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1 GeophysicalResearchLetters RESEARCH LETTER 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, Citation: Niemann, C., et al. (2014), Observation of collisionless shocks in a large current-free laboratory plasma, Geophys. Res. Lett., 41, doi:. 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. Niemann 1, W. Gekelman 1, C. G. Constantin 1, E. T. Everson 1, D. B. Schaeffer 1, A. S. Bondarenko 1, S. E. Clark 1, D. Winske 2, S. Vincena 1, B. Van Compernolle 1, and P. Pribyl 1 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 M A 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].Dissipationinthese 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].Laboratoryexperiments 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 American Geophysical Union. All Rights Reserved. 1

2 BaO-NI cathode Laser target B-field coils anode grid (a) [Schaeffer et al., 2012],untila self-sustained shock propagates away from the piston and is fully carried by the ambient ions. anode (b) X Laser-plasma C 2 H 4 target Thomson collection Y B 0 Z target drive B 0 Thomson beam B-field coils 3 m 50 cm LaB 6 cathode drive beam f/18 lens Bdot probes Spectroscopy fiber probe Figure 1. Schematic of (a) the LAPD and (b) the laser-target and diagnostics configuration. 2. Experiment The experiments were performed on the LAPD at the University of California Los Angeles (UCLA), which has recently been upgraded with a new high-density plasma source. A 17 m 0.6 m large hydrogen plasma with temperatures of T e = 6 ev and T i = 1 ev in an axial field of B 0 = 300 G is produced from two cathode-anode discharges at opposite ends of the machine. One source produces a background plasma (60 cm diameter, n i = cm 3 ) and the second a smaller, denser plasma (20 cm diameter, n i = 1.5 ± 0.5) cm 3 ). Density was measured by Langmuir probes and a microwave interferometer. When the plasma discharge reaches a steady state (5 ms after breakdown), an exploding plasma cloud is produced by irradiating a solid polyethylene (C 2 H 4 ) 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 W/cm 2.Thomsonscatteringspectra obtained with a second probe laser (532 nm, 8 J, 5 ns) yield an electron density n e = 8.0 ± cm 3 and temperature T e = 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 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 (M A = v shock v A > 1) through the magnetized plasma long enough for coupling to occur (τω ci >1, where τ = L v shock is the shock transit time, L is the ambient plasma size along the blow-off axis, and Ω ci 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 > ρ ad = M A c ω pi, where ρ ad is the gyroradius of an ambient ion in the downstream region moving at M A ). Simultaneously, hybrid simulations have predicted that the width of the piston must exceed an ion inertial length (c ω pi )[Omidi et al., 2002]. The mean free path for binary collisions of a shocked ambient ion must exceed the plasma size (λ mfp 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 R m = σ v shock L 1. In addition, hybrid simulations have recently predicted NIEMANN ET AL American Geophysical Union. All Rights Reserved. 2

3 Figure 2. (a) Magnetic stack plots of B z as a function of time for various distances from the target. (b) Comparison of B z (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). for C +4 debris exploding into a hydrogen plasma [Clark et al.,2013]thatthe piston size R M = R b0 M 2 3 must be comparable to or larger than the directed A debris Larmor radius ρ d to assure efficient coupling between the piston and the ambient plasma (R M /ρ d > 0.7). Here R b0 =[3μ 0 E debris (2πB 2 )] 1 3 is the magnetic stopping radius, E debris 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 ahighlymagnetizedambientplasma with densities in excess of cm 3. The experiment described here was designed to meet all these requirements and produces dimensionless parameters comparable to the Earth s bow shock: R M ρ d = 1 ± 0.1 > 0.7, M A 2, L 10 c ω pi = 176 ρ a, λ mfp /L 20, and R m Results and Discussion Figure 2a shows stack plots of the measured magnetic field B z /B 0 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 (M A = 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 tω ci =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 B z /B 0 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 ρ a. 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 ω pe to less than 20 c ω pe at a distance of 40 cm from the target. The measured shock formation time around tω ci = 1 is consistent with theoretical predictions [Cargill et al.,1988],whilethemeasuredcouplingparameterofr M ρ d =1± 0.1 agrees well with the requirements found in hybrid simulations 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 American Geophysical Union. All Rights Reserved. 3

4 Geophysical Research Letters 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 = cm. The debris ions on the other hand are partially slowed down inside the cavity NIEMANN ET AL American Geophysical Union. All Rights Reserved. 4

5 (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 ashock,sincethetargetionscoupleefficientlytotheambientions,thecompressionofthefieldanddensity 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 (M A >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 HDTRA and the DOE Office of Science Early Career Research Program (E-FOA ). 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. References Biskamp, D. 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