probes that can be translated in the x-direction.
allowed detailed scans of the magnetic field over large spatial
regions in the plasma. The three-dimensional magnetic pickup
coils were differentially wound on a 1 mm or 3 mm cube core
(10 turns each axis) and were calibrated to frequencies of up to
100 MHz. Probe signals were recorded using custom-built
100 MHz differential amplifiers coupled to 14 bit, 100 MS/s
digitizers, and numerically integrated to compensate for the
individual frequency response.33 In addition, plasma density
and ion time-of-flight measurements were performed with double sided Langmuir probes.34
III. LASER-PLASMA PISTON
A. Evolution of the diamagnetic cavity
The experiments were performed in a perpendicular geometry (i.e., target-normal and laser blow-off direction
aligned perpendicular to the external field) to investigate the
formation and collapse of the diamagnetic cavity in the presence of the ambient magnetized plasma. The debris ions
have directed Larmor radii of several tens of cm and are
essentially unmagnetized. The lighter electrons are tied to
the field lines (rLarmor;e < 1 mm), causing a radial electric
field and azimuthal electron E B drift. These currents reinforce the pressure driven diamagnetic electron-drift due to
plasma density gradients at the leading-edge of the exploding
plasma (rP B) and thus create azimuthal currents that
ultimately expel the external field.22
In the presence of an ambient magnetized plasma, the
debris cloud can also couple to the ambient plasma, without
binary collisions. From the basic forces acting on the debris
Phys. Plasmas 20, 012108 (2013)
FIG. 2. Magnetic-flux probe measurements of the evolution of the magnetic
field (Bz ) at distances of 4 cm, 9 cm, 14 cm, and 22 cm from the target in
Heþ at 275 G (a). The field compression increases with distance from the
target, reaching a steady B=B0 ¼ 1:5 from 14 to 22 cm. Inside the bubble,
the field is fully expelled but diffuses back into the bubble-volume after
about 1 ls. (b) The contour-plot of the same data is a composite of 80 laser
shots and shows Bz as a function of time with a spatial resolution of 5 mm.
To obtain this data, the perpendicular probe was moved to a different xlocation in each shot. The compression of the expelled field at MA ¼ 1:5,
formation and collapse of the magnetic bubble, and subsequent propagation
of a fast magnetosonic pulse are clearly visible. The dimensionless axes represent the spatial and temporal scales with respect to the upstream ioninertial length and ion-gyroperiod. Downstreaming the length-scales and
time-scales are slightly better, considering the compressed field. The left
dashed line indicates the time of peak compression.
ions, three types of collisionless coupling processes can be
inferred:3 the coupling due to the radial electric field that is
essentially the gradient of the electron pressure (“laminar
coupling”), coupling due to resistive effects from plasma
instabilities driven by the relative streaming of the debris
ions relative to the background ions (“turbulent coupling”),
and the effects of the magnetic field on the debris ions
(“Larmor coupling”). The laminar electric field due to charge
separation of the highly magnetized electrons and unmagnetized ions at the bubble edge results in the piston ions being
decelerated, while it accelerates the ambient ions. Thus, ambient ions are partially picked up by the piston but are not
thermalized. The third mechanism, Larmor coupling, is due
to the azimuthal electric field that accelerates ambient ions
(E B-drift) if the time it takes for the piston to pass is more
than a quarter ambient-ion gyroperiod.3 Hybrid simulations
have recently shown12 that the radial ambient current is created by the difference of debris and background ion gyromotion. Turbulent coupling has been found to be mostly
ineffective in stopping the debris ions.
Figure 2 shows magnetic probe measurements of the
formation and collapse of the diamagnetic cavity that is
formed by a laser-produced carbon-plume exploding into a
stationary Heþ plasma at upstream (i.e., the unperturbed
region ahead of the piston) conditions of ni ¼ 9 1011 cm3
012108-4
Niemann et al.
and Te ¼ 5 eV in 275 G. The complete expulsion of the field
and compression into a thin shell as well as the overall size
and lifetime of the cavity are clearly visible in the contour
plot (Fig. 2(b)), which combines single-point measurements
from 80 separate laser shots conducted over the course of
two days. To obtain this dataset, one magnetic field probe
was moved to a different transverse position (x-axis) for
each shot, while the experiment was repeated at reproducible
laser-target and ambient plasma parameters. The magnitudes
of the transverse magnetic field components (Bx and By , not
shown) are much smaller at a few Gauss since measurements
were performed only at points along the blow-off direction
and perpendicular to the initial field, where the expelled and
compressed field is mostly parallel to the direction of the
external magnetic field.
