PHYSICS OF PLASMAS 21, 056312 (2014)
Laser-driven, magnetized quasi-perpendicular collisionless shocks on the
Large Plasma Devicea)
D. B. Schaeffer,1,b),c) E. T. Everson,1 A. S. Bondarenko,1 S. E. Clark,1 C. G. Constantin,1
S. Vincena,1 B. Van Compernolle,1 S. K. P. Tripathi,1 D. Winske,2 W. Gekelman,1
and C. Niemann1
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
(Received 31 December 2013; accepted 14 March 2014; published online 21 May 2014)
The interaction of a laser-driven super-Alfvenic magnetic piston with a large, preformed
magnetized ambient plasma has been studied by utilizing a unique experimental platform that
couples the Raptor kJ-class laser system [Niemann et al., J. Instrum. 7, P03010 (2012)] to the
Large Plasma Device [Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] at the University of
California, Los Angeles. This platform provides experimental conditions of relevance to space and
astrophysical magnetic collisionless shocks and, in particular, allows a detailed study of the
microphysics of shock formation, including piston-ambient ion collisionless coupling. An
overview of the platform and its capabilities is given, and recent experimental results on the
coupling of energy between piston and ambient ions and the formation of collisionless shocks are
presented and compared to theoretical and computational work. In particular, a magnetosonic pulse
consistent with a low-Mach number collisionless shock is observed in a quasi-perpendicular
C 2014 AIP Publishing LLC.
geometry in both experiments and simulations. V
[http://dx.doi.org/10.1063/1.4876608]
I. INTRODUCTION
Collisionless shocks are prevalent in many astrophysical
and terrestrial space environments, including supernovae
remnants, coronal mass ejections, the solar wind, and ionospheric explosions.1 In many of these systems, the basic
structure can be modeled as that of a magnetic piston driving
a shock through magnetized ambient plasma.2 The shock is
formed when accelerated plasma flows through the ambient
plasma faster than the ambient magnetosonic speed, and
functions to decelerate the ambient plasma in the shock
frame while simultaneously increasing entropy through heating. Unlike hydrodynamic shocks that dissipate energy
through classical collisions over scale lengths on the order of
the classical mean free path, collisionless shock energy is
dissipated through electromagnetic effects over far shorter
length scales. While collisionless shocks have been studied
remotely and in situ by spacecraft for decades, those systems
are difficult to diagnose or largely steady-state. With appropriate dimensional scaling,3,4 laboratory experiments can
thus contribute to an understanding of collisionless shock
formation, while also providing greater control over relevant
parameters and reproducibility. Moreover, experiments can
help validate computational codes and complement spacecraft measurements.
Much previous work has been and continues to be done
on magnetized collisionless shocks in a wide variety of
experimental configurations in the laboratory. Early work on
a)
Paper TI3 6, Bull. Am. Phys. Soc. 58, 284 (2013).
Invited speaker.
c)
Electronic mail: dschaeffer@physics.ucla.edu
b)
1070-664X/2014/21(5)/056312/8/$30.00
h-pinches successfully created quasi-perpendicular (shock
normal perpendicular to the background magnetic field)
shocks, but they did not separate from the piston.5–8 Later
experiments that combined a laser-produced plasma with a
h-pinch achieved some success in creating a shock-like
structure that separated from the piston.9,10 Other experiments studied the diamagnetic cavity generated by a subAlfvenic (MA ¼ v=vA < 1, where vA is the Alfven speed)
laser-driven plasma in an external magnetic field,11–15 while
more recent work has focused on studying collisionless
shocks by combining a laser-plasma with a Z-pinch16 or
through field-reversed configuration (FRC) plasma guns.17
At the University of California, Los Angeles (UCLA), we
utilize a unique experimental platform based on an earlier
design study3 that combines a high-power, laser-driven superAlfvenic magnetic piston with a large preformed, magnetized
ambient plasma. Though dimensionless parameters of relevance to magnetized space shocks, such as the Alfven Mach
number MA or shock formation length scale, are only marginally satisfied experimentally, this has the advantage not readily
accessible to spacecraft of providing a regime where the microphysics of shock formation can be studied in detail. In particular, how energy is coupled between the piston and ambient
plasma and what dissipation mechanisms are important in
shock formation can be investigated and used to benchmark relevant computational codes. Furthermore, the large scale of the
ambient plasma (a few c=xpi across the background magnetic
field, several hundred c=xpi along the field) is an ideal platform
for comparing quasi-perpendicular and quasi-parallel shock
geometries, which can be achieved by simply rotating the propagation direction of the piston relative to the background field.
