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. Plain Language Summary Waves in some plasma systems can grow, rather than damp, in time drawing energy from the departures from equilibrium. We present a means of efficiently determining if a particular system is susceptible to such unstable behavior. Such determination is typically made by solving a difficult mathematical problem or making simplifying assumptions about the system. Our technique is compared to previously studied cases with good agreement. We then discuss plans for future application of the technique to measurements of the solar wind, a hot and tenuous magnetized plasma that fills our solar system.