Cosmic-ray propagation in simulations of cross-helical plasma turbulence

Turbulence is a ubiquitous phenomenon in astrophysical plasmas. Most of these systems exhibit a property called cross helicity, a non-zero correlation between velocity fluctuations and magnetic-field fluctuations. In the presence of a magnetic mean-field, such as in the solar wind or in the interstellar medium, cross helicity is equivalent to an imbalance between Alfven waves co- and counter-propagating with respect to the mean-field direction. Although this imbalance can have a dramatic influence on the heating and scattering rate of charged particles which propagate through the plasma, it is often neglected in computational studies of turbulent particle transport. In an effort to remedy this situation, we present numerical simulations of magnetohydrodynamic turbulence in which we can control the energy and the cross helicity of the system, without injecting kinetic or magnetic helicity as an unwanted side effect. Varying the strength of a magnetic guide-field allows us to determine the degree of anisotropy that the system assumes as a steady-state configuration. Detailed analysis proves that these simulations conform to theoretical models of realistic turbulence. The diffusion of cosmic-ray particles in turbulent plasmas is often calculated using quasilinear theory and a simplified description of the electromagnetic-field spectra. By computing the trajectories of test-particles in dynamically evolving turbulence simulations with non-zero cross helicity, we study whether such quasilinear predictions of the heating rate of charged particles are valid under realistic conditions. Theory and numerical results agree well for particles propagating at the Alfven velocity, unless resistive effects play a dominant role. Furthermore, strongly anisotropic field configurations are used to compare quasilinear pitch-angle diffusion coefficients with measurements of test-particle scattering after one gyroperiod. In particular, we focus on the scaling of the scattering rate with cross helicity. We observe excellent agreement in simulations of both balanced and imbalanced turbulence and explain the role of the magnetic moment, an approximate invariant of charged-particle motion, for pitch-angle scattering on timescales of several gyroperiods.Turbulenz ist in astrophysikalischen Plasmen allgegenwärtig. Viele solche Systeme weisen eine sogenannte Kreuz-Helizität auf, also eine von Null verschiedene Korrelation zwischen Geschwindigkeits- und Magnetfeld-Fluktuationen. In einer anisotropen Magnetfeldgeometrie, z. B. im Sonnenwind oder dem interstellaren Medium, deutet die Kreuz-Helizität auf ein Ungleichgewicht zwischen Alfven-Wellen, die sich in Richtung des gemittelten Feldes ausbreiten, und solchen, die in die Gegenrichtung propagieren, hin. Obwohl dieses Ungleichgewicht die stochastische Beschleunigung und Streuung, die geladene Teilchen in einem Plasma erfahren, dramatisch beeinflusst, wurde es in bisherigen numerischen Studien über turbulenten Teilchentransport gemeinhin außer Acht gelassen. In dieser Arbeit nun werden rechnergestützte Simulationen von magnetohydrodynamischer Turbulenz präsentiert, in denen die Energie und die Kreuz-Helizität kontrolliert werden können, ohne jedoch kinetische oder magnetische Helizität als unerwünschte Nebenwirkung zu erzeugen. Die Stärke des mittleren Magnetfeldes bestimmt dabei die Anisotropie des Gleichgewichtszustandes. Die Simulationen erfüllen in allen Parameterbereichen die Vorhersagen, die theoretische Modelle für realistische Plasmaturbulenz treffen. Die Diffusion kosmischer Strahlung in turbulenten Plasmen wird häufig im Rahmen der quasilinearen Theorie unter Heranziehung eines stark vereinfachten Turbulenzspektrums berechnet. Indem die Trajektorien von Testteilchen in dynamischen Turbulenzsimulationen mit Kreuz-Helizität berechnet werden, lassen sich quasilineare Ergebnisse für die Beschleunigungsrate geladener Teilchen nachprüfen. Theorie und numerische Simulation stimmen für Teilchen mit der Alfven-Geschwindigkeit gut überein, solange resistive Effekte vernachlässigt werden können. Weiterhin werden aus der quasilinearen Theorie berechnete Diffusionskoeffizienten mit numerisch ermittelten Streuraten für Testteilchen nach einer Gyroperiode in stark anisotropen Feldkonfigurationen verglichen, wobei der Schwerpunkt erneut beim Einfluss der Kreuz-Helizität liegt. Für alle verwendeten Werte der Kreuz-Helizität ergibt sich eine exzellente Übereinstimmung zwischen Simulationsergebnis und Vorhersage. Schließlich wird die Rolle des magnetischen Moments, einer adiabatischen Invarianten bei der Bewegung geladener Teilchen in einem Magnetfeld, für die Streuung über Zeitskalen von mehreren Gyroperioden erläutert

