Whistler turbulence at the magnetopause: 1. Reduced equations and linear theory

A set of reduced nonlinear equations is presented, which describes the dynamics of a current layer at scale sizes below the ion skin depth. At these scales the ion motion can be ignored. These equations contain the effects of electron inertia and the Hall term with the intent of describing small-scale turbulence in the environment of the magnetopause. Magnetic shear effects are also included. It is found that the entire spectrum is linearly unstable either to the current gradient instability or to a kink-type mode. The kink-like instability, in contrast to the current gradient instability, also exists in the limit of massless electrons. The growth rate increases with decreasing current layer width and the jump of the north-south component of the magnetic field across the magnetopause.

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