We have previously used this platform to generate
21, 056312-1
C 2014 AIP Publishing LLC
V
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Phys. Plasmas 21, 056312 (2014)
quasi-perpendicular shock-precursors,18 large-amplitude shear
Alfven waves,19 and large-scale diamagnetic cavities.20
In this paper, we outline the above platform and report
recent experimental and computational results that demonstrate the formation of a quasi-perpendicular collisionless
shock, as well as the collisionless coupling of energy
between a magnetic piston and a magnetized ambient
plasma. We begin with an overview of the physics of pistonambient ion coupling and relevant computational simulations
in Sec. II. We then describe the experimental platform and
setup in Sec. III. In Sec. IV, we present experimental results
and discussion before concluding in Sec. V.
II. THEORY AND SIMULATIONS
It is helpful to start with a simple overview of how a
laser-ablated plasma can lead to collisionless shock formation (for reference to a typical simulation or experimental
setup, see Figs. 1 and 2). Much computational work21,22 has
been done that can provide a more thorough overview. We
start with a preformed, magnetized ambient plasma. At initial time, a super-Alfvenic debris plasma shell moving radially is generated by ablating a target with a high-energy
laser. As the debris expands, the higher electron density in
the debris shell compared to the ambient plasma leads to a
net azimuthal electron gyration in the shell that is manifested
as a diamagnetic current. Additionally, at early times, the debris ions are unmagnetized and free-stream through the background field, while the debris electrons, being much less
massive, are retarded. This sets up a radial electric field that
in turn causes an azimuthal E B motion for (primarily) the
electrons, reinforcing the diamagnetic current. At later times
when the space-charge separation is negligible, this current
is maintained in a similar manner by radial electron pressure
FIG. 1. A 2D spatial contour plot at late time from a hybrid simulation initialized to representative experimental parameters, showing the basic features seen in experiments. Red and blue dots are debris and ambient ions,
respectively, while the contour is the scaled magnetic field amplitude in ^
z.
The target is represented by the solid gray box at (0,0) and is irradiated by a
laser (not part of simulation) from þ^
x . Labeled in the figure are: (1) the formation of a magnetic cavity by debris ions; (2) the piston edge coming to a
stop as debris energy is transferred to the ambient plasma; (3) fast debris
ions decoupling and slipping through the background; (4) a low-Mach number quasi-perpendicular collisionless shock separating from the piston.
FIG. 2. (a) Schematic layout of a representative experiment. (b) Cartoon
cross-section of the LAPD plasma in a two-cathode configuration. (c)
Coordinate system when viewed from the top of the LAPD.
gradients. The current acts to expel the background field
within the current layer while compressing the field at the
layer’s edge.13,14 As a result, a diamagnetic cavity and magnetosonic pulse are formed as the debris plasma expands into
the background field. This combination of debris plasma and
diamagnetic cavity is the piston. At intermediate times, the
piston couples energy and momentum to the ambient plasma,
slowing down in the process. In turn, the ambient ions are
accelerated to a drift speed on the order of the initial debris
speed and eventually carry the magnetosonic pulse as they
separate from the piston. At late times, provided enough
energy has been transferred from the piston to the ambient
plasma, the accelerated ambient ions will overrun stationary
ambient ions, causing the magnetosonic pulse to steepen into
a shock. It is worth pointing out that in this model, the shock
only exists in the ambient plasma, with the piston solely providing a means to transfer laser energy to the ambient ions.
The physics of wave steepening and dissipation necessary for collisionless shock formation, as well as the basic
features of a formed shock, have been extensively studied.1
We focus here instead on how energy might be coupled
between the piston and the ambient plasma, beginning with
some general criteria for when that coupling is most effective. Since the diamagnetic cavity is simple to measure
experimentally, we cast the following discussion in terms
that relate to the cavity size.23 The initial kinetic energy
Ed ¼ 12 md Nd v2d in a debris plasma of Nd ions in a sphere of
radius R can be partitioned, ignoring energy sinks like shear
Alfven waves, into two terms
B20 1
4p 3
2
þ m a n a vd R ;
(1)
Ed ¼
8p 2
3
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Schaeffer et al.