Cosmic-ray propagation in simulations of cross-helical plasma turbulence

Turbulence is a ubiquitous phenomenon in astrophysical plasmas. Most of these systems exhibit a property called cross helicity, a non-zero correlation between velocity fluctuations and magnetic-field fluctuations. In the presence of a magnetic mean-field, such as in the solar wind or in the interstellar medium, cross helicity is equivalent to an imbalance between Alfven waves co- and counter-propagating with respect to the mean-field direction. Although this imbalance can have a dramatic influence on the heating and scattering rate of charged particles which propagate through the plasma, it is often neglected in computational studies of turbulent particle transport. In an effort to remedy this situation, we present numerical simulations of magnetohydrodynamic turbulence in which we can control the energy and the cross helicity of the system, without injecting kinetic or magnetic helicity as an unwanted side effect. Varying the strength of a magnetic guide-field allows us to determine the degree of anisotropy that the system assumes as a steady-state configuration. Detailed analysis proves that these simulations conform to theoretical models of realistic turbulence. The diffusion of cosmic-ray particles in turbulent plasmas is often calculated using quasilinear theory and a simplified description of the electromagnetic-field spectra. By computing the trajectories of test-particles in dynamically evolving turbulence simulations with non-zero cross helicity, we study whether such quasilinear predictions of the heating rate of charged particles are valid under realistic conditions. Theory and numerical results agree well for particles propagating at the Alfven velocity, unless resistive effects play a dominant role. Furthermore, strongly anisotropic field configurations are used to compare quasilinear pitch-angle diffusion coefficients with measurements of test-particle scattering after one gyroperiod. In particular, we focus on the scaling of the scattering rate with cross helicity. We observe excellent agreement in simulations of both balanced and imbalanced turbulence and explain the role of the magnetic moment, an approximate invariant of charged-particle motion, for pitch-angle scattering on timescales of several gyroperiods.Turbulenz ist in astrophysikalischen Plasmen allgegenwärtig. Viele solche Systeme weisen eine sogenannte Kreuz-Helizität auf, also eine von Null verschiedene Korrelation zwischen Geschwindigkeits- und Magnetfeld-Fluktuationen. In einer anisotropen Magnetfeldgeometrie, z. B. im Sonnenwind oder dem interstellaren Medium, deutet die Kreuz-Helizität auf ein Ungleichgewicht zwischen Alfven-Wellen, die sich in Richtung des gemittelten Feldes ausbreiten, und solchen, die in die Gegenrichtung propagieren, hin. Obwohl dieses Ungleichgewicht die stochastische Beschleunigung und Streuung, die geladene Teilchen in einem Plasma erfahren, dramatisch beeinflusst, wurde es in bisherigen numerischen Studien über turbulenten Teilchentransport gemeinhin außer Acht gelassen. In dieser Arbeit nun werden rechnergestützte Simulationen von magnetohydrodynamischer Turbulenz präsentiert, in denen die Energie und die Kreuz-Helizität kontrolliert werden können, ohne jedoch kinetische oder magnetische Helizität als unerwünschte Nebenwirkung zu erzeugen. Die Stärke des mittleren Magnetfeldes bestimmt dabei die Anisotropie des Gleichgewichtszustandes. Die Simulationen erfüllen in allen Parameterbereichen die Vorhersagen, die theoretische Modelle für realistische Plasmaturbulenz treffen. Die Diffusion kosmischer Strahlung in turbulenten Plasmen wird häufig im Rahmen der quasilinearen Theorie unter Heranziehung eines stark vereinfachten Turbulenzspektrums berechnet. Indem die Trajektorien von Testteilchen in dynamischen Turbulenzsimulationen mit Kreuz-Helizität berechnet werden, lassen sich quasilineare Ergebnisse für die Beschleunigungsrate geladener Teilchen nachprüfen. Theorie und numerische Simulation stimmen für Teilchen mit der Alfven-Geschwindigkeit gut überein, solange resistive Effekte vernachlässigt werden können. Weiterhin werden aus der quasilinearen Theorie berechnete Diffusionskoeffizienten mit numerisch ermittelten Streuraten für Testteilchen nach einer Gyroperiode in stark anisotropen Feldkonfigurationen verglichen, wobei der Schwerpunkt erneut beim Einfluss der Kreuz-Helizität liegt. Für alle verwendeten Werte der Kreuz-Helizität ergibt sich eine exzellente Übereinstimmung zwischen Simulationsergebnis und Vorhersage. Schließlich wird die Rolle des magnetischen Moments, einer adiabatischen Invarianten bei der Bewegung geladener Teilchen in einem Magnetfeld, für die Streuung über Zeitskalen von mehreren Gyroperioden erläutert