The magnetic pulse expands initially at vpiston ¼ 5 107
cm=s and is super-Alfvenic at MA ¼ vpiston =vA ¼ 1:5, where
pffiffiffiffiffiffiffiffiffiffiffiffiffi
vA ¼ B= l0 ni mi is the Alfven speed. The pulse is also
hyper-sonic at Ms ¼ vpiston =vs ¼ 35, where vs is the ionsound speed. This velocity is consistent with empirical scaling laws for the ablation plume at the laser parameters
used.35 The field compression factor increases as the bubble
grows and reaches a maximum value of B=B0 ¼ 1:5 at a distance of 14 cm from the target. This compression ratio is
maintained until the bubble stagnates at 22 cm and is consistent with the Rankine-Hugoniot jump conditions for a
shock,36 although the piston only travels for a fraction of a
gyroperiod (txci ¼ 0:5 considering the initial ambient
plasma parameters, or txci ¼ 0:75 in the downstream region
considering field compression). The thickness of the pulse is
around 1 cm and on the order of 10 c=xpe , which is comparable to the thickness of the ramp in a collisionless shock.5
When the bubble stagnates and the piston stops, the magnetic
compression continues to propagate as a fast magnetosonic
pulse through the ambient plasma, gradually decreasing in
speed to MA ¼ 1 at twice the bubble stopping radius. This
pulse eventually dissipates due to geometrical effects and
collisional and electron Landau damping in the upstream
plasma, and broadens to a width of several tens of electronskin-depths (c=xpe ). Hybrid simulations of the formation
time of perpendicular shocks show that a shock can form in
two ways, either by a hot ion-beam or by a cloud of hot electrons.37 In the hot-electron case, which is more relevant to
the experiment described here, coupling between the debrisplasma and the ambient plasma is provided by the presence
of laminar electric fields due to the electron pressure gradient
across the bubble interface. The formation time is on the
order of x1
ci depending on the electron b (i.e., the ratio of
plasma energy density to magnetic field energy density), and
is quite close to the duration of our experiment. Shock formation is slower in the hot-ion case, where coupling is due
to the Larmor motion of the energetic ions, as in most extraterrestrial shocks.
The maximum size of the bubble is around 23 cm when
defined as the volume where the ambient field is reduced by
more than half. Complete-field expulsion occurs only in a volume with a size of around 17 cm. We note, however, that some
field reduction is observed out to distances in excess of 30 cm.
The size of a diamagnetic bubble can be estimated from a
Phys. Plasmas 20, 012108 (2013)
simple energy balance, considering that the kinetic energy of
the debris Edebris ¼ V B2 =ð2l0 Þ þ 1=2 ni mi Vv2ambient is fully
converted to magnetic energy in the bubble volume V and kinetic energy of the ambient ions that start streaming in the bubble explosion direction due to collisionless coupling.3
Assuming a spherical bubble of radius RB , consistent with twodimensional hybrid simulations,11 and neglecting the energy in
the compressed shell, the maximum bubble radius can be calculated as RB ¼ ½3l0 Edebris =ð2pB2 Þ1=3 ð1þMA2 Þ1=3 , where the
dependence on MA ¼ vambient =vA stems from the B2 and ni
terms in the magnetic and kinetic energy, respectively. Hybrid
simulations show that Larmor-coupling accelerates the initially
stationary ambient ions to the piston velocity in a quarter gyroperiod p=2 xci .12 Additional coupling may be provided by
the radial (“laminar”) electric field. For the present parameters
the bubble stagnates after t ¼ 0.7 ls or txci 0:5 and the ambient ions in at least half of the bubble volume should acquire
the piston velocity. The magnetic energy contained in the bubble volume is around 1.3 J, which is only 6% of the on-target
laser energy. Considering that about half of the ambient ions
expelled from the bubble should have acquired the piston velocity and a total energy around 2 J, the overall conversion efficiency from the laser to the ambient medium would be around
13%. We note, however, that there is no measurement of the
ambient ion velocity in the present experiment and no in-situ
comparison with a vacuum expansion to quantify the coupling
to the background ions. Without collisionless coupling (or laminar coupling) the energy now lost to kinetic energy of streaming ambient ions would be available for additional field
expulsion and should increase the size of the bubble by 30%.
Experiments performed at identical laser-target parameters in a
neon background (A ¼ 20) yield the same bubble-stopping radius within the accuracy of the measurement. While neonambient ions moving at an identical velocity as the helium ions
would contain a factor of five more energy, Larmor coupling
proceeds five times slower so that not much momentum transfer is expected for neon at the current conditions, consistent
with the observed insensitivity of the bubble size to the ambient ion mass. The bubble size roughly obeys the ðE=B2 Þ1=3
scaling in experiments with varying magnetic field (see
Table I), and reduces to 11 6 2 cm and 5 6 2 cm diameters for
600 G and 1800 G, respectively. This indicates that coupling
between the debris ions and the ambient plasma is comparable
in all three cases. This assumption is reasonable, since higher
fields will not only decrease the ion-gyroperiod (x1
ci ), but also
the bubble size and thus the piston transit time. We observe
variations in the peak compression B=B0 at the cavity edge
with MA . Reducing the blow-off speed to 3:5 107 cm=s by
defocusing the laser beam (MA ¼ 1:1) decreases the peak compression to B=B0 ¼ 1:3. In neon (MA ¼ 3:4), we measure
compression ratios of 1.4. These are well below the values predicted by the magnetohydrodynamic jump-conditions,38 since
an ambient neon plasma is only weakly magnetized and collisionless coupling is inefficient during the short bubble transit
times. At 1800 G in helium (MA ¼ 0:36), the measured peak
compression was DB ¼ 300 G or B=B0 ¼ 1:2.
The cavity collapses roughly 0.5 ls after it stagnates and
much faster than the magnetic diffusion time l0 rR2B 100 ls,
pffiffiffiffiffiffi
where r ¼ 50p1=2 20 ðkTe Þ3=2 =ð me e2 Z lnK) is the plasma
012108-5
Niemann et al.
Phys. Plasmas 20, 012108 (2013)
TABLE I. Summary of measured key-parameters for experiments with different ambient ion species, external field, and laser-blow-off velocity (vp ).
The on-target laser energy was kept constant at 20 J for all runs. The blowoff velocity was varied in run 2 by defocusing the laser-beam. The maximum bubble size DB is defined here as the diameter of the volume with a
depth below B=B0 < 0:4. At 1800 G, there are not enough fast debris ions to
fully expel the field, and the depth of the bubble is at most B=B0 ¼ 0:4. The
table also lists the peak compression ratio Bz =B0 at the edge of the cavity,
the total current Ienc carried by the shear-wave, the wave amplitude dBy =B0
at a distance of 5.2 m from the target, the center location (xcenter ), and the
width of the current channel. Also shown are the energy EA carried by the
shear-wave, and the frequencies of the shear-wave (f A ) and the fast wave
(f MS ).
