We consider ion heating by turbulent Alfvén waves (AWs) and kinetic Alfvén waves (KAWs) with wavelengths (measured perpendicular to the magnetic field) that are comparable to the ion gyroradius and frequencies ω smaller than the ion cyclotron frequency Ω. As in previous studies, we find that when the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity ε = δv ρ /v ⊥ , where v ⊥ (v ) is the component of the ion velocity perpendicular (parallel) to the background magnetic field B 0 , and δv ρ (δB ρ ) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when ε ≪ ε crit , where ε crit is a dimensionless constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when ε > ε crit , the proton heating rate exceeds the cascade power that would be present in strong balanced KAW turbulence with the same value of δv ρ , and magnetic-moment conservation is violated even when ω ≪ Ω. For the random-phase waves in our test-particle simulations, ε crit ≃ 0.2. For protons in low-β plasmas, ε ≃ β −1/2 δB ρ /B 0 , and ε can exceed ε crit even when δB ρ /B 0 ≪ ε crit , where β is the ratio of plasma pressure to magnetic pressure. The heating is anisotropic, increasing v 2 ⊥ much more than v 2 when β ≪ 1. (In contrast, at β 1 Landau damping and transit-time damping of KAWs lead to strong parallel heating of protons.) At comparable temperatures, alpha particles and minor ions have larger values of ε than protons and are heated more efficiently as a result. We discuss the implications of our results for ion heating in coronal holes and the solar wind.

We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations, and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohms's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species, and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate, analytically and numerically, that the five-moment model reduces to the widely used Hall Magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic Particle-In-Cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The tenmoment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohms law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.

Filamentation due to the growth of a Weibel-type instability was observed in the interaction of a pair of counter-streaming, ablatively-driven plasma flows, in a supersonic, collisionless regime relevant to astrophysical collisionless shocks. The flows were created by irradiating a pair of opposing plastic (CH) foils with 1.8 kJ, 2-ns laser pulses on the omega ep laser system. Ultrafast laserdriven proton radiography was used to image the Weibel-generated electromagnetic fields. The experimental observations are in good agreement with the analytical theory of the Weibel instability and with particle-in-cell simulations.Astrophysical shock waves play diverse roles, including energizing cosmic rays in the blast waves of astrophysical explosions [1], and generating primordial magnetic fields during the formation of galaxies and clusters [2]. These shocks are typically collisionless, and require collective electromagnetic fields [3], as Coulomb collisions alone are too weak to sustain shocks in high-temperature astrophysical plasmas. The class of Weibel-type instabilities [4][5][6] (including the classical Weibel and currentfilamentation instabilities) is one such collective mechanism that has been proposed to generate a turbulent magnetic field in the shock front and thereby mediate shock formation in cosmological shocks [7] and blast wave shocks in gamma ray bursts [8][9][10] and supernova remnants [11]. These instabilities generate magnetic field de novo by tapping into non-equilibrium features in the electron and ion distributions functions. The classical form of the Weibel instability is driven by temperature anisotropy [4], but counterstreaming ion beams, as occurs in the present context, provides an equivalent drive mechanism [6]. A related current filamentation instability of relativistic electron beams [12] has also previously been observed in experiments driven by ultraintense lasers [13].We report experimental identification an ion-driven Weibel-type instability generated in the interaction of two counterstreaming laser-produced plasma plumes. A pair of opposing CH targets was irradiated by kJ-class laser pulses on the OMEGA EP laser laser system, driving a pair of ablative flows toward the collision region at the midplane between the two foils. Due to the long mean-free-path between ions in opposing streams, the streams interpenetrate, establishing supersonic counterstreaming conditions in the ion populations, while the electrons form a single thermalized cloud. Meanwhile, the plasma density is also sufficient so that the the ion skin depth d i = (m i /µ 0 ne 2 ) 1/2 , is much smaller than the system size L. These conditions allow the growth of an ion-driven Weibel instability, for which d i is the characteristic wavelength [14][15][16]. The Weibel-generated electromagnetic fields were observed with an ultrafast pro- ton radiography technique [17], and identified through good agreement with analytic theory [6] and particle-incell simulations, discussed below. Figure 1 shows a schematic of the experiments...

