Kristopher G. Klein

Predicted impacts of proton temperature anisotropy on solar wind turbulence

Particle velocity distributions measured in the weakly collisional solar wind are frequently found to be non-Maxwellian, but how these non-Maxwellian distributions impact the physics of plasma turbulence in the solar wind remains unanswered. Using numerical solutions of the linear dispersion relation for a collisionless plasma with a bi-Maxwellian proton velocity distribution, we present a unified framework for the four proton temperature anisotropy instabilities, identifying the associated stable eigenmodes, highlighting the unstable region of wavevector space, and presenting the properties of the growing eigenfunctions. Based on physical intuition gained from this framework, we address how the proton temperature anisotropy impacts the nonlinear dynamics of the \Alfvenic fluctuations underlying the dominant cascade of energy from large to small scales and how the fluctuations driven by proton temperature anisotropy instabilities interact nonlinearly with each other and with the fluctuations of the large-scale cascade. We find that the nonlinear dynamics of the large-scale cascade is insensitive to the proton temperature anisotropy, and that the instability-driven fluctuations are unlikely to cause significant nonlinear evolution of either the instability-driven fluctuations or the turbulent fluctuations of the large-scale cascade.

ENERGY DISSIPATION AND LANDAU DAMPING IN TWO- AND THREE-DIMENSIONAL PLASMA TURBULENCE

Plasma turbulence is ubiquitous in space and astrophysical plasmas, playing an important role in plasma energization, but the physical mechanisms leading to dissipation of the turbulent energy remain to be definitively identified. Kinetic simulations in two dimensions (2D) have been extensively used to study the dissipation process. How the limitation to 2D affects energy dissipation remains unclear. This work provides a model of comparison between two- and three-dimensional (3D) plasma turbulence using gyrokinetic simulations; it also explores the dynamics of distribution functions during the dissipation process. It is found that both 2D and 3D nonlinear gyrokinetic simulations of a low-beta plasma generate electron velocity-space structures with the same characteristics as that of linear Landau damping of Alfven waves in a 3D linear simulation. The continual occurrence of the velocity-space structures throughout the turbulence simulations suggests that the action of Landau damping may be responsible for the turbulent energy transfer to electrons in both 2D and 3D, and makes possible the subsequent irreversible heating of the plasma through collisional smoothing of the velocity-space fluctuations. Although, in the 2D case where variation along the equilibrium magnetic field is absent, it may be expected that Landau damping is not possible, a common trigonometric factor appears in the 2D resonant denominator, leaving the resonance condition unchanged from the 3D case. The evolution of the 2D and 3D cases is qualitatively similar. However, quantitatively the nonlinear energy cascade and subsequent dissipation is significantly slower in the 2D case.

MEASURING COLLISIONLESS DAMPING IN HELIOSPHERIC PLASMAS USING FIELD–PARTICLE CORRELATIONS

An innovative field-particle correlation technique is proposed that uses single-point measurements of the electromagnetic fields and particle velocity distribution functions to investigate the net transfer of energy from fields to particles associated with the collisionless damping of turbulent fluctuations in weakly collisional plasmas, such as the solar wind. In addition to providing a direct estimate of the local rate of energy transfer between fields and particles, it provides vital new information about the distribution of that energy transfer in velocity space. This velocity-space signature can potentially be used to identify the dominant collisionless mechanism responsible for the damping of turbulent fluctuations in the solar wind. The application of this novel field-particle correlation technique is illustrated using the simplified case of the Landau damping of Langmuir waves in an electrostatic 1D-1V Vlasov-Poisson plasma, showing that the procedure both estimates the local rate of energy transfer from the electrostatic field to the electrons and indicates the resonant nature of this interaction. Modifications of the technique to enable single-point spacecraft measurements of fields and particles to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, yielding a method with the potential to transform our ability to maximize the scientific return from current and upcoming spacecraft missions, such as the Magnetospheric Multiscale (MMS) and Solar Probe Plus missions.

Kinetic scale density fluctuations in the solar wind

We motivate the importance of studying kinetic scale turbulence for understanding the macroscopic properties of the heliosphere, such as the heating of the solar wind. We then discuss the technique by which kinetic scale density fluctuations can be measured using the spacecraft potential, including a calculation of the timescale for the spacecraft potential to react to the density changes. Finally, we compare the shape of the density spectrum at ion scales to theoretical predictions based on a cascade model for kinetic turbulence. We conclude that the shape of the spectrum, including the ion scale flattening, can be captured by the sum of passive density fluctuations at large scales and kinetic Alfven wave turbulence at small scales.

Diagnosing collisionless energy transfer using field–particle correlations: gyrokinetic turbulence

Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behavior of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measurements produce a velocity-dependent signature of the collisionless damping mechanism. We extend this work by constructing field-particle correlations using data sets drawn from single points in strongly driven, turbulent, electromagnetic gyrokinetic simulations to demonstrate that this technique can identify the collisionless mechanisms operating in such systems. The correlations velocity-space structure agrees with expectations of resonant mechanisms transferring energy collisionlessly in turbulent systems. This work motivates the eventual application of field-particle correlations to spacecraft measurements in the solar wind, with the ultimate goal to determine the physical mechanisms that dissipate magnetized plasma turbulence.

Characterizing fluid and kinetic instabilities using field-particle correlations on single-point time series

A recently proposed technique correlating electric fields and particle velocity distributions is applied to single-point time series extracted from linearly unstable, electrostatic numerical simulations. The form of the correlation, which measures the transfer of phase-space energy density between the electric field and plasma distributions and that had previously been applied to damped electrostatic systems, is modified to include the effects of drifting equilibrium distributions of the type that drive counter-streaming and bump-on-tail instabilities. By using single-point time series, the correlation is ideal for diagnosing dynamics in systems where access to integrated quantities, such as energy, is observationally infeasible. The velocity-space structure of the field-particle correlation is shown to characterize the underlying physical mechanisms driving unstable systems. The use of this correlation in simple systems will assist in its eventual application to turbulent, magnetized plasmas, with the ul...

Applying Nyquist's method for stability determination to solar wind observations

The role instabilities play in governing the evolution of solar and astrophysical plasmas is a matter of considerable scientific interest. The large number of sources of free energy accessible to such nearly-collisionless plasmas makes general modeling of unstable behavior, accounting for the temperatures, densities, anisotropies, and relative drifts of a large number of populations, analytically difficult. We therefore seek a general method of stability determination that may be automated for future analysis of solar wind observations. This work describes an efficient application of the Nyquist instability method to the Vlasov dispersion relation appropriate for hot, collisionless, magnetized plasmas, including the solar wind. The algorithm recovers the familiar proton temperature anisotropy instabilities, as well as instabilities that had been previously identified using fits extracted from in situ observations in Gary et al. [2016]. Future proposed applications of this method are discussed.

Astrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond

We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. Turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it, and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (2015). At scales at and below the ion Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalisation of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a general free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy can cause large variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects the turbulent fluctuation spectra, the differential heating of particle species, and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.

The Statistical Properties of Solar Wind Temperature Parameters Near 1 au

We present a long-duration (

Large-scale Control of Kinetic Dissipation in the Solar Wind

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