Experiment
1
2
3
4
5
Ambient
B (G)
vp (cm/s)
vA (cm/s)
MA ¼ vp =vA
DB (cm)
Bz =B0 edge
Ienc (kA)
dBy =B shear
xcenter (cm)
Width (cm)
EA (J)
f A (kHz)
f A =f ci
f MS (MHz)
He
275
5:0 107
3:3 107
1.5
2061
1.5
1
6%
3
20
0.9
40
0.4
0.5–1
He
275
3:5 107
3:3 107
1.1
2061
1.3
1
6%
3
20
0.9
40
0.4
0.5–1
He
600
5:0 107
6:5 107
0.77
1162
…
0.6
2.5%
3
15
0.4
120
0.5
1–2
He
1800
5:0 107
1:4 108
0.36
562
1.2
0.4
1%
8
10
0.2
370
0.5
5–8
Ne (A ¼ 20)
275
5:0 107
1:5 107
3.4
2061
1.4
0.6
4%
5
20
0.3
11
0.5
…
Spitzer-conductivity, and RB is the magnetic bubble radius.
Like previous work,9 we approximate the scale-length as the
bubble radius RB since the cavity is filled with the bulk plasma
from the laser-blow-off. Other work20 has found threedimensional current systems permeating the entire bubble,
with amplitudes much smaller than the diamagnetic current at
the edge of the bubble. Initially the diffusion proceeds anomalously fast until the field in the bubble is restored to around
B=B0 ¼ 80%. The diffusion rate then slows to near classical.
Fast anomalous diffusion is a common feature of experiments
on interpenetrating plasma clouds.7–9,39–41 Similar bubblelifetimes have also been reported from experiments at the
LAPD with smaller lasers, driving smaller cavities at lower
blow-off velocities.20 Since the bubbles here are an order of
magnitude larger in size, comparable diffusion times indicate
significantly larger diffusion coefficients (by a factor of 100),
consistent with the faster piston speeds and higher cross-field
currents. We note that at later times, during the collapse of the
cavity, we observe variations in both transverse field components that are comparable to the ambient field. The apparent
early diffusion near the target (at Dx ¼ 38 cm and 0.8 ls in
Fig. 2(b)) is in fact due to a rotation of the field direction from
Bz to Bx and By , probably caused by geometrical effects near
the edge of the bubble.
The magnetic field data display high-frequency oscillations in the lower-hybrid range xLH ¼ xpi =ð1 þ x2pe =x2ce Þ1=2
ðxce xci Þ1=2 , indicative of the growth of micro-instabilities
responsible for the anomalous field diffusion. Similar pulsations are observed in the ion-saturation current from Langmuir
probes (see Sec. III B). The nature of these high-frequency
oscillations is a topic under investigation. Magnetic fluctuations
inside the cavity are also observed in hybrid simulations,11
especially near the edge of the bubble. The large-Larmor radius
Rayleigh-Taylor instability grows to large amplitudes on timescales faster than x1
ci due to the population of fast debris ions
with Larmor-radii larger than the bubble stopping radius.8,20
Also the modified two-stream instability and the lower-hybrid
drift instability have been proposed or observed to explain fast
field diffusion in earlier work.40–43 Experiments performed
with identical ambient plasma parameters but increased focal
spot size and thus lower blow-off velocity (3:5 107 cm=s)
display similar oscillations inside the cavity but at significantly
reduced amplitude (factors 2–5). Simultaneously, the diffusion
time increases from 0.5 ls to 2 ls. This behavior is consistent
with a reduced growth of micro-instabilities when the crossfield current at the edge of the bubble decreases.
B. Fast electron generation at the bubble edge
Figure 3 shows ion-saturation-current measurements
inside the diamagnetic cavity performed with a Langmuir
probe biased at a fixed potential of 70 V with respect to the
anode of the discharge circuit,34 which is at plasma potential.
The probe thus excludes all bulk plasma electrons and measures both ion saturation current (Isat ) and electrons with sufficient energy to overcome the 70 V probe bias, corresponding
to velocities above 3:5 108 cm=s. The exposed area of the
probe was positioned such that it was facing away from the
laser target. The voltage drop across a 10 X resistor was
measured through an optical isolator on a 100 MS/s, 14 bit
digitizer. The contour plot (Fig. 3(a)) shows a composite of
FIG. 3. Ion-saturation-current measurements show electron heating at the
edge of the diamagnetic cavity, and the blow-off plasma filling the bubble
volume (a). The contours of the magnetic field (for B=B0 ¼ 20% and 50%)
as well as the time of peak compression from Fig. 2(b) are shown for comparison. The contour (a) is a composite of 20 separate laser shots with the
Langmuir probe moved to different distances from the laser-target (in the
direction perpendicular to the external field). (b) Evolution of Isat and the
Bdot-probe signal 13 cm from the target. The first negative spike in the
Langmuir probe signal coincides with the time of peak-compression, while
the second negative spike occurs during field expulsion. The Isat data also
display high frequency (10 MHz) oscillations inside the bubble.
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Niemann et al.
Phys. Plasmas 20, 012108 (2013)
20 laser shots where the probe was moved transverse to the
external magnetic field in 1 or 2 cm increments as the experiment was repeated with reproducible laser and plasma parameters identical to those in Fig. 2. We observe a negative
double-spike at the edge of the bubble out to distances of
15 cm from the target due to electrons above 70 eV.
