Geophysical Research Letters
RESEARCH LETTER
10.1002/2014GL061820
Key Points:
• First laboratory observation of
collisionless shocks of
cosmic relevance
• First measurement of shock
formation time
• Measured upper bound of
debris-ambient coupling criterion
Correspondence to:
C. Niemann,
cniemann@ucla.edu
Citation:
Niemann, C., et al. (2014),
Observation of collisionless shocks
in a large current-free laboratory
plasma, Geophys. Res. Lett., 41,
doi:10.1002/2014GL061820.
Received 10 SEP 2014
Accepted 10 OCT 2014
Accepted article online 15 OCT 2014
Observation of collisionless shocks in a large
current-free laboratory plasma
C. Niemann1 , W. Gekelman1 , C. G. Constantin1 , E. T. Everson1 , D. B. Schaeffer1 , A. S. Bondarenko1 ,
S. E. Clark1 , D. Winske2 , S. Vincena1 , B. Van Compernolle1 , and P. Pribyl1
1 Department of Physics and Astronomy, University of California, Los Angeles, California, USA, 2 Los Alamos National
Laboratory, Los Alamos, New Mexico, USA
Abstract
We report the first measurements of the formation and structure of a magnetized collisionless
shock by a laser-driven magnetic piston in a current-free laboratory plasma. This new class of experiments
combines a high-energy laser system and a large magnetized plasma to transfer energy from a laser plasma
plume to the ambient ions through collisionless coupling, until a self-sustained MA ∼ 2 magnetosonic
shock separates from the piston. The ambient plasma is highly magnetized, current free, and large enough
(17 m × 0.6 m) to support Alfvén waves. Magnetic field measurements of the structure and evolution of the
shock are consistent with two-dimensional hybrid simulations, which show Larmor coupling between the
debris and ambient ions and the presence of reflected ions, which provide the dissipation. The measured
shock formation time confirms predictions from computational work.
1. Introduction
Collisionless shock waves are important mechanisms for converting ram pressure into thermal energy and
affect the particle and field distribution throughout the universe [Treumann, 2009]. Dissipation in these
shocks is provided by self-generated electromagnetic fields due to plasma turbulence on scale lengths far
shorter than the classical mean free path. Collisionless shocks observed in the heliosphere by spacecraft,
such as the Earth’s bow shock [Russel and Greenstadt, 1979] or coronal mass ejections, and astrophysical
shocks in supernova remnants [Spicer et al., 1990] are mediated by magnetic reflection. The formation of
these shocks has never been measured in situ, since spacecraft data are currently limited to quasi-stationary
shocks, such as Earth’s bow shock. Shock formation has been modeled numerically with particle-fluid hybrid
codes [Cargill et al., 1988; Clark et al., 2013], but the predicted formation times and scale lengths have never
been confirmed by experiments. The nonstationary behavior of magnetized shocks due to reflected ions is
governed by the same physics as initial shock formation and has recently raised the issue of shock formation
and reformation to the forefront [Lembege and Savoini, 1992; Lobzin et al., 2007].
Well-scaled laboratory experiments can reproduce the physics of collisionless shocks in a controlled setting,
despite orders of magnitude differences in spatial and temporal scales [Drake, 2000]. Laboratory experiments can provide insight into the microphysics of shocks that can only be limitedly studied in space,
including the formation of a shock, the nature of microinstabilities, and the transport of debris ions across
the shock ramp. Early laboratory experiments employed plasma-pinch devices driving imploding pistons
and were limited to perpendicular shocks in current-carrying plasmas, where the shocks could not separate
from the piston [Biskamp, 1973]. Laser plasma experiments can overcome those limitations but are challenging, since they must simultaneously provide a highly magnetized plasma and a high-beta piston. Previous
experiments with laser plasmas exploding into ambient gas [Borovsky et al., 1984] or photoionized plasma
[Ripin et al., 1984] failed to sufficiently magnetize or ionize the background, while some progress has been
made in understanding coupling in experiments combining laser plasmas with a theta-pinch [Zakharov,
2003]. More recent laser experiments have focused on unmagnetized shocks [Fox et al., 2013].
In this letter, we present the very first observation of a magnetized collisionless shock of cosmic relevance
in a current-free laboratory plasma. This new class of laser experiments employs a high-energy Nd:glass
laser system [Niemann et al., 2012] and the Large Plasma Device (LAPD) [Gekelman et al., 1991], uniquely
combining an energetic super-Alfvénic debris cloud with a large (17 m × 0.6 m), current-free, highly magnetized, quiescent, and well-characterized ambient plasma. Unlike previous plasma-pinch experiments,
this approach transfers momentum from the debris to the ambient ions through collisionless coupling
NIEMANN ET AL.
©2014. American Geophysical Union. All Rights Reserved.
