The electron distribution function downstream of the solar-wind termination shock: Where are the hot electrons?

In the majority of the literature on plasma shock waves, electrons play the role of "ghost particles," since their contribution to mass and momentum flows is negligible, and they have been treated as only taking care of the electric plasma neutrality. In some more recent papers, however, electrons play a new important role in the shock dynamics and thermodynamics, especially at the solar-wind termination shock. They react on the shock electric field in a very specific way, leading to suprathermal nonequilibrium distributions of the downstream electrons, which can be represented by a kappa distribution function. In this paper, we discuss why this anticipated hot electron population has not been seen by the plasma detectors of the Voyager spacecraft downstream of the solar-wind termination shock. We show that hot nonequilibrium electrons induce a strong negative electric charge-up of any spacecraft cruising through this downstream plasma environment. This charge reduces electron fluxes at the spacecraft detectors to nondetectable intensities. Furthermore, we show that the Debye length $\lambda _{\mathrm D}^{\kappa}$ grows to values of about $\lambda _{\mathrm D}^{\kappa}/\lambda _{\mathrm D}\simeq 10^{6}$ compared to the classical value $\lambda _{\mathrm D}$ in this hot-electron environment. This unusual condition allows for the propagation of a certain type of electrostatic plasma waves that, at very large wavelengths, allow us to determine the effective temperature of the suprathermal electrons directly by means of the phase velocity of these waves. At moderate wavelengths, the electron-acoustic dispersion relation leads to nonpropagating oscillations with the ion-plasma frequency $\omega _{\mathrm p}$ , instead of the traditional electron plasma frequency.Comment: 6 pages, 2 figure

NHDS: The New Hampshire Dispersion Relation Solver

NHDS is the New Hampshire Dispersion Relation Solver. This article describes the numerics of the solver and its capabilities. The code is available for download on https://github.com/danielver02/NHDS.Comment: 3 pages, 1 figur

A Parallel-Propagating Alfv\'enic Ion-Beam Instability in the High-Beta Solar Wind

We investigate the conditions under which parallel-propagating Alfv\'en/ion-cyclotron waves are driven unstable by an isotropic ($T_{\perp \alpha} = T_{\parallel\alpha}$) population of alpha particles drifting parallel to the magnetic field at an average speed $U_{\alpha}$ with respect to the protons. We derive an approximate analytic condition for the minimum value of $U_{\alpha}$ needed to excite this instability and refine this result using numerical solutions to the hot-plasma dispersion relation. When the alpha-particle number density is $\simeq 5$ of the proton number density and the two species have similar thermal speeds, the instability requires that $\beta_{\rm p} \gtrsim 1$, where $\beta_{\rm p}$ is the ratio of the proton pressure to the magnetic pressure. For $1\lesssim \beta_{\mathrm p}\lesssim 12$, the minimum $U_{\alpha}$ needed to excite this instability ranges from $0.7v_{\mathrm A}$ to $0.9v_{\mathrm A}$, where $v_{\mathrm A}$ is the Alfv\'en speed. This threshold is smaller than the threshold of $\simeq 1.2v_{\mathrm A}$ for the parallel magnetosonic instability, which was previously thought to have the lowest threshold of the alpha-particle beam instabilities at $\beta_{\mathrm p}\gtrsim 0.5$. We discuss the role of the parallel Alfv\'enic drift instability for the evolution of the alpha-particle drift speed in the solar wind. We also analyze measurements from the \emph{Wind} spacecraft's Faraday cups and show that the $U_{\alpha}$ values measured in solar-wind streams with $T_{\perp \alpha}\approx T_{\parallel\alpha}$ are approximately bounded from above by the threshold of the parallel Alfv\'enic instability.Comment: 8 pages, 7 figure

Spectral evolution of two-dimensional kinetic plasma turbulence in the wavenumber-frequency domain

We present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumber-frequency domain. We apply hybrid plasma simulations in a simplified two-dimensional geometry to demonstrate our method and its applicability to plasma turbulence in the ion kinetic regime. We identify four dispersion relations: ion-Bernstein waves, oblique whistler waves, oblique Alfv\'en/ion-cyclotron waves, and a zero-frequency mode. The energy partition and frequency broadening are evaluated for these modes. The method allows us to determine the evolution of decaying plasma turbulence in our restricted geometry and shows that it cascades along the dispersion relations during the early phase with an increasing broadening around the dispersion relations.Comment: 11 pages, 4 figure

Instabilities Driven by the Drift and Temperature Anisotropy of Alpha Particles in the Solar Wind

