Explosive phenomena such as supernova remnant shocks and solar flares have demonstrated evidence for the production of relativistic particles. Interest has therefore been renewed in collisionless shock waves and magnetic reconnection as a means to achieve such energies. Although ions can be energized during such phenomena, the relativistic energy of the electrons remains a puzzle for theory. We present supercomputer simulations showing that efficient electron energization can occur during turbulent magnetic reconnection arising from a strong collisionless shock. Upstream electrons undergo first-order Fermi acceleration by colliding with reconnection jets and magnetic islands, giving rise to a nonthermal relativistic population downstream. These results shed new light on magnetic reconnection as an agent of energy dissipation and particle acceleration in strong shock waves.

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How electrons get accelerated to relativistic energies in a high-Mach-number quasi-perpendicular shock is presented by means of ab initio particle-in-cell simulations in three dimensions. We found that coherent electrostatic Buneman waves and ion-Weibel magnetic turbulence coexist in a strongshock structure whereby particles gain energy during shock-surfing and subsequent stochastic drift accelerations. Energetic electrons that initially experienced the surfing acceleration undergo pitchangle diffusion by interacting with magnetic turbulence and continuous acceleration during confinement in the shock transition region. The ion-Weibel turbulence is the key to the efficient nonthermal electron acceleration.PACS numbers: 52.35. Tc, 52.65.Rr, 96.50.Pw, 98.70.Sa Elucidating the acceleration mechanisms of charged particles have been of great interests in laboratory, space, and astrophysical plasma physics. Among other mechanisms, a collisionless shock is thought to be an efficient particle accelerator. This idea has been strengthened by radio, X-ray, and gamma-ray observations of astrophysical objects such as supernova remnant shocks, indicating that protons and electrons are efficiently accelerated to TeV energies at such very strong shock waves [1][2][3][4]. Efficient electron acceleration at high-Mach-number shocks was also recently suggested by in-situ measurements at Saturn's bow shock [5]. Motivated by these circumstances, laboratory experiments using high-power laser facilities have emerged to provide a new platform for tackling such problems [6][7][8][9][10][11].The diffusive shock acceleration (DSA) theory [12, 13] has provided a solution to observational evidences for efficient accelerations at collisionless shocks, as it predicts a power-law energy spectrum of particles having a spectral index that is close to the values suggested by multiwavelength observations. As the DSA theory presumes pre-existing mildly energetic particles, pre-acceleration mechanisms are required to provide a seed population for DSA, particularly for electrons [14,15]. The connection between pre-acceleration and DSA remains a critical issue in shock acceleration theory.One possible pre-acceleration mechanism is the socalled shock drift acceleration (SDA), in which a particle gains energy in the shock transition region during its gradient-|B| drift. For an electron with a Larmor radius much smaller than the shock thickness, the interaction time with the shock (and hence the energy gain) is * ymatumot@chiba-u.jp † Also at Institute for Global Prominent Research, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan determined by the adiabatic theory [16][17][18]. Subsequent acceleration can be realized by self-generated electromagnetic waves excited by accelerated electrons [19][20][21][22][23]. Alternatively, the shock surfing acceleration (SSA) becomes particularly important for electrons in highMach-number perpendicular shocks [24][25][26][27]. This process uses large-amplitude electrostatic waves generated by the Bun...

A two-dimensional electromagnetic particle-in-cell simulation with the realistic ion-to-electron mass ratio of 1836 is carried out to investigate the electrostatic collisionless shocks in relatively high-speed ͑ϳ3000 km s −1 ͒ plasma flows and also the influence of both electrostatic and electromagnetic instabilities, which can develop around the shocks, on the shock dynamics. It is shown that the electrostatic ion-ion instability can develop in front of the shocks, where the plasma is under counterstreaming condition, with highly oblique wave vectors as was shown previously. The electrostatic potential generated by the electrostatic ion-ion instability propagating obliquely to the shock surface becomes comparable with the shock potential and finally the shock structure is destroyed. It is also shown that in front of the shock the beam-Weibel instability gradually grows as well, consequently suggesting that the magnetic field generated by the beam-Weibel instability becomes important in long-term evolution of the shock and the Weibel-mediated shock forms long after the electrostatic shock vanished. It is also observed that the secondary electrostatic shock forms in the reflected ions in front of the primary electrostatic shock.

The saturation mechanism of the Weibel instability is investigated theoretically by considering the evolution of currents in numerous cylindrical beams that are generated in the initial stage of the instability. Based on a physical model of the beams, it is shown that the magnetic field strength attains a maximum value when the currents in the beams evolve into the Alfvén current and that there exist two saturation regimes. The theoretical prediction of the magnetic field strength at saturation is in good agreement with the results of two-dimensional particle-in-cell simulations for a wide range of initial anisotropy. * Electronic address: katoutn@cc.nao.ac.jp

We show that the Weibel-mediated collisionless shocks are driven at non-relativistic propagation speed (0.1c < V < 0.45c) in unmagnetized electron-ion plasmas by performing two-dimensional particle-in-cell simulations. It is shown that the profiles of the number density and the mean velocity in the vicinity of the shock transition region, which are normalized by the respective upstream values, are almost independent of the upstream bulk velocity, i.e., the shock velocity. In particular, the width of the shock transition region is ∼ 100 ion inertial length independent of the shock velocity. For these shocks the energy density of the magnetic field generated by the Weibel-type instability within the shock transition region reaches typically 1-2% of the upstream bulk kinetic energy density. This mechanism probably explains the robust formation of collisionless shocks, for example, driven by young supernova remnants, with no assumption of external magnetic field in the universe.

A two-dimensional particle-in-cell simulation is performed to investigate weakly magnetized perpendicular shocks with a magnetization parameter of σ = 6 × 10 −5 , which is equivalent to a high Alfvén Mach number M A of ∼ 130. It is shown that current filaments form in the foot region of the shock due to the ion-beam-Weibel instability (or the ion filamentation instability) and that they generate a strong magnetic field there. In the downstream region, these current filaments also generate a tangled magnetic field that is typically 15 times stronger than the upstream magnetic field. The thermal energies of electrons and ions in the downstream region are not in equipartition and their temperature ratio is T e /T i ∼ 0.3 − 0.4. Efficient electron acceleration was not observed in our simulation, although a fraction of the ions are accelerated slightly on reflection at the shock. The simulation results agree very well with the Rankine-Hugoniot relations. It is also shown that electrons and ions are heated in the foot region by the Buneman instability (for electrons) and the ion-acoustic instability (for both electrons and ions). However, the growth rate of the Buneman instability is significantly reduced due to the relatively high temperature of the reflected ions. For the same reason, ion-ion streaming instability does not grow in the foot region.

The experimental demonstration of the formation of a strong electrostatic (ES) collisionless shock has been carried out with high-speed counterstreaming plasmas, produced by a high-power laser irradiation, without external magnetic field. The nearly four times density jump observed in the experiment shows a high Mach-number shock. This large density jump is attributed to the compression of the downstream plasma by momentum transfer by ion reflection of the upstream plasma. Particle-in-cell (PIC) simulation shows the production of a collisionless high Mach-number ES shock with counterstreaming interaction of two plasma slabs with different temperatures and densities, as pointed out by Sorasio et al. [Phys. Rev. Lett. 96, 045005 (2006)]. It is speculated that the shock discontinuity is balanced with the momentum of incoming and reflected ions and the predominant pressure of the electrons in the downstream with PIC simulation.