where the first term is energy that is used to expel the background field B0, and the second is energy used to accelerate a
mass density mana of ambient ions to speed vd. If all the
energy goes into expelling the background field, the resulting
cavity radius R ¼ RB ¼ ð3Nd md v2d =B20 Þ1=3 is known as the
magnetic stopping radius. Conversely, if all the energy is
used to accelerate ambient ions to the debris speed, the
debris will expand to the equal mass radius R ¼ RM
ð2=3Þ
¼ ð3Nd md =4pma na Þ1=3 . Note that the ratio RB =RM ¼ MA ,
so that if we want energy to be coupled to the ambient
plasma, we require that RM < RB or MA > 1, i.e., that the debris ions be super-Alfvenic. Since it can also be shown24 that
debris ions traveling too fast will slip through the ambient
plasma without coupling, it is necessary to have a further
constraint on the debris ions. We have shown previously in
simulations25 that for a debris plasma dominated by a single
ion species (see Sec. IV A for further discussion), the condition RM =qd > 0:7, where qd is the debris ion gyroradius,
must be satisfied for a shock to form. A comparable (though
more stringent) criterion is that R=qd > 1, i.e., the cavity size
is large enough that the debris ions stop within the cavity.
How energy is actually coupled between the piston and
ambient plasma has been detailed elsewhere,23,24 and we
summarize it here for completeness. It can be shown26 that
for the super-Alfvenic, low be plasmas of interest here, the
dominant coupling mechanism is due to laminar instead of
turbulent electromagnetic fields. The laminar electric field
Elam can be derived from the electron momentum equation
and Ampere’s law
X
Ji B
rp
1
B ðr B Þ i
; (2)
Elam ¼ e ene 4pene
cene
where the first term is the electron pressure gradient, the second term is the magnetic pressure and curvature, and the third
is the ion current or Larmor term. It can be further shown that
as MA increases, the Larmor term, and hence Larmor coupling, becomes increasingly dominant over the other two.
This Larmor electric field is induced by the changing magnetic field as the debris ions move past (Elarmor / Jd B0 ),
and in turn causes a Elarmor B0 drift-like motion of the ambient ions in the same direction as Jd .
We use 2D hybrid simulations to study the process of
piston-ambient coupling and subsequent shock formation.
The simulations utilize a 2D3V collisionless Darwin hybrid
code in two Cartesian spatial dimensions with threedimensional fields and velocities.22 The ions are simulated
kinetically using the particle-in-cell technique, while the
electrons are treated as an inertial-less, charge-neutralizing
fluid. The simulations do not include the laser-target interaction, but focus on a plasma expanding out from a planar target perpendicular to a uniform magnetic field into an
ambient plasma at experimental conditions. In Fig. 1, a simulation under representative plasma conditions illustrates the
main features outlined above, including the formation of a
magnetic cavity and sweeping out of ambient ions, the coupling and stagnation of debris ions at the cavity edge, the
decoupling of faster debris ions, and the formation of a low
Phys. Plasmas 21, 056312 (2014)
Mach number collisionless shock. Simulations for specific
experimental parameters are presented in Sec. IV C.
III. EXPERIMENTAL PLATFORM
To study magnetized collisionless shocks, we use an experimental platform comprised of two facilities at UCLA.
The first is the Phoenix Laser Laboratory,27 run by the HighEnergy Density Physics (HEDP) plasma group, which consists of two laser systems. Raptor, a high-energy kJ-class
laser (1053 nm, 25 ns, 1012 W/cm2), is used to drive the magnetic piston. A smaller laser, Phoenix (1064 nm, 5 ns, 20 J,
1011 W/cm2), can be used for diagnostic measurements such
as Thomson scattering.
The second facility is the Large Plasma Device
(LAPD),28 run by the Basic Plasma Science Facility
(BASPF). The LAPD provides a well-characterized and
highly reproducible magnetized ambient plasma. This plasma
is well-suited for laser shock experiments because it is large
scale (10.6 m perpendicular to the background field, 18 m
parallel), steady-state (10 ms), quiescent and current-free, and
customizable in both background field (0.2–1.8 kG) and ambient gas fill (H2, He, Ne, Ar, etc.). We utilize the LAPD in a
two-cathode configuration. A BaO-coated Ni cathode generates a 160 cm, lower-density (na 2 1012 cm3 ) main
plasma, while a LaB6 (lanthanum hexaboride) cathode generates a smaller 140 cm, higher-density (na 2 1013 cm3 )
core plasma roughly centered on the main one (see Fig. 2(b)).
The ambient plasma has a typical electron temperature
Te ¼ 6 eV and ion temperature Ti ¼ 1 eV. The background
field is oriented axially (^z ) along the machine, with x^ oriented
horizontally perpendicular to the field and y^ oriented vertically
(see Fig. 2(c)).