Observations of magnetic reconnection between colliding plumes of magnetized laser-produced plasma are presented. Two counter-propagating plasma flows are created by irradiating oppositely placed plastic (CH) targets with 1.8 -kJ, 2 -ns laser beams on the Omega EP Laser System. The interaction region between the plumes is pre-filled with a low-density background plasma and magnetized by an externally applied magnetic field, imposed perpendicular to the plasma flow, and initialized with an X-type null point geometry with B = 0 at the midplane and B = 8 T at the targets. The counter-flowing plumes sweep up and compress the background plasma and the magnetic field into a pair of magnetized ribbons, which collide, stagnate, and reconnect at the midplane, allowing the first detailed observations of a stretched current sheet in laser-driven reconnection experiments. The dynamics of current sheet formation are in good agreement with first-principles particle-in-cell simulations that model the experiments.PACS numbers: 52.27.-h, 52.35.Vd, 52.65. Rr, 52.72.+v, 94.30.cp Throughout the Universe, magnetic reconnection allows the magnetic field to change its topology and thereby allow an explosive release of stored energy [1][2][3]. Recently, a number of experiments have been carried out studying magnetic reconnection using laser-driven plasmas [4][5][6][7][8]. These experiments are in many ways complementary to traditional reconnection experiments with magnetized discharge plasmas [3]. Some notable features include the high plasma beta, strong inflows, and strong magnetic flux pile-up. This regime is very interesting as there are a number of space and astrophysical contexts where supersonic, magnetized flows collide, such as interactions of planetary magnetospheres with the solar wind [9], interaction of the solar wind with the interstellar medium at the heliopause [10,11], and pulsar windtermination shocks [12], to name only a few.Previous laser-driven experiments studied the reconnection of the self-generated (e.g., Biermann battery) magnetic fields between colliding laser-produced plasma plumes [4][5][6][7][8]. Magnetic field annihilation [5] has been observed, as well as plasma jets [4,[6][7][8] and electron energization [8]. This Letter presents, for the first time, results on reconnection of an externally applied magnetic field by counter-propagating, laser-driven colliding highenergy density (HED) plasmas. These experiments are based on new techniques for externally controlled magnetization of ablated plasma plumes. The geometry of this externally magnetized plasma experiment makes it amenable to end-to-end simulation with particle-in-cell codes modeling the entire progression of the experiment, including plasma formation and assembly of the current sheet. While previous results in HED plasmas could infer reconnection through annihilation of the magnetic field [5], this work is the first to observe clear stagnation of the counter-propagating magnetized ribbons and the formation of an extended reconnection layer. T...

Reconnection in nature is generically not quasi-steady. Most often, it is impulsive or bursty, characterized not only by a fast growth rate but a rapid change in the time-derivative of the growth rate. New results, obtained by asymptotic analyses and high-resolution numerical simulations ͓using Adaptive Mesh Refinement͔ of the Hall magnetohydrodynamics ͑MHD͒ or two-fluid equations, are presented. Within the framework of Hall MHD, a two-dimensional collisionless reconnection model is considered in which electron inertia provides the mechanism for breaking field lines, and the electron pressure gradient plays a crucial role in controlling magnetic island dynamics. Current singularities tend to form in finite time and drive fast and impulsive reconnection. In the presence of resistivity, the tendency for current singularity formation slows down, but the reconnection rate continues to accelerate to produce large magnetic islands that eventually become of the order of the system size, quenching near-explosive growth. By a combination of analysis and simulations, the scaling of the reconnection rate in the nonlinear regime is studied, and its dependence on the electron and the ion skin depth, plasma beta, and system size is determined.

