The ion temperature gradient instability in a linear machine

Abstract

It is shown that anisotropy in the ion temperature gradient has a substantial effect on the ion temperature gradient driven mode. A gradient in the parallel temperature is needed for an instability to occur and a gradient in the perpendicular temperature gradient further enhances the instability indirectly as long as the frequency of the mode is near ion resonance. The physical reason for this important role difference is presented. The Columbia Linear Machine (CLM) [Phys. Rev. Lett. 57, 1729 (1986)] is being redesigned to produce and identify the ion temperature gradient driven ηi mode. Using the expected parameters, detailed predictions of the mode characteristics in the CLM have been developed. These include growth rate and real frequency as a function of the azimuthal number m, the drive parameter ηi ≡d(ln Ti)/d(ln n), and the parallel wavenumber k∥. Strong multimode instabilities are expected. Because the ion parallel and perpendicular ion temperature gradients are expected to differ significantly, the roles of ηi∥ and ηi⊥ are differentiated, and this difference is exploited for a stabilization scheme of the mode. Since all gradients are significantly variable over the expected radial wavelength of the mode, a nonlocal radial differential equation has been derived. With some approximations, this can be reduced to a Weber-type equation, which has been solved.