A typical experimental setup utilizing this platform is
shown in Fig. 2. A rectangular carbon target of either graphite or HDPE (high-density polyethylene C2H4) is embedded
within the LAPD ambient plasma 30 cm from the machine
center axis. To study quasi-perpendicular shocks, the target
normal is oriented across the background field along x^ (the
laser-plasma is ablated normal to the target surface, regardless of the laser’s angle of incidence). Coordinates are
defined such that z ¼ 0 corresponds to the plane of the target
normal, y ¼ 0 corresponds to the target normal axis, and
x ¼ 0 corresponds to the target position (i.e., x ¼ 30 cm is the
center axis of the machine). The Raptor laser (250 J),
focused with a 1.8 m focal length lens to a 0.8–2 mm2 spot
size, is used to ablate a debris plasma. Differentially wound
magnetic flux (“bdot”) probes29 measure the ^z component of
the magnetic field up to 60 cm from the target along x^.
Additional bdot probes measure all three components of the
magnetic field up to 10 m from the target along ^
z . The probe
signals are sent through custom-built 150 MHz differential
amplifiers and coupled to fast (1.25 GHz) 10-bit digitizers. A
second frequency-doubled (532 nm, 10 J) beam from the
Phoenix laser, delayed arbitrarily relative to the Raptor
beam, is used for Thomson scattering. The beam is focused
either along x^ or slightly offset (z ¼ 2.5 cm) along y^ up to
x ¼ 30 cm from the target with a 1.5 m focal length lens
through baffled input and output windows. A custom-built
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Phys. Plasmas 21, 056312 (2014)
fiber probe at z ¼ 30 cm images light at a 90 scattering angle
through a 75 mm focal length lens onto a linear array of 40
100 lm UV-grade glass fibers. The fibers are coupled to a
1=4-m Acton spectrometer and Princeton Instruments (PI)
MAX 4 intensified charge-coupled device (ICCD) camera
with a 3 ns gate width. A second set of fiber probes with a 20
200 lm linear fiber array collects line-integrated light
emitted from the debris or ambient plasma for spectroscopy.
The light is coupled to a 3=4-m SPEX spectrometer and
PIMAX 2 ICCD camera.
IV. RESULTS AND DISCUSSION
A. Debris characterization
Characterizing the debris plasma is important for deriving the initial conditions used by both shock formation criteria (see Sec. II) and simulations. To that end, a carbon debris
plasma, generated by ablating a graphite target with a 100 J
Raptor beam (2 1011 W/cm2), was studied as it expanded
into a He ambient plasma (na 2 8 1012 cm3 ) in a 200
or 300 G background magnetic field (see Table I: Run 2-3).
Spectroscopic measurements were made of debris ion
states between CII and CV (Cþ1 and Cþ4, respectively. See
Fig. 3(c)). The spectra were spatially integrated along the
blowoff (^
x ) and time-integrated from 200–250 ns after ablation. After computing the Doppler shifts (relative to a NIST
standard) and widths of each ion species, a clear separation
of velocity distribution by ion species is seen, with higher
charge states corresponding to faster velocities (see Fig.
3(a)). This implies that the debris ions are ablated in distinct
shells by charge state, with the overlap between shells resulting from a velocity spread in the ablated ions.
Electron density and temperature measurements were
taken with Thomson scattering. The Thomson scattered light
was imaged such that the spatial dimension centered 4 cm
from the target was aligned along the blowoff axis, and spatially resolved Thomson spectra were collected between
250–1000 ns after ablation. Because the background magnetic field was small, the Thomson scattered spectrum was
fit with the full non-magnetic spectral density function30 convolved with the instrument function using a LevenbergMarquardt best-fit algorithm. At 250 ns (comparable to the
time spectroscopic measurements were taken), the Thomson
scattered light was collective (a ¼ 0.8), yielding an electron
and
temperature
density
ne ¼ 8:061:5 1016 cm3
Te ¼ 7.5 6 0.5 eV at 2.5 6 0.4 cm from the target.
If the number of debris ions were comparable in different
species shells, multiple density peaks would be expected over
time at a given location in the Thomson signal. In fact, only
one primary density peak is seen (see Fig. 3(b)), suggesting
that the dominant charge state is the one associated with this
peak (by at least an order of magnitude from the sensitivity of
the Thomson diagnostic). The plasma region associated with
the density peak was modeled using synthetic non localthermodynamic-equilibrium (non-LTE), time-dependent spectra generated by the collisional-radiative code PrismSPECT.31
The resulting spectrum at the Thomson-derived parameters
yielded a mean charge state Z ¼ 4:1, implying CV is the
dominant charge state (see Fig. 3(c)). Note that since the spectroscopic measurements were line-of-sight integrated, the
measured spectra will be brighter for lower ionization stages
TABLE I. Experimental parameters for four different experimental runs.