Recent experiments have observed magnetic reconnection in high-energy-density, laser-produced plasma bubbles, with reconnection rates observed to be much higher than can be explained by classical theory. Based on fully kinetic particle simulations we find that fast reconnection in these strongly driven systems can be explained by magnetic flux pile-up at the shoulder of the current sheet and subsequent fast reconnection via two-fluid, collisionless mechanisms. In the strong drive regime with two-fluid effects, we find that the ultimate reconnection time is insensitive to the nominal system Alfvén time.Magnetic reconnection [1,2], the change of magnetic topology in the presence of plasma, is observed in space, laboratory, and, most recently, laser-produced high-energy-density (HED) plasmas [3][4][5][6]. Reconnection plays a key role in energy release by plasma instabilities, as in solar flares or magnetospheric substorms, and the change in topology allows the rapid heat transport associated with sawtooth relaxation in magnetic fusion devices [7]. The observation of reconnection in HED plasmas suggests that it may also play a role in inertial confinement fusion, and indeed recent work has now observed the generation of large-scale magnetic fields during inertial fusion implosions [8].We investigate recent experimental observations [3-6] of fast magnetic reconnection between the HED plasma bubbles created by focusing terawatt (TW)-class lasers (∼kJ/ns) down to sub-millimeter-scale spots on a plastic or metal foil. The foil is ionized into hemispherical bubbles that expand supersonically off the surface of the foil. Each bubble is found to self-generate a strong magnetic field of order megagauss (MG), which forms a toroidal ribbon wrapping around the bubble. If multiple bubbles are created at small separation, the bubbles expand into one another, and the opposing magnetic fields are squeezed together and seen to reconnect (Fig. 1). The rates of reconnection are observed to be fast, and unexplained by classical Sweet-Parker theory [3,4]. Reconnection has also been observed between laser-producedplasma bubbles immersed in a background plasma and magnetic field [9], though we focus here on reconnection between HED bubbles driven by kJ-class lasers.It is of great interest to bring these results in line with what is already known about reconnection. As mentioned above, there are a number of new features in these laserdriven experiments, such as the high energy density in the plasma and magnetic field. Perhaps their most notable feature is the very strong reconnection drive: the opposing magnetic fields are driven together by the expanding bubbles at sonic and super-Alfvénic velocities. Such a strongly-driven regime has not been previously accessible in experiments, but may aid understanding of reconnection at the Earth's magnetopause (where the driver of reconnection is the super-Alfvénic solar wind) and other astrophysical contexts with high plasma β (accretion disks, stellar interiors), or with colliding supersonic, ma...

Recent increases in supercomputing power, driven by the multi-core revolution and accelerators such as the IBM Cell processor, graphics processing units (GPUs) and Intel's Many Integrated Core (MIC) technology have enabled kinetic simulations of plasmas at unprecedented resolutions, but changing HPC architectures also come with challenges for writing efficient numerical codes. This paper describes the Plasma Simulation Code (psc), an explicit, electromagnetic particle-in-cell code with support for different order particle shape functions. We focus on two distinguishing features of the code: patch-based load balancing using space-filling curves, and support for Nvidia GPUs, which achieves a substantial speed-up of up to more than 6× on the Cray XK7 architecture compared to a CPU-only implementation.Germaschewski / 00 (2015) 1-28 2 of explicit particle-in-cell methods (see, e.g., [3,4]), explicit particle-in-cell methods scale efficiently to the largest supercomputers available today and are commony used to address challenging science problems.The Plasma Simulation Code (psc) is an explicit, electromagnetic particle-in-cell code implementing similar methods as, e.g., vpic [5], osiris[6] and vorpal [7]. psc is based on H. Ruhl's original version [8], but has been rewritten as modular code that supports flexible algorithms and data structures. Beyond its origin in the field of laser-plasma interaction, psc has been used in studies of laser-induced plasma bubbles [9, 10, 11, 12], particle acceleration [13], and closure aspects in magnetic reconnection [14].In this paper, we will review the main underlying particle-in-cell methods, and then focus on two distinguishing features implemented in psc: Patch-based load balancing and GPU support. Patch-based dynamic load balancing addresses both performance and memory issues in simulations where many particles move between local domains. GPU support enhances performance by more than 6× on the Cray XK7 architecture by making use of the Nvidia K20X GPU. Particle-in-cell method Kinetic description of plasmasThe particle-in-cell method [15,16,4] solves equations of motion for particles and Maxwell's equations to find forces between those particles, which is very similar to the first-principle description of a plasma as a system of charged particles. It is, however, better understood as a numerical method to solve the Vlasov-Maxwell system of equations that describes the time evolution of the particle distribution function f s (x, p, t) where s indicates the species:

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