Inside the bubble, we observe the positive ion-saturation
current from the laser-blow-off plasma. The first negative
spike coincides with the ramp on the Bdot-probe signal
where the magnetic field is compressed (Fig. 3(b)) and is due
to adiabatic heating (dB=dt > 0). The second negative spike
occurs at the time of maximum field expulsion and may be
due to Ohmic heating by the diamagnetic current, or by
anomalous heating by micro-instabilities.44 Inside the bubble, the plasma density n can be calculated from the ion saturation current Isat ¼ 0:61neAðkTe =mi Þ1=2 , if the temperature
Te is known (A ¼ 1 mm2 is the exposed area of the electrode,
and mi is the ion mass). A temperature around 10 eV several
cm from the laser target was measured in a different experiment with similar parameters,45 in good agreement with
radiation-hydrodynamic simulations.46 The measured ionsaturation current is roughly consistent with these temperatures and 1015 debris ions ablated from the target, assuming
that the bulk of these ions are stopped and evenly distributed
throughout the bubble as suggested by the data. The Isat signal inside the bubble is approximately constant over 2 ls,
even though the bubble collapses at around t ¼ 1 ls. After
2 ls, the plasma dissipates, and the probe no longer draws a
detectable ion-saturation current.
C. Hybrid simulations
The experiment was modeled with a two dimensional
hybrid code.11 In the hybrid mode, the ions are treated as particles in self-consistently generated electromagnetic fields,
while the electrons are modeled as an inertialess, chargeneutralizing fluid, thus, eliminating the shortest length and
time scales associated with the electron dynamics. The electron temperature is modeled to fluctuate adiabatically
Te ðx; yÞ ¼ Te0 ðne ðx; yÞ=n0 Þce 1 ;
(1)
where ce ¼ 5=3.47 Particles are tracked in two spatial coordinates (x and y, perpendicular to the external magnetic field)
using three-dimensional velocities and fields. The simulation
does not model the laser-plasma interaction explicitly but is
initiated with a cloud of debris ions (Cþ4 ) exploding at
MA 1:5 isotropically into an ambient Heþ plasma at conditions consistent with the experiment (n0 9 1011 cm3 ;
B0 275 G; Ti 1 eV; Te 5 eV). A mean charge state of
Cþ4 was determined by spectroscopic measurements performed in a related experiment at similar laser energies45
and is also consistent with radiation-hydrodynamic and
collisional-radiative modeling.46
Figure 4(a) shows the evolution of the magnetic field in
a space-time streak plot, displaying Bz along x at a fixed y
position (y ¼ 0) at various times. The exploding debris cloud
is originally located in the center of the simulation box at
x ¼ y ¼ 0. The field-expulsion and compression, and the for-
FIG. 4. Hybrid simulation of the laser-plasma expansion in the preformed
plasma and magnetic field. (a) Streak plot of the magnetic field profile during the first txci along the x-axis. A debris cloud containing Cþ4 explodes
spherically into a Heþ background in 275 G from x ¼ 0 at MA 1:5. The
formation of the diamagnetic cavity and magnetosonic pulse propagating
away from the bubble are clearly visible. Plots (b) and (c) show the background and debris ion densities, respectively.
mation of the diamagnetic cavity are clearly visible. In the
simulation, the number of ions in the debris cloud was
adjusted to create a bubble with a size of 0:45c=xpi
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Niemann et al.
(22 cm), consistent with the experiment. Figure 4(a) shows a
magnetic field compression of 1:5, which corresponds to
the Alfvenic Mach number of the debris expansion and is
consistent with the MHD-jump conditions. Figures 4(b) and
4(c) show streak plots similar to that of the magnetic field,
but show the background and debris ion densities relative to
n0 , where n0 is the initial density of the Heþ background
plasma. The background ions are pushed out of the diamagnetic bubble as they are accelerated by the piston. Figure
4(c) shows that around txci 0:5 some debris stagnates or
turns around, and some moves outward at a sub-Alfvenic
speed. It can be seen by these figures that the debris ions initiate a magnetosonic pulse which then separates from the debris cloud and propagates out radially; however, the pulse
does not steepen into a shock under these conditions.
When the piston stagnates at txci 0:5, the bulk of the
debris ions piles up at the bubble edge as shown in Figure 5.
The weak magnetosonic pulse can be seen just outside of the
dense ring of debris ions. Complete magnetic field expulsion
can be seen inside of the ring of debris ions. A few test particles were chosen to illustrate the motion of various background and debris ions. The yellow lines show two different
debris ion particles, a fast ion which makes it out past the
majority of the debris ions, and one that slows and diffuses
back into the bubble at a later time. The light blue lines show
two background Heþ ions which clearly couple to the debris
ions and move outward radially.
Fast shocks in space at these low Mach numbers
(MA 1:5) are observed, but the dissipation is usually only
in the electrons. In the hybrid-model we use, there is effectively no resistivity or resistive heating. Ion reflection is the
only dissipation mechanism, but the phase space (not shown)
does not show clear evidence for reflected ions. Using Eq.
(1), with Te0 ¼ 5 eV and ne =n0 1:5, it should be noted
that adiabatic compression will only heat the background
electron temperature to 7 eV. This suggests some other
form of heating (e.g., anomalous, resistive) is responsible for
FIG. 5. A composite image of the magnetic field strength Bz , a sampling of
background ions (blue dots), a sampling of debris ions (red dots), along with
trajectories of a couple of background (light blue) and debris (yellow) ion
trajectories throughout the course of the simulation. The markers on the trajectories correspond to the test particle’s current position at txci ¼ 0:5.