1
Geophysical Research Letters
BaO-NI
cathode
10.1002/2014GL061820
anode
grid
Laser
target
(a)
B-field coils
B0
anode
Thomson beam
3m
LaB6
cathode
[Schaeffer et al., 2012], until a
self-sustained shock propagates away
from the piston and is fully carried by the
ambient ions.
2. Experiment
The experiments were performed on
the LAPD at the University of California
Los Angeles (UCLA), which has recently
drive
Laser-plasma
been upgraded with a new high-density
beam
f/18
plasma source. A 17 m × 0.6 m large
C2H4 target
lens
hydrogen plasma with temperatures
of Te = 6 eV and Ti = 1 eV in an axial
field of B0 = 300 G is produced from
Thomson
collection
two cathode-anode discharges at opposite ends of the machine. One source
Bdot
probes
produces a background plasma (60 cm
Y
diameter, ni = 2 × 1012 cm−3 ) and the
Spectroscopy
X
Z
fiber probe
second a smaller, denser plasma (20 cm
B0
B-field
diameter, ni = 1.5 ± 0.5) × 1013 cm−3 ).
coils
50 cm
Density was measured by Langmuir
probes and a microwave interferometer.
Figure 1. Schematic of (a) the LAPD and (b) the laser-target and
When the plasma discharge reaches a
diagnostics configuration.
steady state (5 ms after breakdown), an
exploding plasma cloud is produced by
irradiating a solid polyethylene (C2 H4 ) target embedded inside the magnetized plasma with an energetic
laser pulse (200 J at 1053 nm, 25 ns pulse width) at a laser intensity of 1013 W/cm2 . Thomson scattering spectra obtained with a second probe laser (532 nm, 8 J, 5 ns) yield an electron density ne = 8.0 ± 1.5 × 1016 cm−3
and temperature Te = 7.5 ± 0.5 eV 250 ns after the laser pulse at 2.5 ± 0.4 cm from the target [Schaeffer et al.,
2014]. Comparison of self-emission spectra with synthetic, nonlocal thermal equilibrium, time-dependent
spectra in combination with the measured plasma parameters yield an average charge state of Z = 4.1,
implying C+4 is the dominant debris charge state. The structure and evolution of the diamagnetic cavity
[Niemann et al., 2013] and the shock in the ambient plasma were measured with a five-tip array of differentially wound magnetic flux probes (B-dot probes) with a 1 mm diameter core and 10 mm coil spacing
[Everson et al., 2009]. The target surface and debris blow-off direction were directed perpendicular to the
external field (x axis in Figure 1) and was offset by 30 cm from the center of the vacuum vessel, thus providing an ambient plasma interaction length of L = 60 cm. The reproducibility of the ambient plasma and
stability of the laser system (±5% variation in laser energy) allowed to construct a complete spatial profile by
translating the magnetic flux probe array along the blow-off axis (x axis) between laser shots. The velocity of
the fast debris ions driving the magnetic pulse is estimated from the dynamics of the diamagnetic cavity to
be 500 ±50 km/s.
(b)
target
drive
2.1. Scaling Parameters
Laboratory experiments of relevance to heliospheric magnetosonic shocks must fulfill a number of conditions, expressed in terms of dimensionless scaling parameters [Drake, 2000; Constantin et al., 2009]. The
piston must drive a magnetic pulse at supermagnetosonic speed (MA = vshock ∕vA > 1) through the magnetized plasma long enough for coupling to occur (𝜏Ωci >1, where 𝜏 = L∕vshock is the shock transit time,
L is the ambient plasma size along the blow-off axis, and Ωci is the ambient ion cyclotron frequency). This
is equivalent to providing a plasma size large enough to include the orbit of one shocked ambient ion
(L > 𝜌ad = MA ⋅ c∕𝜔pi , where 𝜌ad is the gyroradius of an ambient ion in the downstream region moving
at MA ). Simultaneously, hybrid simulations have predicted that the width of the piston must exceed an ion
inertial length (c∕𝜔pi ) [Omidi et al., 2002]. The mean free path for binary collisions of a shocked ambient ion
must exceed the plasma size (𝜆mfp ≫ L), and the plasma conductivity 𝜎 due to electron-ion collisions must
be large enough to avoid significant dissipation due to Ohmic heating in the shock ramp, equivalent to a
magnetic Reynolds number Rm = 𝜎 vshock L ≫ 1. In addition, hybrid simulations have recently predicted
NIEMANN ET AL.
©2014. American Geophysical Union. All Rights Reserved.
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Geophysical Research Letters
Figure 2. (a) Magnetic stack plots of Bz as a function of time for various
distances from the target. (b) Comparison of Bz (t) at x = 35 cm with
(black) and without (red) the ambient plasma. (c) Structure of the pulse
before (t = 0.3 μs) and after a shock is formed (t = 0.7 μs).
