On ion temperature gradient and parallel velocity shear instabilities

The local dispersion relation for waves with frequencies in the range of the diamagnetic frequencies omega(j)(*) and parallel wave numbers satisfying the conditions k(parallel to)c(s)/omega(e)(*)similar to1 and qRk(parallel to)>>1 has been obtained in the framework of kinetic theory keeping the equilibrium density, temperature, and parallel velocity gradients into account (j is the species index, qR the connection length, and c(s) the speed of sound). The analysis applies to the cases where the radial scale of the oscillations is comparable to or smaller than the equilibrium length scale. As the velocity-space integral appearing in the dispersion relation can be calculated only in asymptotic limits, exact instability criteria are obtained by means of the Nyquist diagram. Defining tau(i)=T-i/T-e, eta(i)=partial derivative(r) ln T-i/partial derivative(r) ln N-i, and zeta =partial derivative(r)U(parallel to,i)/c(s)partial derivative(r) ln N-i, it is found that unstable modes appear for eta(i)>1+root1-zeta(2)/(1+tau(i)) (which agrees with the standard ion temperature gradient instability condition eta(i)>2 if zeta=0) and 0root2 if eta(i)=0). The center of the unstable range is characterized by the relation k(parallel to)c(s)/omega(e)(*)=-zeta/2(1+tau(i)) from which it follows that qRk(parallel to)>1 is verified if [k(beta)a(s)/2(1+tau(i))]qRpartial derivative(r)U(parallel to,i)/c(s)>1 (k(beta) is the wave vector component in the direction of the binormal). The oscillations are not tied, under those conditions, to any particular rational surface; the roles of magnetic shear, trapped electrons, ion gyroradius and torus curvature are moreover negligible. The growth/decay rate of the oscillations has been calculated in the neighborhood of marginal (in)stability; the excitation/damping mechanism is (inverse) ion Landau damping. The wave frequency is a function of position so that localization of a wave packet results from a competition between linear growth and distortion (wave breaking in smaller eddies). Applications of the theory include the transition from the edge localized mode-free to enhanced D alpha high confinement regime and intermittency. (C) 2004 American Institute of Physics