Phys. Plasmas 20, 012108 (2013)
the electron heating seen in Subsection III B. This is consistent with earlier experiments on magnetic pinches, which
showed that only 20% of electron heating is due to adiabatic
and Ohmic heating, while the rest is due to plasma
turbulence.48
It should be noted that the length scales within this simulation are less than the ion inertial length ðc=xpi Þ. The diamagnetic bubble radius is currently only 0:5 c=xpi . Since
the hybrid implementation assumes the electrons are massless and high frequency electron effects are left out, length
scales much less than the ion inertial length may be somewhat meaningless.50 Future experiments will take advantage
of a new plasma source that supports higher densities in
excess of 1013 cm3 (Ref. 23) and a larger laser system that
supports larger bubbles. Hybrid simulations using the larger
ion density (smaller c=xpi ) show that a full-blown collisionless shock does indeed form at these improved ambient
plasma conditions, with a diamagnetic bubble that spans
multiple ion inertial lengths.24
WAVES
IV. EMISSION OF SHEAR-ALFVEN
A. Review of earlier low-power experiments
Earlier laser experiments at the LAPD at lower laser
energies (1 J) and sub-Alfvenic expansion velocities discovered that streams of fast electrons, generated by the laserplasma interaction, launch shear Alfven waves, even though
the lifetime of the bubble is much shorter than the period of
the waves.9 These experiments investigated the coupling to
shear-waves both in parallel9 and perpendicular laser-blowoff geometries,17 as well as the interaction of two colliding
laser-plasma bubbles.18,49 Measured shear waves had frequencies at about 1=2 f ci . Work done in argon has also shown
wave phenomena above the cyclotron frequency that displayed characteristics of compressional Alfven waves.9 The
directed Larmor radius of the debris ions rLarmor;D was several times larger than the bubble size ( ¼ rLarmor;D =DB 5),
as was the wavelength of the shear-waves (DB =kA 0:1). As
a result, it was estimated that only 0.5% of the initial laser
energy was converted into shear-waves. The peak wave
1=3
fields were found to scale as vte =vA and were on the order
of 1 G (vthe is the thermal electron speed). These shear waves
have been explained theoretically by Cherenkov radiation of
Alfven waves by field aligned suprathermal electrons at
mean speeds above the Alfven velocity.51 In a separate
experiment,19 quasielectrostatic whistler waves have been
observed to be generated by fast electrons escaping laserproduced plasmas. A more recent experiment observed oscillations in the 10 MHz range at the bubble edge that were
identified as static flute-like structures translating past the
probes, related to the large-Larmor radius Rayleigh Taylor
instability,20 and consistent with earlier work done at the Naval Research Laboratory.6,8
n wave generation at higher power
B. Shear-Alfve
Like previous laser-plasma experiments in the LAPD at
low-power, our rapidly expanding cavities launch shear-Alfven
waves, albeit at higher amplitude and larger spatial extent.
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Niemann et al.
Phys. Plasmas 20, 012108 (2013)
FIG. 7. Evolution of the shear-wave amplitude as a function of distance
from the target. The figure shows the magnetic field magnitude at the transverse location where it peaks, at distances of Dz ¼ 0:3 m (black), 1.0 m
(blue), 2.9 m (green), and 6.8 m (red). The magnitude drops from 80 G near
the target to less than 20 G at a distance of several meters.
FIG. 6. A shear-Alfven wave is launched by the diamagnetic bubble and propagates over several meters along the machine (z-axis) at vA ¼ 3:3 107 cm=s.
A fast wave procedes the shear-wave at 3 108 m=s, corresponding to
electrons with a kinetic energy of 25 eV. (a) Evolution of By and Bz at y ¼ 0,
Dz ¼ 6:8 m from the target, and x ¼ 9 cm from the center of the plasma column. (b) Contour plot of the transverse field component (By ) as a function of
time and spatial coordinate along the field (z). The plot is comprised of simultaneous measurements from 9 magnetic pickup coils distributed at longitudinal
positions Dz between 2 m and 6.8 m. (c) Total transverse field component
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
B2x þ B2y as a function of both transverse dimensions in a vertical plane at
Dz ¼ 6:8 m from the target at t ¼ 20 ls. The coaxial current system is clearly
visible and is aligned with the center of the plasma column. The arrows indicate the transverse direction of the magnetic field, while the rectangle at
(x,y) ¼ (9, 0) cm indicates the probe location for plots (a) and (b).
Figure 6(a) shows a typical magnetic flux probe signal
of the transverse field component (By ) recorded 6.8 m axially
from the target, at (x,y) ¼ (12 cm, 0). A shear-Alfven pulse
with an amplitude around 15 G (or dB=B ¼ 5%) is clearly
visible passing the probe around 20 ls after the laser is fired.
We measure an axial field component dBz (dashed red line)
that is around 1/10 of By (solid black line), characteristic of a
shear wave. The horizontal field component (Bx ) at y ¼ 0 is
nearly zero (not shown). The frequency of the shear-wave is
initially around 40 kHz and below the cyclotron frequency
(0:4 fci ), corresponding to a wavelength of 8.3 m. We measure field fluctuations as high as 70 G (or dB=B > 25%) at
the probe closest to the target (Dz ¼ 0:3 m), decreasing to
40 G (or dB=B ¼ 15%) at a distance of 1–1.5 m, and to 20 G
at distances above 4 m (Figure 7). These experiments were
performed in the kinetic regime, as the Alfven speed is about
half the thermal electron speed. Therefore, Landau damping
could damp the wave and explain the decrease of the field
magnitude with distance from the target. The broadening of
the waves with distance from the source (Figure 7) is due to
dispersion, as the phase-velocity of the wave depends on the
transverse wavelength (k? ).52 At later times (not shown), after several transit times of the wave, the signal is dominated
by lower frequency oscillations due to standing waves in the
17 m long He-plasma column.