Three ambient density values are listed for Run 4, corresponding to different
parts of the ambient density profile in the LAPD. Elaser is the average ontarget laser energy, Ilaser is the on-target laser intensity, B0 is the background
magnetic field, Z is the average debris charge state, and 2RC is the magnetic
cavity size. Xci is the ambient ion cyclotron frequency, na is the ambient ion
density, vA is the Alfven speed, and c=xpi(c=xpe) is the ambient ion(electron) inertial length.
Parameter
Run 2
Run 3
Run 4
2 RC
(J)
90 6 3
(1011 W/cm2) 1.4 6 0.3
(G)
200
H2
4.1a
(cm)
50 6 1
100 6 5
1.6 6 0.4
200
He
4.1a
40 6 1
100 6 5
1.8 6 0.4
300
He
4.1
33 6 1
180 6 10
11 6 5
300
H2
4.0b
> 55
X1
ci
na
vA
c=xpi
c=xpe
(ls)
(1012 cm3)
(km/s)
(cm)
(cm)
13.1
361
120
25.8
0.30
8.7
461
150
20.3
0.24
2.2
12 6 1
190
6.6
0.15
Elaser
Ilaser
B0
Gas
Z
a
Run 1
3.3
261
280
14.7
0.34
661
270
9.3
0.22
261
460
16.1
0.38
Value inferred from another run in similar conditions.
Value estimated from spectroscopy, which showed CV as the most intense
line.
b
FIG. 3. (a) Velocity distributions derived from Doppler spectroscopic measurements of CII-CV. A distinct separation in charge state is seen, indicating
that the debris ions are coming off the target in shells. (b) Electron density
vs. time 2.5 cm from the target, measured at multiple times (3 ns resolution)
with spatially resolved imaging Thomson scattering. A single strong density
peak at 250 ns implies that most of the debris ions belong to one charge state
shell. (c) Measured spectra (solid) line-integrated along the blowoff axis and
time-integrated from 200–250 ns after ablation. PrismSPECT synthetic spectra (dashed) generated at the plasma conditions given by Thomson scattering
at 250 ns after ablation agree well with several observed spectral lines and
show that the dominant charge state is CV. Discrepancies between the synthetic and measured spectra are due to contributions from other charge state
shells.
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(due to contributions from other debris shells) compared to
the synthetic spectra. Using the time-of-flight of the density
peak in the Thomson spectra, the speed of the CV debris shell
was estimated to be vd ¼ 100 6 30 km/s, while using the electron temperature profile (not shown), for which more spatial
data are available, the speed was estimated to be
vd ¼ 130 6 80 km/s. This is consistent with the velocity distributions in Fig. 3(a). A smaller density peak at 800 ns
(ne ¼ 1:360:3 1016 cm3 ; Te ¼ 1:5þ0:4
0:3 eV) appears to correspond to a slower CII debris shell using the same analysis.
Previous experiments18 have shown that the debris
expansion is roughly spherical, so that the number of ablated
CV ions Nd can be estimated from the Thomson-measured
electron density in a corresponding sphere. Using the derived
mean charge state, the result Nd ¼ 1.6 6 0.5 1017 is in good
agreement with the number of ablated ions 2.0 6 0.2 1017
derived using an empirical mass ablation rate32 and the
above laser parameters.
B. Piston-ambient coupling
Since the diamagnetic cavity size can yield information
about how effectively the piston is coupling to the ambient
plasma, measurements of the cavity size in a variety of
plasma conditions were made with magnetic flux probes. In
Fig. 4(a)), a plot has been constructed such that points that
lie along the dashed line are consistent with all laser energy
being used to expel the background field, and no energy
FIG. 4. (a) Plot of magnetic cavity size vs. magnetic stopping radius
RB ¼ ð6Elaser =B20 Þ1=3 . The dashed line is generated by assuming all available
laser energy is used to expel background magnetic field, i.e., RC / RB .
