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

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

Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities

Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in $\beta_{\parallel \mathrm p}\equiv 8\pi n_{\mathrm p}k_{\mathrm B}T_{\parallel \mathrm p}/B^2$ and in $R_{\mathrm p}\equiv T_{\perp \mathrm p}/T_{\parallel \mathrm p}$, where $T_{\perp \mathrm p}$ and $T_{\parallel \mathrm p}$ are the perpendicular and parallel temperatures of the protons, $B$ is the magnetic field strength, and $n_{\mathrm p}$ is the proton density. If the amplitude of the compressive fluctuations is large enough, $R_{\mathrm p}$ crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of $R_{\mathrm p}$ away from the marginal stability boundary until the fluctuating value of $R_{\mathrm p}$ stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov--Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of $R_{\mathrm p}$ is close to unity.Comment: 11 pages, published in Ap

Do Teachers’ Race, Gender, and Ethnicity Matter? Evidence From the National Education Longitudinal Study of 1988

Using data from the National Educational Longitudinal Study of 1988 (NELS), the authors find that the match between teachers\u27 race, gender, and ethnicity and those of their students had little association with how much the students learned, but in several instances it seems to have been a significant determinant of teachers\u27 subjective evaluations of their students. For example, test scores of white female students in mathematics and science did not increase more rapidly when the teacher was a white woman than when the teacher was a white man, but white female teachers evaluated their white female students more highly than did white male teachers

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.

Consumption, savings, and the meaning of the wealth effect in general equilibrium

Consumption (Economics) ; Wealth ; Saving and investment ; Equilibrium (Economics)