10.1002/2014GL061820
for C+4 debris exploding into a hydrogen plasma [Clark et al., 2013] that the
−2∕3
piston size RM = Rb0 MA must be comparable to or larger than the directed
debris Larmor radius 𝜌d to assure efficient coupling between the piston and
the ambient plasma (RM /𝜌d > 0.7). Here
Rb0 = [3𝜇0 Edebris ∕(2𝜋B2 )]1∕3 is the magnetic stopping radius, Edebris is the total
kinetic energy in the laser blow-off, and
B is the external magnetic field. This
coupling criterion is also the most stringent and requires a sufficiently energetic
debris cloud at sufficiently small yet
super-Alfvénic blow-off velocity. A relevant laser experiment must therefore
combine both an energetic driver and
a highly magnetized ambient plasma
with densities in excess of 1013 cm−3 .
The experiment described here was
designed to meet all these requirements
and produces dimensionless parameters
comparable to the Earth’s bow shock:
RM ∕𝜌d = 1 ± 0.1 > 0.7, MA ≥ 2,
L ≈ 10 c∕𝜔pi = 176 𝜌a , 𝜆mfp /L ≈ 20, and
Rm ≈ 104 .
2.2. Results and Discussion
Figure 2a shows stack plots of the measured magnetic field Bz /B0 for various
distances x from the laser target. Each trace shows the typical signature of a diamagnetic laser plasma cavity, including an initial field compression followed by complete field expulsion. The magnetic pulse ahead
of the cavity travels at 370 ± 20 km/s, which is super-Alfvénic (MA = 2.2 ± 0.3). The magnetic piston, i.e., the
leading edge of the diamagnetic cavity, slows from 500 km/s near the target to 200 km/s in the center of
the vessel. About 20 cm from the target, corresponding to tΩci =1, the magnetosonic pulse starts to steepen
into a shock and to separate from the piston. The ramp continues to steepen up to a distance of 40 cm from
the target, at which point the ambient plasma density drops sharply, and the shock dissipates. The measured field compression of Bz /B0 ≥2 is consistent with the Rankine-Hugoniot jump conditions for a shock.
In comparison with expansion into vacuum (Figure 2b), the field compression is significantly larger with the
ambient plasma and the leading edge of the magnetic pulse expands faster, indicating that the pulse is carried by ambient ions which have been accelerated by the piston. Simultaneously, the trailing edge of the
pulse (i.e., the piston) moves much slower, indicative of energy transfer to the ambient plasma. The magnetic pulse in vacuum has a significantly shallower ramp due to fast ions that slip through the magnetic
field, causing a weak magnetic disturbance ahead of the pulse. The spatial profile (Figure 2c) shows a ramp
with a width of a few millimeters and a downstream region between the piston and the ramp of 30 ambient
ion gyroradii 𝜌a . In comparison to earlier times before the shock is formed (blue dashed line in Figure 2c), the
structure of the shock shows a significantly steeper and faster ramp, and a much broader, more compressed
pulse. In addition, the ramp of the shock steepens from an initial 40 c∕𝜔pe to less than 20 c∕𝜔pe at a distance
of 40 cm from the target. The measured shock formation time around tΩci = 1 is consistent with theoretical
predictions [Cargill et al., 1988], while the measured coupling parameter of RM ∕𝜌d = 1 ± 0.1 agrees well with
the requirements found in hybrid simulations.
2.3. Hybrid Simulations and Summary
The experiment was modeled with a two-dimensional, collisionless, electromagnetic Darwin hybrid code
[Winske and Gary, 2007]. In the hybrid mode the ions are treated kinetically using the particle-in-cell technique, while electrons are modeled as a massless, charge-neutralizing, adiabatic fluid. Particles are tracked
NIEMANN ET AL.
©2014. American Geophysical Union. All Rights Reserved.
3
Geophysical Research Letters
10.1002/2014GL061820
in two spatial coordinates (x and y, perpendicular to the external magnetic
field Bz ) using three-dimensional velocities and fields. The simulation does not
model details of the laser-plasma interaction but is initiated with a cloud of
C+4 debris ions at the origin, exploding
at 500 km/s conically at ± 30◦ perpendicular to the magnetic field, consistent
with the actual experimental parameters.
Debris ions are initialized with a thermal spread comparable to the streaming
velocity. The ambient hydrogen plasma
is modeled as a cylinder with the density
profile as measured in the experiment.
Figure 3a shows the spatial distribution
of Bz at tΩci = 1.8 after the laser pulse.
The diamagnetic cavity is clearly visible
(dark blue) as well as the shock that has
separated from the piston and propagates radially outward. The bulk of the
debris ions stops at the edge of the bubble as indicated by the white dots that
represent a subset of debris ions used in
the simulation. A small population of fast
debris ions decouples from the bubble
and gyrates in the external field, since
their ion current is not sufficient to set
up coupling electric fields [Hewett et al.,
2011]. Trajectories of select debris (white)
and ambient (black) ions are shown that
illustrate the debris stopping at the bubble edge and expulsion of ambient ions.
