Numerical study of tilt stability of prolate field-reversed configurations

Global stability of the field-reversed configuration (FRC) has been investigated numerically using both three-dimensional magnetohydrodynamic and hybrid (fluid electron and δf particle ion) simulations. The stabilizing effects of velocity shear and finite ion Larmor radius (FLR) on the n = 1 internal tilt mode in the prolate FRCs have been studied. Sheared rotation is found to reduce the growth rate, however a large rotation rate with Mach number of M ≳ 1 is required in order for significant reduction in the instability growth rate to occur. Kinetic effects associated with large thermal ion orbits have been studied for different kinetic equilibria. The simulations show that there is a reduction in the tilt mode growth rate due to FLR effects, but complete linear stability has not been found, even when the thermal ion gyroradius is comparable to the distance between the field null and the separatrix. The instability existing beyond the FLR theory threshold could be due to the resonant interaction of the wave with ions whose Doppler shifted frequency matches the betatron frequency.