Experiments at low energy or with sub-Alfvenic pistons in various plasma
conditions fall on the dashed line. Only high-energy, super-Alfvenic parameters yield cavity sizes consistent with energy being coupled to the ambient
plasma. (b) Measured Heþ1 (468.6 nm) spectra (with instrumental broadening) in the ambient plasma, showing additional broadening due to ion heating and electric fields with a debris plasma (solid) compared to without
(dashed), as well as intensification compared to without (dotted-dashed). (c)
Inset: Fourier decomposition of the Heþ1 spectrum with a debris plasma,
showing a strong component at the modulation spacing (dashed).
Phys. Plasmas 21, 056312 (2014)
being used to move the ambient ions (i.e., RC / RB ).
Previous experiments20 with a low-energy (20 J) ablator
beam in a He or H ambient plasma and 275 or 600 G background field indicated that the cavity size was consistent
with the magnetic stopping radius, independent of whether
the piston was sub- or super-Alfvenic. Similarly, experiments in an H ambient plasma (see Table I: Run 1) with a
higher-energy (100 J) ablator beam but sub-Alfvenic piston
also created cavities consistent with field expulsion only.
However, under the same conditions but with a superAlfvenic piston (by changing to a He plasma, Table I:
Run 2), the cavity sizes shrank, indicating that some of the
laser energy did not go into expelling the background field.
This behavior is consistent with the coupling criteria detailed
in Sec. II. In particular, looking at a super-Alfvenic case
(B0 ¼ 300 G) with a magnetic cavity 2RC ¼ 33 6 1 cm, the
coupling parameter RM=qd ¼ 1.9 6 0.3 > 0.7, estimated using
the derived charge state and blowoff speed in the same
plasma conditions from Sec. IV A, suggests that
debris-ambient ion coupling should be part of the energy
partition.
As detailed in Sec. II, laminar electric fields are
expected to play a role in the collisionless coupling of piston
to ambient ions. Using the fact that the presence of an electric field causes a Stark broadening of spectral lines, measurements were made in He ambient plasmas to look for
evidence of laminar electric fields relevant to coupling (see
Table I: Run 2). 2D hybrid simulations initialized to the
same experimental conditions indicate that the laminar electric field reaches a maximum amplitude of 0.8 6 0.3 kV/cm
in the leading edge of the piston.
Data from Heþ1 lines (468.6 and 320.3 nm), time integrated 2–3 ls after ablation 30 cm from the target, show a
large increase in intensity relative to their background values
(I=I0 103, see Fig. 4(b)). This is coincident with the passing
of the leading edge of the piston and implies that a hot electron population was deposited into the ambient plasma. Fig.
4(b) shows that the Heþ1 lines are also significantly broadened in the presence of a debris plasma. Without a debris
plasma, the Heþ1 line widths are determined only by
Doppler broadening due to the ambient ion temperature.
Since these Heþ1 lines are actually comprised of several
lines that could not be spectrally resolved, the Doppler contribution (after correcting for instrumental broadening) was
determined by comparing the measured spectra to synthetic
spectra at various temperatures generated by PrismSPECT.
The results for both Heþ1 lines were comparable (Ti 1 eV).
When the same analysis is undertaken for those lines with a
debris plasma, the Doppler contributions are significantly
different for each line, suggesting that ion heating is not
solely responsible for the increased broadening. Since Stark
broadening is the only other dominant broadening mechanism, the relative contribution of Doppler to Stark broadening can be determined self-consistently by comparing the
two Heþ1 lines. The results suggest that additional ion heating is negligible, and most of the broadening is due to electric fields.
The spectrum in Fig. 4(b) shows regularly spaced modulations atop the main signal, which, in accordance with time-
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Schaeffer et al.
Phys. Plasmas 21, 056312 (2014)
dependent Stark broadening, indicates the existence of a harmonic electric field. A Fourier decomposition (see Fig. 4(c))
shows a clear component (k ¼ 36 6 1 nm1) at the modulation spacing, corresponding to a frequency x ¼ 2.4 6 0.1
xpe. This frequency and experiments performed elsewhere33
suggest that the electric field corresponds to a beam-plasma
instability rather than a more slowly varying laminar electric
field. (Note that such high-frequency fields are not modeled
by the hybrid simulations due to the assumption of
inertial-less, charge-neutralizing electrons.) Using an
approximation33 to the time-dependent theory, the associated
electric field amplitude is calculated to be 7.9 6 0.3 kV/cm,
significantly higher than the peak simulated laminar field
magnitudes. While these results do not preclude the presence
of laminar electric fields in the piston-ambient ion coupling
regime, they indicate that distinguishing between laminar
and harmonic components through Stark spectroscopy will
be challenging.
