Effect of a weak ion collisionality on the dynamics of kinetic electrostatic shocks

In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.Comment: Published in J. Plasma Phy

Electron Energization in Reconnection: Eulerian versus Lagrangian Perspectives

Particle energization due to magnetic reconnection is an important unsolved problem for myriad space and astrophysical plasmas. Electron energization in magnetic reconnection has traditionally been examined from a particle, or Lagrangian, perspective using particle-in-cell (PIC) simulations. Guiding-center analyses of ensembles of PIC particles have suggested that Fermi (curvature drift) acceleration and direct acceleration via the reconnection electric field are the primary electron energization mechanisms. However, both PIC guiding-center ensemble analyses and spacecraft observations are performed in an Eulerian frame. For this work, we employ the continuum Vlasov-Maxwell solver within the Gkeyll simulation framework to re-examine electron energization from a kinetic continuum, Eulerian, perspective. We separately examine the contribution of each drift energization component to determine the dominant electron energization mechanisms in a moderate guide-field Gkeyll reconnection simulation. In the Eulerian perspective, we find that the diamagnetic and agyrotropic drifts are the primary electron energization mechanisms away from the reconnection x-point, where direct acceleration dominates. We compare the Eulerian (Vlasov Gkeyll) results with the wisdom gained from Lagrangian (PIC) analyses.Comment: 10 pages, 7 figure

Reduced convergence and the local smoothness parameter: bridging two different descriptions of weak lensing amplification

Weak gravitational lensing due to the inhomogeneous matter distribution in the universe is an important systematic uncertainty in the use of standard candles in cosmology. There are two different descriptions of weak lensing amplification, one uses a local smoothness parameter $\tilde{\alpha}$, the other uses reduced convergence $\eta= 1+ \kappa/|\kappa_{min}|$ (where $\kappa$ is convergence). The $\tilde{\alpha}$ description involves Dyer-Roeder distance $D_A(\tilde{\alpha}|z)$ ($\tilde{\alpha}=1$ corresponds to a smooth universe); it is simple and convenient, and has been used by the community to illustrate the effect of weak lensing on point sources such as type Ia supernovae. Wang (1999) has shown that the $\tilde{\alpha}$ description can be made realistic by allowing $\tilde{\alpha}$ to be a local variable, the local smoothness parameter. The $\eta$ description has been used by Wang, Holz, & Munshi (2002) to derive a universal probability distribution (UPDF) for weak lensing amplification. In this paper, we bridge the two different descriptions of weak lensing amplification by relating the reduced convergence $\eta$ and the local smoothness parameter $\tilde{\alpha}$. We give the variance of $\tilde{\alpha}$ in terms of the matter power spectrum, thus providing a quantitative guidance to the use of Dyer-Roeder distances in illustrating the effect of weak lensing. The by-products of this work include a corrected definition of the reduced convergence, and simple and accurate analytical expressions for $D_A(\tilde{\alpha}|z)$. Our results should be very useful in studying the weak lensing of standard candles.Comment: Revised and expanded version. ApJ accepte

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

The existence and properties of low Mach-number ($M \gtrsim 1$) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model, we study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.Comment: In Plasma Physics and Controlled Fusio

Collisionless energy transfer in kinetic turbulence: field-particle correlations in Fourier space

Turbulence is ubiquitously observed in nearly collisionless heliospheric plasmas, including the solar wind and corona and the Earth's magnetosphere. Understanding the collisionless mechanisms responsible for the energy transfer from the turbulent fluctuations to the particles is a frontier in kinetic turbulence research. Collisionless energy transfer from the turbulence to the particles can take place reversibly, resulting in non-thermal energy in the particle velocity distribution functions (VDFs) before eventual collisional thermalization is realized. Exploiting the information contained in the fluctuations in the VDFs is valuable. Here we apply a recently developed method based on VDFs, the field-particle correlation technique, to a $\beta=1$, solar-wind-like, low-frequency Alfv\'enic turbulence simulation with well resolved phase space to identify the field-particle energy transfer in velocity space. The field-particle correlations reveal that the energy transfer, mediated by the parallel electric field, results in significant structuring of the ion and electron VDFs in the direction parallel to the magnetic field. Fourier modes representing the length scales between the ion and electron gyroradii show that energy transfer is resonant in nature, localized in velocity space to the Landau resonances for each Fourier mode. The energy transfer closely follows the Landau resonant velocities with varying perpendicular wavenumber $k_\perp$ and plasma $\beta$. This resonant signature, consistent with Landau damping, is observed in all diagnosed Fourier modes that cover the dissipation range of the simulation.Comment: 31 pages, accepted by JPP, minor improvements compared to v