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+ ${O}^{+}$ abundance >40%ne $\left( > 40\%\ {\mathrm{n}}_{\mathrm{e}}\right)$. 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 γm/Ωp $\left({\gamma }_{m}/{{\Omega }}_{p}\right)$ 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 ρp ${\rho }_{\mathrm{p}}$, smaller than expected from observations. These inconsistencies could potentially be attributed to diffusion and non‐linear growth processes. Plain Language Summary Plasma instabilities have well‐defined relationships between the wavevector and the frequency captured in the dispersion relation. Linear kinetic theory provides a basis for interpreting instability growth rates and scale sizes in simulations and observations with small plasma fluctuations. However, it cannot describe the fate of the instability such as the maximum amplitude, nor its interactions with other modes. The ion cyclotron (IC) and mirror mode (MM) instabilities lead to fluctuations of different frequencies and spatial scales. Their growth occurs when the plasma exhibits temperature perpendicular‐to‐magnetic‐field greater than some threshold of the temperature parallel‐to‐magnetic‐field direction known as temperature anisotropy. Each instability has a