C. Collisionless shock formation
To study quasi-perpendicular collisionless shock formation, an array of five differentially wound magnetic flux
coils, spaced 1 cm apart and measuring the ^z -component of
magnetic field, were positioned along x^ from 15 to 55 cm
from the target. The parameters of the debris and ambient
plasmas are listed in Table I: Run 4. At around 280 ns
(0:1 X1
ci ) after ablation, a diamagnetic cavity and magnetosonic pulse have formed in the usual way (see Figs. 5(a)
and 5(b)). The leading edge of the magnetic pulse moves at
MA ¼ 1.5 6 0.1 with a magnetic compression Bz =B0
¼ 1:660:1. The pulse has a shallow ramp (40 c=xpe) that
ends at the cavity edge. However, by 675 ns (0:3 X1
ci ) the
pulse shows very different behavior (see Fig. 5(b)). The
magnetic compression has increased to Bz =B0 ¼ 2:060:1
and moves at MA ¼ 2.1 6 0.1, consistent with the
Rankine-Hugoniot jump conditions,34 which state that the
downstream magnetic field scales as MA. Additionally,
the ramp of the compression has steepened to a width
d ¼ 2067 c=xpe ¼ 0:560:2 c=xpi , similar to the magnetic
ramps seen on collisionless space shocks.1 Lastly, the width
of the pulse has increased to D ¼ 1:460:2 c=xpi , showing a
significant separation of the front of the compression from
the cavity edge. This can be further seen in Fig. 5(a), where
at t ¼ 675 ns the front of the compression is moving faster
than the cavity edge (MA ¼ 2.1 6 0.1 vs MA ¼ 1.6 6 0.1).
These features suggest that a low-Mach number
quasi-perpendicular collisionless shock has formed and is beginning to separate from the piston (see also Table II).
Comparison to shots taken in vacuum (107 Torr)
under the same conditions indicates that the above features
are tied to the ambient plasma (see Fig. 5(c)). Comparing
two temporal profiles taken 37 cm from the target reveals
several key differences. The magnetic pulse in vacuum has a
much shallower ramp due to the decoupling of faster debris
ions that carry some magnetic compression with them. The
width of the pulse in vacuum is also much narrower, and
appears to be linked to the edge of the cavity (similar to the
magnetic pulses seen early in time with an ambient plasma).
FIG. 5. (a) Temporal magnetic field profiles at different spatial locations. A
magnetosonic pulse tied to the cavity edge is seen early in time, before beginning to separate from the piston and broaden (dashed). Spatial lineouts
(dotted-dashed) at three times are plotted in (b). A comparison to early times
(dotted-dashed) shows a significantly steeper, broader, more compressed,
and faster magnetic pulse (solid) at later times, consistent with a low-Mach
number collisionless shock. Late in time (dotted-dotted-dashed) the pulse
smears out as the high-density plasma region (gray overlay) ends. (c)
Temporal profiles 37 cm from the target show the influence of an ambient
plasma (solid) compared to vacuum (dotted-dashed). With an ambient
plasma, the resulting magnetic pulse is steeper, broader, faster at its leading
edge and slower at the cavity edge.
Finally, the cavity moves more slowly with an ambient
plasma (350 vs. 390 6 20 km/s), consistent with energy
being coupled to the ambient ions, while the leading
TABLE II. Necessary conditions to form a collisionless shock using parameters from the first column in Run 4 in Table I. RM=qd and D0=qd are conditions on piston-ambient ion coupling, where RM is the equal mass radius, qd
is the debris directed gyroradius, and D0 is the system size. D0=qa,s
expresses the condition that the ambient ions are sufficiently magnetized,
where qa,s is the downstream ambient ion directed gyroradius. T ¼ D0=vA is
the shock transit time and for the downstream ambient ions, (c=xpi,s) is the
inertial length, X1
ci;s is the cyclotron period, and kii,s is the ion-ion mean free
path. Since the ambient ions are accelerated by the magnetic piston within a
gyroperiod (i.e., within a gyroradius from the target) and continue interacting with non-perturbed ambient ions until the edge of magnetic cavity,
D0 ¼ 2RC was chosen as the system size.
Condition
Lab value
2.1 6 0.1
1.4 6 0.3
>2.3
> 7.9
Super-Alfvenic
Sufficient coupling
Sufficient coupling
Magnetized
M A>1
RM =qd > 1
D0 =qd > 1
D0 =qa;s > 1
Sufficient space
D0 ðc=xpi;s Þ1 > 1
> 12.2
Sufficient time
Collisionless
T X1
ci;s > 1
kii;s =D0 > 1
> 2.8
1
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056312-7
Schaeffer et al.
magnetic compression moves more quickly (530 vs.