Simultaneous measurements of this type with an array
of 10 magnetic field probes distributed along the plasma column at distances Dz between 2 and 6.8 m from the target are
shown in Fig. 6(b). All probes were located in the horizontal
(xz) plane through the plasma column center (y ¼ 0), at a
transverse distance of x ¼ 12 cm from the center of the
machine where the wave-amplitude was close to the maximum. The traveling shear-Alfven wave is clearly visible,
propagating along the magnetic field at 3:3 107 cm=s,
which is consistent with the Alfven speed computed at the
plasma parameters. Figure 6(c) shows measurements of the
transverse magnetic field components in the xy-plane at
Dz ¼ 6:8 m from the target at the time when the shear-wave
amplitude peaks (20 ls). To obtain this data, one magnetic
field probe was moved in two-dimensions over 20 cm horizontally and 12 cm vertically. The contour-plot is a composite of 77 high-energy laser shots performed over the course
of two days, and shows the total unfiltered transverse field
component ðB2x þ B2y Þ1=2 , while the vector-plot indicates the
orientation of the field. In contrast to earlier work with lowpower lasers9 or helical antennas we do not observe two
anti-parallel current channels but a wide, quasi-coaxial current system centered near the plasma column (x,y) ¼ ( 3,0)
cm, with the magnetic field vanishing in the center and peaking approximately 10 cm radially from the symmetry axis.
The symmetry axis of the shear-wave current system at
x ¼ 3 cm is thus located close to the projection of the bubble edge at the time of peak diamagnetism (x ¼ 7 cm), and
has no relation to the location of the target (x ¼ 13 cm). The
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Niemann et al.
Phys. Plasmas 20, 012108 (2013)
FIG. 9. Auto-spectrum of the magnetic flux probe signal from Figure 6(a)
[i.e., By at (x,y,z) ¼ (12,0,680) cm]. The exploding laser-plasma creates
waves over a large frequency range in the ambient plasma, both above and
below the ion cyclotron frequency (f ci ¼ 0:1 MHz). The data display a compressional mode at early times around 5–10 ls, decreasing in frequency
from 1 MHz to 0.5 MHz, as well as a shear-Alfven wave at later times
around 20 ls at a frequency around 40 kHz 0:4 f ci .
FIG. 8. Evolution of the transverse magnetic field component By at y ¼ 0 as
a function of transverse position across the plasma column (x), at a distance
of Dz ¼ 5:2 m from the target in the axial direction (a). The contour plot
shows a composite of 45 laser shots where the magnetic probe was moved to
a different x-position in each shot. A shear-Alfven wave passes that probe
roughly 15 ls after the laser-trigger, consistent with an Alfven speed of
330 km/s. A fastwave is also visible preceding the shear-wave. (b) Line-out
of By as a function of x at the time when the peak of the pulse passes the
probe (t ¼ 15 ls). The data are consistent with a pseudo-coaxial current system centered near the middle of the plasma column (x ¼ 3 cm) although the
target was located at x ¼ 13 cm. The shear-wave carries a total current
around 1 kA distributed over a 20 cm diameter channel, creating a traverse
field up to 15 G (or dB=B ¼ 5%). We observe current densities around
3 A=cm2 in the center with a return current around 1 A=cm2 carried in a
concentric shell.
temporal evolution of By as a function of transverse position
(x-axis) at y ¼ 0 is shown in Fig. 8. The quasi-coaxial character of the current system centered at x 3 cm is evident,
with the maximum field amplitude 10 cm from the current
channel. The current density that produces such a current
system is shown in Fig. 8(b) and is around 3 A=cm2 and
close to the electron saturation current (Isat;e ¼ n vth;e e).
The total current carried by the wave is on the order of 1 kA.
The rapid fall-off of the field outside the current-channel
(faster than 1=Dx) can only be explained with a negative
return current around 1 A=cm2 in a surrounding shell. In
the shear-Alfven wave, the current along the magnetic field
is carried by electrons, while the current across the field is
carried by ions due to the ion-polarization drift. Although the
data suggests that Ienc vanishes at large x, the spatial range
covered in this measurement was not large enough to show
that the net-current through any plane is exactly zero. In helium we measure shear-Alfven wave velocities of 650 km/s
and 1400 km/s for magnetic fields of 600 G and 1800 G,
respectively (see table I). These velocities are consistent
with the computed Alfven speed, considering that the plasma
density increases from 8:5 1011 cm3 at 275 G to 2 1012 cm3 at 1800 G.
A fast wave is also observed, propagating along the
plasma column at a wavefront velocity around 3 108 cm=s,
corresponding to a beam of electrons with a kinetic energy
of 25 eV. At an axial distance of 6.8 m from the target, we
observe low amplitude fluctuations of the magnetic field signal as early as 350 ns after the laser-trigger, corresponding to
velocities in excess of 2 109 cm=s. These perturbations are
due to the presence of a high-energy tail of supra-thermal
electrons with keV energies. We observe field fluctuations of
a few Gauss in all three orthogonal components. Figure 9
shows the auto spectrum of the flux-probe signal from Fig.
6(a). The compressional mode is clearly visible at a frequency decreasing from 1 MHz at early times to 0.5 MHz
just before the arrival of the shear-wave.
