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A heat flux in a high-
plasma with low collisionality triggers the whistler instability. Quasilinear theory predicts saturation of the instability in a marginal state characterized by a heat flux that is fully controlled by electron scattering off magnetic perturbations. This marginal heat flux does not depend on the temperature gradient and scales as
. We confirm this theoretical prediction by performing numerical particle-in-cell simulations of the instability. We further calculate the saturation level of magnetic perturbations and the electron scattering rate as functions of
and the temperature gradient to identify the saturation mechanism as quasilinear. Suppression of the heat flux is caused by oblique whistlers with magnetic-energy density distributed over a wide range of propagation angles. This result can be applied to high-
astrophysical plasmas, such as the intracluster medium, where thermal conduction at sharp temperature gradients along magnetic-field lines can be significantly suppressed. We provide a convenient expression for the amount of suppression of the heat flux relative to the classical Spitzer value as a function of the temperature gradient and
. For a turbulent plasma, the additional independent suppression by the mirror instability is capable of producing large total suppression factors (several tens in galaxy clusters) in regions with strong temperature gradients.
We have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We find that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can eventually trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value
is the seed charge density and
is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than
, thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies.
The Wisconsin Plasma Astrophysics Laboratory (WiPAL) is a flexible user facility designed to study a range of astrophysically relevant plasma processes as well as novel geometries that mimic astrophysical systems. A multi-cusp magnetic bucket constructed from strong samarium cobalt permanent magnets now confines a
, fully ionized, magnetic-field-free plasma in a spherical geometry. Plasma parameters of
provide an ideal testbed for a range of astrophysical experiments, including self-exciting dynamos, collisionless magnetic reconnection, jet stability, stellar winds and more. This article describes the capabilities of WiPAL, along with several experiments, in both operating and planning stages, that illustrate the range of possibilities for future users.
Current models of pulsar magnetospheres typically assume either a complete absence of plasma or abundant ideal plasma filling the magnetosphere in order to compute the field structure. The latter condition is thought to be closer to reality, but we know of a number of pulsars in which the ideal conditions break down, resulting in dissipation and high-energy emission. In this work we formulate a resistive force-free scheme that allows us to consider the effects of resistive plasma and accelerating fields on the magnetospheric structure. We run numerical simulations to construct a family of resistive solutions that smoothly bridges the gap between the vacuum and the force-free magnetosphere solutions. We further provide a self-consistent model for the spin-down of intermittent pulsars, pulsars which appear to transition between radio-loud and radio-quiet states with different spin-down rates. Finally, we present models for high-energy emission from reconnecting current sheets in Gamma-ray pulsars.
The inner workings of pulsar magnetospheres have fascinated and confused researchers since the discovery of pulsars. I will review the status of magnetospheric models, including vacuum, space-charge-limited and resistive force-free MHD. I will highlight model predictions for the integrated pulsar quantities (such as spin down and torques) and the observational consequences of calculated magnetic field structure. Particularly, high-energy emission from pulsars allows putting new constraints on the geometry of the emission region and the physics of particle acceleration in the magnetosphere.
Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ≪1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron–ion shock front. This potential is responsible for electron energization.
Plasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vector-potential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instability.
I review the theoretical understanding of the global structure of pulsar magnetospheres concentrating on recent progress in force-free electrodynamics and first-principles simulations of magnetospheres.
We present results of time-dependent numerical modeling of the internal structure of the collisionless shock terminating the pulsar wind in Crab Nebula. We treat the equatorial relativistic wind as composed of ions and electron-positron plasma with an embedded toroidal magnetic field. Relativistic cyclotron instability of the ion ring downstream from the shock is found to launch outward propagating magnetosonic waves. Due to the fresh supply of ions crossing the shock, the time-dependent process achieves a limit-cycle pattern, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in magnetic field and pair density associated with these waves as well as their propagation speed qualitatively reproduce the features observed in the wisps.
We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.
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