The ambient ions are partially swept
Figure 3. Two-dimensional hybrid simulation showing (a) the spatial
outside the cavity by the electric and
contour plot of Bz /B0 and n∕n0 , (b) spatial lineouts of the magnetic
magnetic fields at the bubble edge. At
field, ambient density and 10X debris density along the blow-off axis
this time the shock is fully separated
y = 0, (c) temporal evolution of Bz /B0 along the blow-off axis, and (d)
phase space of debris (red) and ambient (blue) ions. Figures 3a, 3b, and from the piston and is carried by the
ambient ions, as indicated by the small
3d represent the time tΩci = 1.8. The white (black) lines in Figure 3a
show trajectories of select debris (ambient) ions, while the white dots
contour strip of the ambient plasma denindicate the location of debris ions at tΩci = 1.8.
sity n∕n0 between y = 20 cm and 30 cm.
Due to the conical blow-off geometry
and the gyration of the ambient ions, the expansion is not symmetric and the shock is most clearly visible
in the upper right quadrant, while data collection in the experiment was limited to the blow-off axis (y = 0).
However, the simulation still shows strong shock features along y = 0. Figure 3c shows the temporal evolution of Bz along the blow-off axis. The initial pulse moves slightly faster than the bulk of the debris. As it
steepens into a shock at x = 20 cm, its velocity decreases to MA = 2. When the shock encounters the end
of the high-density plasma at x = 45 cm, the velocity increases with the Alfvén speed before it dissipates.
Lineouts of the magnetic field, and the ambient ion density along the blow-off axis at tΩci = 1.8 (Figure 3b)
show a compression comparable to the experiment and consistent with the jump conditions for a shock.
The debris ions are stopped inside the bubble, and the shock is carried by the ambient plasma. The phase
space plot (Figure 3d) at tΩci = 1.8 shows that the ambient ions have been partially swept out of the cavity
and have been accelerated up to MA ∼ 2 in the downstream region. Ambient ions that have been reflected
off the shock ramp gyrate upstream of the shock with velocities up to MA ∼ 4, as indicated by the ring distribution between x = 50–60 cm. The debris ions on the other hand are partially slowed down inside the cavity
NIEMANN ET AL.
©2014. American Geophysical Union. All Rights Reserved.
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Geophysical Research Letters
10.1002/2014GL061820
(x = 40 cm), while the fastest debris are decoupled and travel upstream ahead of the shock. The hybrid simulations reproduce the basic features and evolution of the experiment and confirm that the pulse is indeed
a shock, since the target ions couple efficiently to the ambient ions, the compression of the field and density is consistent with the jump conditions, and reflected ions provide the dissipation of the shock. While
the 2-D simulations describe the early times of the explosion well, accurately modeling later times when
the cavity elongates and ions and plasma waves propagate along the magnetic field would require all three
spatial dimensions.
In summary, we have produced the first magnetosonic shock in a current-free laboratory plasma and have
measured the structure and evolution of the ramp. The measurements validate numerical predictions that
a shock will form when the directed Larmor radius of the debris does not exceed the equal mass radius
of the debris cloud by more than a factor of 1.4 and provide an upper bound for the coupling criterion.
Two-dimensional hybrid simulations reproduce the basic features and evolution of the experiment well and
show that a magnetosonic shock wave separates from the piston, which is carried by the ambient ions. The
data in combination with the hybrid simulations show that Larmor coupling [Spicer et al., 1990] is the dominant coupling mechanism for accelerating the ambient ions to the debris velocity, as opposed to laminar
coupling [Niemann et al., 2013]. The hybrid code does not model plasma instabilities related to the electron
cross-field current, and ion reflection is the only dissipation mechanism. The good agreement between the
data and the simulation therefore indicates that—similar to stronger shocks—microinstabilities only play a
minor role in the dissipation of these shocks. This new experimental platform will allow detailed studies of
the microphysics of magnetized shocks in arbitrary shock geometries in a controlled laboratory setting. In
the near future the facility will also support experiments on supercritical shocks (MA >3) using higher laser
intensities, as well as the very first laboratory experiments on quasi-parallel shocks that propagate along the
magnetic field.
Acknowledgments
This work was supported by the
Defense Threat Reduction Agency
under contract HDTRA1-12-1-0024 and
the DOE Office of Science Early Career
Research Program (E-FOA-0000395).
The experiments were performed at
the UCLA Basic Plasma Science Facility
(BaPSF) supported by DOE/NSF.
W.K. Peterson thanks Radu Presura
and one anonymous reviewer for their
assistance in evaluating this paper.
NIEMANN ET AL.
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