Waves and Instabilities in Saturn's Magnetosheath: 2. Dispersion Relation Analysis

The WHAMP (Rönnmark, 1982, https://inis.iaea.org/search/search.aspx?orig_q=RN:14744092) and LEOPARD (Astfalk & Jenko, 2017, https://doi.org/10.1002/2016ja023522) dispersion relation solvers were used to evaluate the growth rate and scale size for mirror mode (MM) and ion cyclotron (IC) instabilities under plasma conditions resembling Saturn's magnetosheath in order to compare observations to predictions from linear kinetic theory. Instabilities and waves are prevalent in planetary magnetosheaths. Understanding the origin and conditions under which different instabilities grow and dominate can help shed light on the role each instability plays in influencing the plasma dynamics of the region. For anisotropic plasmas modeled with bi-Maxwellian particle distribution, the dispersion, growth rate, and scale size of MM and IC were studied as functions of proton temperature anisotropy, proton plasma beta, and oxygen ion abundance. The dispersion solvers showed that the IC mode dominated over MM under typical conditions in Saturn's magnetosheath, but that MM could dominate for high enough $O^{+}$ abundance $\left(>40\%n_e\right)$. These water ion-rich plasma conditions are occasionally found in Saturn's magnetosheath (Sergis et al., 2013, https://doi.org/10.1002/jgra.50164). The maximum linear growth rates $\left({\gamma }_m/{\Omega }_p\right)$ for MM ranged from 0.02 to 0.2, larger than expected from observations. The scale size at maximum growth rate ranged from 4 to 12 ${\rho }_p$, smaller than expected from observations. These inconsistencies could potentially be attributed to diffusion and non-linear growth processes.