Analysis of the current‐diffusive ballooning mode

Abstract

The current‐diffusive ballooning mode is analyzed in the tokamak plasma. This mode is destabilized by the current diffusivity (i.e., the electron viscosity) and stabilized by the thermal conductivity and ion viscosity. By use of the ballooning transformation, the eigenmode equation is solved. An analytic solution is obtained by the strong ballooning limit. Numerical calculation is also performed to confirm the analytic theory. The growth rate of the mode and the mode structure are analyzed. The stability boundary is derived in terms of the current diffusivity, thermal conductivity, ion viscosity, and the pressure gradient for the given shear parameter. This result is applied to express the thermal conductivity in terms of the pressure gradient, magnetic configurational parameters (such as the safety factor, shear, and aspect ratio), and the Prandtl numbers.