On ion temperature gradient and parallel velocity shear instabilities

• Published in: Physics of plasmas 2004-05, Vol.11 (5), p.2106-2118
• Main Authors: Rogister, Andre L., Singh, Raghvendra, Kaw, Predhiman K.
• Format: Article
• Language: English
• ISSN: 1070-664X; 1089-7674
• DOI: 10.1063/1.1677177

The local dispersion relation for waves with frequencies in the range of the diamagnetic frequencies ω j * and parallel wave numbers satisfying the conditions k ∥ c s /ω e * ∼1 and qRk ∥ ≫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 τ i =T i /T e , η i =∂ r   ln  T i /∂ r   ln  N i , and ζ =∂ r U ∥,i /c s ∂ r   ln  N i , it is found that unstable modes appear for η i >1+ 1−ζ 2 /(1+τ i ) (which agrees with the standard ion temperature gradient instability condition η i >2 if ζ=0) and 0