We investigate the conditions under which parallel-propagating Alfv\'en/ion-cyclotron (A/IC) waves and fast-magnetosonic/whistler (FM/W) waves are driven unstable by the differential flow and temperature anisotropy of alpha particles in the solar wind. We focus on the limit in which $w_{\parallel \alpha} \gtrsim 0.25 v_{\mathrm A}$, where $w_{\parallel \alpha}$ is the parallel alpha-particle thermal speed and $v_{\mathrm A}$ is the Alfv\'en speed. We derive analytic expressions for the instability thresholds of these waves, which show, e.g., how the minimum unstable alpha-particle beam speed depends upon $w_{\parallel \alpha}/v_{\mathrm A}$, the degree of alpha-particle temperature anisotropy, and the alpha-to-proton temperature ratio. We validate our analytical results using numerical solutions to the full hot-plasma dispersion relation. Consistent with previous work, we find that temperature anisotropy allows A/IC waves and FM/W waves to become unstable at significantly lower values of the alpha-particle beam speed $U_\alpha$ than in the isotropic-temperature case. Likewise, differential flow lowers the minimum temperature anisotropy needed to excite A/IC or FM/W waves relative to the case in which $U_\alpha =0$. We discuss the relevance of our results to alpha particles in the solar wind near 1 AU.Comment: 13 pages, 13 figure

Magnetohydrodynamic Slow Mode with Drifting He++^{++}: Implications for Coronal Seismology and the Solar Wind

The MHD slow mode wave has application to coronal seismology, MHD turbulence, and the solar wind where it can be produced by parametric instabilities. We consider analytically how a drifting ion species (e.g. He$^{++}$) affects the linear slow mode wave in a mainly electron-proton plasma, with potential consequences for the aforementioned applications. Our main conclusions are: 1. For wavevectors highly oblique to the magnetic field, we find solutions that are characterized by very small perturbations of total pressure. Thus, our results may help to distinguish the MHD slow mode from kinetic Alfv\'en waves and non-propagating pressure-balanced structures, which can also have very small total pressure perturbations. 2. For small ion concentrations, there are solutions that are similar to the usual slow mode in an electron-proton plasma, and solutions that are dominated by the drifting ions, but for small drifts the wave modes cannot be simply characterized. 3. Even with zero ion drift, the standard dispersion relation for the highly oblique slow mode cannot be used with the Alfv\'en speed computed using the summed proton and ion densities, and with the sound speed computed from the summed pressures and densities of all species. 4. The ions can drive a non-resonant instability under certain circumstances. For low plasma beta, the threshold drift can be less than that required to destabilize electromagnetic modes, but damping from the Landau resonance can eliminate this instability altogether, unless $T_{\mathrm e}/T_{\mathrm p}\gg1$.Comment: 35 pages, 5 figures, accepted for publication in Astrophys.

A Modified Version of Taylor's Hypothesis for Solar Probe Plus Observations

The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentric distances less than $10 R_{\odot}$. Near Earth, spacecraft measurements of fluctuating velocities and magnetic fields taken in the time domain are translated into information about the spatial structure of the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion of SPP, however, the solar-wind speed is comparable to the Alfv\'en speed, and Taylor's hypothesis in its usual form does not apply. In this paper, we show that, under certain assumptions, a modified version of Taylor's hypothesis can be recovered in the near-Sun region. We consider only the transverse, non-compressive component of the fluctuations at length scales exceeding the proton gyroradius, and we describe these fluctuations using an approximate theoretical framework developed by Heinemann and Olbert. We show that fluctuations propagating away from the Sun in the plasma frame obey a relation analogous to Taylor's hypothesis when $V_{\rm sc,\perp} \gg z^-$ and $z^+ \gg z^-$, where $V_{\rm sc,\perp}$ is the component of the spacecraft velocity perpendicular to the mean magnetic field and $\bm{z}^+$ ($\bm{z}^-$) is the Elsasser variable corresponding to transverse, non-compressive fluctuations propagating away from (towards) the Sun in the plasma frame. Observations and simulations suggest that, in the near-Sun solar wind, the above inequalities are satisfied and $\bm{z}^+$ fluctuations account for most of the fluctuation energy. The modified form of Taylor's hypothesis that we derive may thus make it possible to characterize the spatial structure of the energetically dominant component of the turbulence encountered by SPP.Comment: 5 pages, 1 figure, accepted in ApJ Lette

On the Conservation of Cross Helicity and Wave Action in Solar-Wind Models with Non-WKB Alfven Wave Reflection

The interaction between Alfven-wave turbulence and the background solar wind affects the cross helicity in two ways. Non-WKB reflection converts outward-propagating Alfven waves into inward-propagating Alfven waves and vice versa, and the turbulence transfers momentum to the background flow. When both effects are accounted for, the total cross helicity is conserved. In the special case that the background density and flow speed are independent of time, the equations of cross-helicity conservation and total-energy conservation can be combined to recover a well-known equation derived by Heinemann and Olbert that has been interpreted as a non-WKB generalization of wave-action conservation. This latter equation (in contrast to cross-helicity and energy conservation) does not hold when the background varies in time.Comment: 9 pages, 1 figure, in press at Ap