Global structure of mirror modes in the magnetosheath

A global stability analysis of mirror modes in the magnetosheath is presented. The analysis is based upon the kinetic‐MHD formulation which includes relevant kinetic effects such as Landau resonance and gradient drift effects related to inhomogeneities in the background density, temperature, pressure and its anisotropy, magnetic field, and plasma flow velocity. Pressure anisotropy provides the free energy for the global mirror mode. The local theory of mirror modes predicts purely growing modes in the frame of the moving plasma confined to the unstable magnetosheath region; however, the nonlocal theory that includes the effects of gradients and plasma flow predicts modes with real frequency which propagate with the flow from the magnetosheath toward the magnetopause boundary. The real frequency is of the order of a combination of the diamagnetic drift frequency and the Doppler shift frequency associated with plasma flow. The real frequency is not simply a Doppler‐shifted frequency obtained from local calculation. Rather, it is determined from a boundary value constraint on an eigenvalue problem and can differ significantly from the local Doppler‐shifted frequency. Without plasma flow, the diamagnetic drift frequency provides a wave phase velocity in the direction of the magnetopause so that wave energy accumulates against the magnetopause boundary, and the amplitude is skewed in that direction. Such a wave structure might be observed under conditions of small magnetosheath flow. For larger plasma flow (Alfvén Mach number ≥ 0.1), the flow also causes a real phase velocity in the direction of the flow, but the phase velocity increases from a small value near the bow shock to nearly the flow velocity as the wave propagates toward the magnetopause. As a result, wave amplitude is large where the phase velocity is small and small where the phase velocity is large resulting in a skew in wave amplitude toward the bow shock.