Drift-reduced fluid modeling of rapidly rotating plasmas

Abstract

In this paper, we investigate the effects of rapid rotation (Mach number M ~ 1) on plasma fluid stability, focusing specifically on Kelvin-Helmholtz (KH) and interchange instabilities - including both magnetic-curvature-driven (CDI) and rotation-driven (RDI) interchanges. Building on previous studies of shear flow stabilization, we utilize a drift- reduced fluid approach rather than standard magnetohydrodynamics to capture finite Larmor-radius effects. To achieve this, the drift-reduced equations were modified to include the centrifugal force and implemented in hermes-3 (Dudson et al. 2024), an extension to the BOUT++ (Dudson et al. 2009) framework. Because plasma rotation both drives the RDI and provides stabilizing shear flow, we find that the global plasma stability is sensitive to background profile characteristics. We identify three distinct regimes of RDI behavior and establish a simple criterion based on the density and velocity profiles to predict RDI susceptibility. This approach is similar to recent local gyrokinetic studies of shear flow that compared instability growth rates to shearing rates (Ivanov et al. 2025). Finally, by examining cases where the plasma is both interchange- and KH-unstable, we find that global KH modes make the plasma less resistant to RDI.

Figures (15)

• Figure 1: Time slices of velocity for the ramped case, labeled in time units normalized to the ion cyclotron frequency. As the simulation evolves, the sheared profile breaks up and begins to form vortices typical of 2D fluid turbulence.
• Figure 2: Linear growth rates for sinusoidal velocity profile with periodic boundary conditions. The estimated growth rates from hermes-3 closely match the curve produced by the semi-analytic model.
• Figure 3: Time slices of electron pressure demonstrating interchange instability driven by magnetic curvature. The heavier fluid at the top eventually begins to mix with the lighter fluid at the bottom.
• Figure 4: Interchange growth rates with ion and electron pressure gradients swapped. The larger gradient is a factor of 5 larger than the smaller gradient in both cases. For $\kappa_i \gg \kappa_e$, FLR effects are more prominent, causing the growth rate to decrease more rapidly as $k_\perp \rho_i \xrightarrow{} 1$. The hermes-3 simulation results (markers) show good agreement with the theoretical expression of \ref{['eq:flr_dispersion']} (solid lines).
• Figure 5: Interchange instability at $t=0$, the early stage, and later stage after being returned to a semi-laminar state by shear flow. The instability initially grows in the central region where the shear flow is weakest, before being sheared away as it spreads toward the edges. The white lines indicate the predicted width of the flattened region.