C. Coupling efficiency
The coupling-efficiency to shear-Alfven waves can be estimated by integrating the measured magnetic-field profile B(r)
(Fig. 8(b)) over the volume of the current system. The
Ð energy
in the wave can be calculated as EA ¼ 1=ð2l0 Þ BðrÞ2 dV,
where dV ¼ 2pr dr dz is the volume of the wave, and r is
the radial distance from the center of the current system. Using
the wavelength to define the wave volume (dz ¼ 8.3 m) will
give a lower limit that ignores trailing oscillations at much
lower amplitude. An upper limit can be estimated from the total
length of the plasma column (dz ¼ 17 m). This estimate also
includes the kinetic energy of the flowing plasma in the region
around the magnetic field node (dBy ¼ 0). We find an energy
EA around 0.9 J, corresponding to a coupling efficiency of 5%
from the laser to Alfven waves. The coupling efficiency from
the diamagnetic cavity to the shear-wave is much higher at
around 70%. In addition, a magnetic energy around 50 mJ is
contained in the compressional mode, which is too small to
affect the total energy budget. Compared to earlier work at
lower laser energies,9 we observe coupling efficiencies from
the laser to Alfven waves an order of magnitude higher and
shear-waves that contain an energy two-orders of magnitude
higher. Field amplitudes in the present experiments are only an
order of magnitude higher, since the width of the current system is also larger. Using higher background fields decreases the
bubble size, and the current in the shear-wave decreases from
1 kA at 275 G to 600 A at 600 G and 400 A at 1800 G. We thus
observe the largest wave amplitudes and the highest coupling
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Niemann et al.
Phys. Plasmas 20, 012108 (2013)
FIG. 10. Variation of the By signal with
laser-energy 6.8 m axially from the target
at (x,y) ¼ (10,0) cm (a). The frequency of
the fast wave and the temporal shape and
arrival time of the shear-Alfven pulse are
independent of the laser-energy. The
transverse field during the passage of the
shear-Alfven pulse at around 20 ls as
well as the compressional mode around
10 ls scale linearly with the on-target
laser-energy (b). The amplitude of the
shear-wave is a factor of two larger than
the amplitude of the largest pulse in the
compressional wave-train.
efficiency in helium at low fields. Experiments in neon yield
smaller currents (600 A), and the total energy in the wave
decreases to 300 mJ. In experiments with varying magnetic
field and ambient mass (table I), the frequency of the shearwave is always around 0:5 fci over a large range of gyrofrequencies between 21 kHz for neon in 275 G to 685 kHz for
helium in 1800 G. The width of the current system (as measured from maximum to minimum field, see, e.g., Fig. 8(b))
decreases with the ambient field from 20 cm at 275 G to 10 cm
at 1800 G, as the diameter of the diamagnetic cavity shrinks
from 20 cm to 5 cm. The coupling efficiency from the laser to
shear-waves decreases with the external magnetic field from
5% at 275 G to 3% at 600 G and 2% at 1800 G. We measure no
difference in the coupling to shear-waves between shots with
fast (MA ¼ 1:5) and slow (MA ¼ 1:1) laser-blow-offs (Table
I), even though there is more electron heating at the edge of the
bubble at higher speed. The observed reduction in coupling efficiency at higher fields is consistent with earlier work at less
energy17 that found better coupling efficiencies where the cavity lifetime sB ¼ 1=ð4fB ) is closer to the cyclotron frequency
(f B =f ci ! 1). This is equivalent to evaluating the bubble
size DB relative to the Alfven wavelength DB =kA , where
pffiffiffiffiffi
pffiffiffiffiffi
kA vA =fci mi . Thus, DB =kA ðE=B2 Þ1=3 = mi increases
with E but decreases with B and the ambient ion mass mi . In helium at 275 G, the bubble expansion time is sB 1 ls and the
ratio is f B =f ci 2. At 1800 G, the ratio increases to 4. Similarly,
the coupling to Alfven waves decreases as the ambient mass
increases. In neon we measure an energy in the shear-wave that
is only 1/3 that of helium.
The shear-wave amplitude as well as the peak field in
the compressional mode far upstream from the target
(Dz ¼ 6:8 m) at a fixed transverse position (x ¼ 10 cm) are
observed to increase linearly with laser energy (Fig. 10) even
though the size of the bubble scales as E1=3 and the center of
the wave shifts accordingly. Varying the energy between
1.8 J and 25 J changes the amplitude of both the compressional mode and the shear-wave but does not affect the character of the signal (e.g., the compressional mode frequency,
arrival time and shape of shear-wave etc.).
D. Location of the current system
The data show that the current system develops spatially
around a location that is defined by the projection of the bubble
edge rather than the laser target. This suggests that the electrons
that form the shear-wave current system originate from the
edge of the bubble and may be related to the fast electrons
observed in Sec. III B. Figure 11 displays the location xcenter of
the symmetry axis of the shear-wave as a function of axial distance from the target. This location of the peak positive current
density depends strongly on the magnetic field and seems to be
correlated with the projection of the edge of the cavity at the
time of peak diamagnetism (sB ). Specifically, the bubble edge
is centered at xcenter ¼ 7 cm for 275 G, xcenter ¼ 2 cm for
600 G, and xcenter ¼ 8 cm for 1800 G, roughly consistent with
the current center location upstream from the target. In all
cases, the current system is shifting closer to the center of the
vacuum vessel with distance from the target. This observation
differs from earlier work with smaller lasers17 where the peak
positive current density was found approximately at the cavity
center and the return current at the bubble edge. We also
FIG. 11. Center of the axial current system as a function of longitudinal distance from the target for 275 G, 600 G, and 1800 G (a). The target was
located at x ¼ 13 cm with the blow-off directed in the negative x-direction.