420 6 10 km/s), consistent with a pulse that is being carried
by accelerated ambient ions.
At 940 ns after ablation, instead of further separating
from the piston, the magnetic pulse has become significantly
shallower and less compressed (Bz=B0 ¼ 1.7 6 0.1). This is a
result of the inhomogeneous ambient density profile in the
LAPD (see Fig. 5(b)). As the magnetic pulse moves out of
the high-density region of the ambient plasma, both the
Alfven speed and ion inertial length increase, decreasing and
smearing out the leading edge of the magnetic compression
(see Table I: Run 4). Future experiments will expand the
high-density region of the ambient plasma in order to see a
clear separation of the shock from the piston.
The above results have been compared to 2D hybrid
simulations initialized to the same experimental conditions.
The simulations use a two-component ambient plasma, with
one uniform low-density plasma covering the entire simulation domain, and another high-density Gaussian component
centered 4 c=xpi from the initial debris distribution (see
Fig. 6(a)). The debris plasma consists of a cloud of Cþ4 ions
(see Sec. IV A) that expands out conically at 675 at
MA ¼ 2.65. As can be seen in Fig. 6(b), the formation of a
low-Mach number collisionless shock is also reproduced in
the simulations. In particular, a magnetic and ambient density compression consistent with the jump conditions is seen
in Fig. 6(c), while a small population of reflected ambient
ions from the shock front is seen in Fig. 6(d). The simulations also show the dissipation of the shock as it leaves the
high-density ambient plasma, consistent with experimental
observations.
V. CONCLUSION
We have utilized a unique experimental platform at
UCLA to investigate the interaction of a super-Alfvenic,
laser-driven magnetic piston with a large, preformed magnetized ambient plasma. In particular, while we are able to create experimental conditions suitable for laboratory studies
relevant to magnetized collisionless space shocks, those conditions are marginal enough to allow us to uniquely explore
a regime of debris-ambient coupling and collisionless shock
formation not readily available to spacecraft. Recent theoretical and computational work has helped clarify mechanisms
by which coupling and shock formation can occur, and
experiments have seen evidence of collisionless coupling
between super-Alfvenic debris ions and an ambient plasma.
We have also measured in a quasi-perpendicular geometry a
magnetosonic pulse that is consistent with a low-Mach number collisionless shock, though it was not observed to fully
separate from the magnetic piston. Two-dimensional hybrid
simulations initialized to the same experimental conditions
and modeled after measured debris behavior reproduce the
basic features seen in experiments, as well as show the formation of a collisionless shock. Future work will optimize
the plasma conditions so that there is greater coupling
between piston and ambient ions, the magnetic pulse can further separate from the piston, and the resulting shock is
Phys. Plasmas 21, 056312 (2014)
FIG. 6. (a) Spatial contour plot of Bz at initial time from a 2D hybrid simulation. The ambient density is inhomogenous, with a uniform low-density component over the whole domain (not shown) and a high-density Gaussian core
(blue dots) centered at x ¼ 30 cm (4 c=xpi). The debris cloud (red dots) is concentrated at (x,y) ¼ (0,0) in a small disk (1 ¼ 0:25 c=xpi ) with Gaussian intensity. (b) Spatial contour plot of Bz at late time (1 X1
ci ) from the same
simulation. 1D profiles at y ¼ 0 (green dashed) are shown in (c). (c) Magnetic
(solid), ambient density (dotted-dashed), and debris density (dotted-dotted-dashed) profiles at late time showing the formation of a low-Mach number
shock, with magnetic and density compressions consistent with the
Rankine-Hugoniot jump conditions. (d) Phase-space plot of ambient ions at
late time. A small population of reflected ions at x ¼ 30 cm is consistent with
the formation of a shock.
supercritical. We will also transition to oblique and quasiparallel geometries.
ACKNOWLEDGMENTS
We would like to thank the staff of the Large Plasma
Device, Z. Lucky, and M. Drandell for their help in carrying
out these experiments. This work was performed at the Basic
Plasma Science Facility at UCLA, funded by the National
Science Foundation and the Department of Energy, and was
supported by the Defense Threat Reduction Agency (DTRA)
under Contract No. HDTRA1- 12-1-0024 and by the DOE
Office of Science Early Career Research Program (DE-FOA0000395).
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