Pre-acceleration in the Electron Foreshock II: Oblique Whistler Waves

Thermal electrons have gyroradii many orders of magnitude smaller than the finite width of a shock, thus need to be pre-accelerated before they can cross it and be accelerated by diffusive shock acceleration. One region where pre-acceleration may occur is the inner foreshock, which upstream electrons must pass through before any potential downstream crossing. In this paper, we perform a large scale particle-in-cell simulation that generates a single shock with parameters motivated from supernova remnants. Within the foreshock, reflected electrons excite the oblique whistler instability and produce electromagnetic whistler waves, which co-move with the upstream flow and as non-linear structures eventually reach radii of up to 5 ion-gyroradii. We show that the inner electromagnetic configuration of the whistlers evolves into complex non-linear structures bound by a strong magnetic field around 4 times the upstream value. Although these non-linear structures do not in general interact with co-spatial upstream electrons, they resonate with electrons that have been reflected at the shock. We show that they can scatter, or even trap, reflected electrons, confining around $0.8\%$ of the total upstream electron population to the region close to the shock where they can undergo substantial pre-acceleration. This acceleration process is similar to, yet approximately 3 times more efficient than, stochastic shock drift acceleration.Comment: 16 pages, 11 figures, accepted for publication in Ap

Cosmic-ray pitch-angle scattering in imbalanced mhd turbulence simulations

Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.Comment: 13 pages, 15 figures. Accepted by Ap

The electron foreshock at high-Mach-number nonrelativistic oblique shocks

In the Universe matter outside of stars and compact objects is mostly composed of collisionless plasma. The interaction of a supersonic plasma flow with an obstacle results in collisionless shocks that are often associated with intense nonthermal radiation and the production of cosmic ray particles. Motivated by simulations of non-relativistic high-Mach-number shocks in supernova remnants, we investigate the instabilities excited by relativistic electron beams in the extended foreshock of oblique shocks. The phase-space distributions in the inner and outer foreshock regions are derived with a Particle-in-Cell simulation of the shock and used as initial conditions for simulations with periodic boundary conditions to study their relaxation towards equilibrium. We find that the observed electron-beam instabilities agree very well with the predictions of a linear dispersion analysis: the electrostatic electron-acoustic instability dominates in the outer region of the foreshock, while the denser electron beams in the inner foreshock drive the gyroresonant oblique-whistler instability

Pre-acceleration in the Electron Foreshock I: Electron Acoustic Waves

To undergo diffusive shock acceleration, electrons need to be pre-accelerated to increase their energies by several orders of magnitude, else their gyro-radii are smaller than the finite width of the shock. In oblique shocks, where the upstream magnetic field orientation is neither parallel or perpendicular to the shock normal, electrons can escape to the shock upstream, modifying the shock foot to a region called the electron foreshock. To determine the pre-acceleration in this region, we undertake PIC simulations of oblique shocks while varying the obliquity and in-plane angles. We show that while the proportion of reflected electrons is negligible for $\theta_{\rm Bn} = 74.3^\circ$, it increases to $R \sim 5\%$ for $\theta_{\rm Bn} = 30^\circ$, and that, via the electron acoustic instability, these electrons power electrostatic waves upstream with energy density proportional to $R^{0.6}$ and a wavelength $\approx 2 \lambda_{\rm{se}}$, where $\lambda_{\rm{se}}$ is the electron skin length. While the initial reflection mechanism is typically a combination of shock surfing acceleration and magnetic mirroring, we show that once the electrostatic waves have been generated upstream they themselves can increase the momenta of upstream electrons parallel to the magnetic field. In $\lesssim 1\%$ of cases, upstream electrons are prematurely turned away from the shock and never injected downstream. In contrast, a similar fraction are re-scattered back towards the shock after reflection, re-interact with the shock with energies much greater than thermal, and cross into the downstream.Comment: Accepted for publication in ApJ. 15 pages, 15 figure