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Register a new userEnergy Spectrum of the Electrons Accelerated by a Reconnection Electric Field: Exponential or Power Law?
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The direct current (DC) electric field near the reconnection region has been proposed as an effective mechanism to accelerate protons and electrons in solar flares. A power-law energy spectrum was generally claimed in the simulations of electron acceleration by the reconnection electric field. However in most of the literature, the electric and magnetic fields were chosen independently. In this paper, we perform test-particle simulations of electron acceleration in a reconnecting magnetic field, where both the electric and magnetic fields are adopted from numerical simulations of the MHD equations. It is found that the accelerated electrons present a truncated power-law energy spectrum with an exponential tail at high energies, which is analogous to the case of diffusive shock acceleration. The influences of reconnection parameters on the spectral feature are also investigated, such as the longitudinal and transverse components of the magnetic field and the size of the current sheet. It is suggested that the DC electric field alone might not be able to reproduce the observed single or double power-law distributions.
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Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy ($E_c$). The growth rate of LWs increases with the steepness index ($delta$) and decreases with the power-law index ($alpha$). The wave number of the fastest growing LWs ($klambda_D$), decreases with the characteristic velocity of the power-law electrons ($v_{c}=sqrt{2E_{c}/m_{e}}$) and increases with the thermal velocity of ambient electrons ($v_T$). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.
Relativistic shocks propagating into a medium with low magnetization are generated and sustained by small-scale but very strong magnetic field turbulence. This so-called microturbulence modifies the typical shock acceleration process, and in particular that of electrons. In this work we perform Monte Carlo (MC) simulations of electrons encountering shocks with microturbulent fields. The simulations cover a three-dimensional parameter space in shock speed, acceleration efficiency, and peak magnetic field strength. From these, a Markov Chain Monte Carlo (MCMC) method was employed to estimate the maximum electron momentum from the MC-simulated electron spectra. Having estimated this quantity at many points well-distributed over an astrophysically relevant parameter space, an MCMC method was again used to estimate the parameters of an empirical formula that computes the maximum momentum of a Fermi-accelerated electron population anywhere in this parameter space. The maximum energy is well-approximated as a broken power-law in shock speed, with the break occurring when the shock decelerates to the point where electrons can begin to escape upstream from the shock.
The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time $t = t_b$ has an asymptotic decay of $k^{-4/3}$, with corresponding energy spectrum decaying as $k^{-8/3}$. This spectrum is formed by the singularity of the form $(x-x_b)^{1/3}$ in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.
We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.
We report on computer simulations and analytic theory to provide a self-consistent understanding of the role of the reconnection electric field, which extends substantially beyond the simple change of magnetic connections. Rather, we find that the reconnection electric field is essential to maintaining the current density in the diffusion region, which would otherwise be dissipated by a set of processes. Natural candidates for current dissipation are the average convection of current carriers away from the reconnection region by the outflow of accelerated particles, or the average rotation of the current density by the magnetic field reversal in the vicinity. Instead, we show here that the current dissipation is the result of thermal effects, underlying the statistical interaction of current-carrying particles with the adjacent magnetic field. We find that this interaction serves to redirect the directed acceleration of the reconnection electric field to thermal motion. This thermalization manifests itself in form of quasi-viscous terms in the thermal energy balance of the current layer. These quasi-viscous terms act to increase the average thermal energy. Our predictions regarding current and thermal energy balance are readily amenable to exploration in the laboratory or by satellite missions, in particular, by NASAs Magnetospheric Multiscale mission.
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