In each case, the center position was evaluated at the time when the shearwave field is at maximum for each Dz. The data indicate that the current
system that develops into the shear-Alfven wave is centered around the projection of the bubble edge onto the plasma column (see Table I). Specifically, the edge of the bubble is located at x ¼ 7 cm for 275 G, x ¼ 2 cm for
600 G, and x ¼ 8 cm for 1800 G, roughly consistent with the current center
location upstream from the target. We also observe a fast temporal shift of
the current center during the passage of the Alfvenic pulse: (b) shows
the magnetic flux probe signal (dBy ) for B0 ¼ 1800 G at x ¼ 10 cm and
Dz ¼ 1:95 m cm axially from the target. The location of the current center
(i.e., the transverse location x where By changes sign) at 1.6 ls during the
peak of the pulse is located around x ¼ 8 cm and thus the projection of the
edge of the bubble. A few 100 ns after the peak of the pulse the center shifts
rapidly towards the center of the vacuum vessel (x ¼ 0) and the wave
becomes a plasma column resonance.
012108-11
Niemann et al.
observe a shift of xcenter during the passage of the Alfvenic
pulse. For example, for 1800 G, we measure an offset of
xcenter ¼ 8 cm at the time of the peak of the pulse (Fig. 11(b)).
A few 100 ns later, the center shifts rapidly towards the center
of the plasma column. Similar shifts are seen also at lower
fields.
V. CONCLUSION
In summary, we have investigated the dynamics of a
large, laser-driven diamagnetic cavity expanding at superAlfvenic speed into a preformed magnetized plasma. A
super-Alfvenic pulse propagates ahead of the bubble at
MA ¼ 1:5 increasing in amplitude to B=B0 ¼ 1:5 when the
cavity has reached 3/4 of its maximum size. This compression ratio is maintained over a distance of several cm until
the bubble stagnates at txci ¼ 0:5 and is consistent with the
MHD-jump conditions. Bubble sizes in these experiments
were only a fraction of the ion-inertial length (0:5 c=xpi )
and too small for a full-blown shock to separate from the piston. However, the electromagnetic forces at the edge of the
bubble, as well as the resulting cross-field currents and
related micro-instabilities, are similar to those found in the
current-layer of a shock ramp (though without the delicate
balance that keeps a shock stationary in time and the dissipation that conserves energy, momentum, and particle fluxes
across the ramp). Two-dimensional hybrid simulations reproduce the measurements well and show that the majority of
ambient ions are swept out of the bubble volume and accelerated to the piston velocity (MA ¼ 1:5). The simulations
also show that at the present experimental conditions (i.e.,
low Alfven Mach numbers), the coupling is dominated by
laminar electric fields due to the hot-electron cloud in the
blow-off, rather than azimuthal fields and Larmor coupling
due to fast ions.
We measure a magnetic field diffusion that is several
orders of magnitude faster than classical and increases with
the cross-field current at the bubble edge. Inside the bubble,
we observe oscillations in the lower hybrid range with an amplitude that increases as diffusion time decreases. We observe
electron heating at the edge of the bubble in the form of a
high-energy tail of electrons above 70 eV that is not present
before the arrival of the piston. Plasma temperature measurements with Langmuir sweeps were not possible due to the fast
laser-plasma expansion time scales and the limited number of
laser shots. In future experiments, the heating will be directly
investigated with Thomson scattering.45,53
Nonlinear shear-Alfven waves are launched by these
fast-electrons and carry a total current around 1 kA, which is
close to the electron saturation current. We measure coupling
efficiencies in excess of 5% (from the laser-beam to the
waves) and an order of magnitude larger than earlier work
with smaller lasers. The energy in the shear-wave is comparable to the magnetic energy expelled from the bubble
(EA =EB ¼ 0:7) and two orders of magnitude higher than in
previous experiments. The current system is also much wider
(20 cm and comparable to the bubble size) so that the largest fields observed were limited to 70 G or dB=B ¼ 25%.
The peak positive current density in the shear-wave was
Phys. Plasmas 20, 012108 (2013)
found to be correlated with the edge of the bubble, and shifts
towards the plasma column center at large distances from the
target.
Future experiments will take advantage of improved
diagnostics45,46,53,54 and a new plasma-source23 that supports
higher plasma ion densities in excess of 1013 cm3 and will
reduce the ion-inertial length to a few cm. In addition, a new
kilojoule-class laser system24 will increase the on-target
energy tenfold and will drive pistons as large as DB ¼ 50 cm
over sufficient scale lengths (>10 c=xpi ) to launch fullblown collisionless shocks in the ambient plasma55,56 The
higher density will also decrease the Alfven wavelength kA
and thus increase the ratio DB =kA , which is expected to
improve coupling to shear-waves. In addition, the amplitude
of the shear-waves has been found to scale linearly with laser
energy up to energies of 25 J. The higher-energy laser should
therefore drive significantly larger Alfven waves that could
be highly nonlinear (dB=B > 1).
ACKNOWLEDGMENTS
This work was supported by the DOE/NSF Partnership
in Basic Plasma Science under Contract Nos. DE-FG0206ER5406 and NSF05-619, the DOE Office of Science Early
Career Research Program (E-FOA-0000395), and the
Defense Threat Reduction Agency under Contract No.
HDTRA1-12-1-0024. The experiments were performed at
the UCLA Basic Plasma Science Facility (BaPSF). We thank
Z. Lucky, M. Nakamoto, and M. Drandell for technical support during the experiment, and A. Ng and the University of
British Columbia for the donation of the high-energy laser
system.
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