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.

Electron accelerations at high Mach number collision-less shocks are investigated by means of two-dimensional electromagnetic Particle-in-Cell simulations with various Alfvén Mach numbers, ion-to-electron mass ratios, and the upstream electron β e (the ratio of the thermal pressure to the magnetic pressure). We found electrons are effectively accelerated at a super-high Mach number shock (M A ∼ 30) with a mass ratio of M/m = 100 and β e = 0.5. The electron shock surfing acceleration is an effective mechanism for accelerating the particles toward the relativistic regime even in two dimensions with the large mass ratio.Buneman instability excited at the leading edge of the foot in the super-high Mach number shock results in a coherent electrostatic potential structure. While multi-dimensionality allows the electrons to escape from the trapping region, they can interact with the strong electrostatic field several times. Simulation runs in various parameter regimes indicate that the electron shock surfing acceleration is an effective mechanism for producing relativistic particles in extremely-high Mach number shocks in supernova remnants, provided that the upstream electron temperature is reasonably low.

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...

We investigated the efficiency of coherent upstream large-amplitude electromagnetic wave emission via synchrotron maser instability at relativistic magnetized shocks by using two-dimensional particle-in-cell simulations. We considered the purely perpendicular shock in an electron-positron plasma. The coherent wave emission efficiency was measured as a function of the magnetization parameter σ, which is defined by the ratio of the Poynting flux to the kinetic energy flux. The wave amplitude was systematically smaller than that observed in one-dimensional simulations. However, it continued to persist, even at a considerably low magnetization rate, where the Weibel instability dominated the shock transition. The emitted electromagnetic waves were sufficiently strong to disturb the upstream medium, and transverse filamentary density structures of substantial amplitude were produced. Based on this result, we discuss the possibility of the wakefield acceleration model for the production of non-thermal electrons in a relativistic magnetized ion-electron shock.

Electron acceleration mechanism at high Mach number collisionless shocks propagating in a weakly magnetized medium is investigated by a self-consistent two-dimensional particle-in-cell simulation. Simulation results show that strong electrostatic waves are excited via the electron-ion electrostatic two-stream instability at the leading edge of the shock transition region as in the case of earlier one-dimensional simulations. We observe strong electron acceleration that is associated with the turbulent electrostatic waves in the shock transition region. The electron energy spectrum in the shock transition region exhibits a clear powerlaw distribution with spectral index of 2.0−2.5. By analyzing the trajectories of accelerated electrons, we find that the acceleration mechanism is very similar to shock surfing acceleration of ions. In contrast to the ion shock surfing, however, the energetic electrons are reflected by electron-scale electrostatic fluctuations in the shock transition region, but not by the ion-scale cross-shock electrostatic potential. The reflected electrons are then accelerated by the convective electric field in front of the shock. We conclude that the multidimensional effects as well as the self-consistent shock structure are essential for the strong electron acceleration at high Mach number shocks.

The process of electron injection at high Mach number, collisionless, quasi-perpendicular shock waves is investigated by means of one-dimensional electromagnetic particle-in-cell simulations. We find that energetic electrons are generated in two steps: (1) electrons are accelerated nearly perpendicular to the local magnetic field by shock surfing acceleration at the leading edge of the shock transition region, and (2) these preaccelerated electrons are further accelerated by shock drift acceleration. As a result, energetic electrons are preferentially reflected back upstream. Shock surfing acceleration provides sufficient energy for the reflection. Therefore, it is important not only for the energization process itself, but also for triggering the secondary acceleration. We also present a theoretical model of the twostep acceleration mechanism, based on the simulation results, that can predict the injection efficiency for a subsequent diffusive shock acceleration process. We show that the injection efficiency obtained in the present model agrees well with the value obtained from Chandra X-ray observations of SN 1006. At typical supernova remnant shocks, energetic electrons injected by this mechanism can self-generate upstream Alfvén waves, which scatter the energetic electrons themselves.

The first-order Fermi acceleration of electrons requires an injection of electrons into a mildly relativistic energy range. However, the mechanism of injection has remained a puzzle both in theory and observation. We present direct evidence for a novel stochastic shock drift acceleration theory for the injection obtained with Magnetospheric Multiscale (MMS) observations at Earth's bow shock. The theoretical model can explain electron acceleration to mildly relativistic energies at high-speed astrophysical shocks, which may provide a solution to the long-standing issue of electron injection.

We propose a novel electron acceleration mechanism, which we call stochastic shock drift acceleration (SSDA), that extends the standard shock drift acceleration (SDA) for low-energy electrons at a quasiperpendicular shock to include the effect of stochastic pitch-angle scattering. We demonstrate that the steady-state energy spectrum of electrons accelerated within the shock transition region becomes a power-law in the limit of strong scattering. The spectral index is independent of the pitch-angle scattering coefficient. On the other hand, the maximum energy attainable through the mechanism scales linearly with the pitch-angle scattering coefficient. These results have been confirmed by Monte-Carlo simulations that include finite pitch-angle anisotropy. We find that the theory can reasonably well explain in-situ observations of quasi-perpendicular Earth's bow shock. Theoretical scaling law suggests that the maximum energy increases in proportion to the square of the shock speed, indicating that the thermal electrons may be accelerated up to mildly relativistic energies by the SSDA at quasiperpendicular supernova remnant shocks. Therefore, the mechanism provides a plausible solution to the long-standing electron injection problem.