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

Boxicity and separation dimension

A family $\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\mathcal{F}$ in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for $H$ is called the 'separation dimension' of $H$ and is denoted by $\pi(H)$. Equivalently, $\pi(H)$ is the smallest natural number $k$ so that the vertices of $H$ can be embedded in $\mathbb{R}^k$ such that any two disjoint edges of $H$ can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph $H$ is equal to the 'boxicity' of the line graph of $H$. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to WG-2014. Some results proved in this paper are also present in arXiv:1212.6756. arXiv admin note: substantial text overlap with arXiv:1212.675

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