Optical angular momentum in dispersive media

The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum of $\pm\hbar$ per energy $\hbar\omega$, as in vacuum. This result demonstrates the non-trivial interplay of dispersive contributions to optical angular momentum and energy.Comment: 4 page

Force-free collisionless current sheet models with non-uniform temperature and density profiles

We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner [Phys. Plasmas 20, 102117 (2013)] to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)]. In one limit of the parameters, we recover the model of Kolotkov et al. [Phys. Plasmas 22, 112902 (2015)], while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive and give expressions for the pressure, density, temperature, and bulk-flow velocities of the equilibrium, discussing the differences from previous models. We also present some illustrative plots of the distribution function in velocity space

Collisionless distribution functions for force-free current sheets: using a pressure transformation to lower the plasma beta

So far, only one distribution function giving rise to a collisionless nonlinear force-free current sheet equilibrium allowing for a plasma beta less than one is known (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116; Allanson et al., J. Plasma Phys., vol. 82 (3), 2016a, 905820306). This distribution function can only be expressed as an infinite series of Hermite functions with very slow convergence and this makes its practical use cumbersome. It is the purpose of this paper to present a general method that allows us to find distribution functions consisting of a finite number of terms (therefore easier to use in practice), but which still allow for current sheet equilibria that can, in principle, have an arbitrarily low plasma beta. The method involves using known solutions and transforming them into new solutions using transformations based on taking integer powers (N) of one component of the pressure tensor. The plasma beta of the current sheet corresponding to the transformed distribution functions can then, in principle, have values as low as 1/N. We present the general form of the distribution functions for arbitrary N and then, as a specific example, discuss the case for N=2 in detail

Kinetic models of tangential discontinuities in the solar wind

TN acknowledges financial support by the UK's Science and Technology Facilities Council (STFC) via Consolidated Grant ST/S000402/1. OA was supported by the Natural Environment Research Council (NERC) Highlight Topic Grant #NE/P017274/1 (Rad-Sat).Kinetic-scale current sheets observed in the solar wind are frequently approximately force-free despite the fact that their plasma β is of the order of one. In-situ measurements have recently shown that plasma density and temperature often vary across the current sheets, while the plasma pressure is approximately uniform. In many cases these density and temperature variations are asymmetric with respect to the center of the current sheet. To model these observations theoretically we develop in this paper equilibria of kinetic-scale force-free current sheets that have plasma density and temperature gradients. The models can also be useful for analysis of stability and dissipation of the current sheets in the solar wind.PostprintPeer reviewe

On the Two Approaches to Incorporate Wave‐Particle Resonant Effects Into Global Test Particle Simulations

Energetic electron dynamics in the Earth's radiation belts and near-Earth plasma sheet are controlled by multiple processes operating on very different time scales: from storm-time magnetic field reconfiguration on a timescale of hours to individual resonant wave-particle interactions on a timescale of milliseconds. The most advanced models for such dynamics either include test particle simulations in electromagnetic fields from global magnetospheric models, or those that solve the Fokker-Plank equation for long-term effects of wave-particle resonant interactions. The most prospective method, however, would be to combine these two classes of models, to allow the inclusion of resonant electron scattering into simulations of electron motion in global magnetospheric fields. However, there are still significant outstanding challenges that remain regarding how to incorporate the long term effects of wave-particle interactions in test-particle simulations. In this paper, we describe in details two approaches that incorporate electron scattering in test particle simulations: stochastic differential equation (SDE) approach and the mapping technique. Both approaches assume that wave-particle interactions can be described as a probabilistic process that changes electron energy, pitch-angle, and thus modifies the test particle dynamics. To compare these approaches, we model electron resonant interactions with field-aligned whistler-mode waves in dipole magnetic fields. This comparison shows advantages of the mapping technique in simulating the nonlinear resonant effects, but also underlines that more significant computational resources are needed for this technique in comparison with the SDE approach. We further discuss applications of both approaches in improving existing models of energetic electron dynamics

From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov–Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans’ theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of the use of this method with both force-free and non-force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the force-free Harris sheet (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for beta=0.05

An exact collisionless equilibrium for the force-free Harris sheet with low plasma beta

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution

Collisionless current sheet equilibria

Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions