Temperature drift instability (eigenvalue and eigenfunction investigation)

A differential equation for a temperature-drift instability has been solved numerically and analytically in an effort to find the stability boundaries, increment and frequency of the corresponding oscillations. The differential equation has been studied for eigen values and eigen functions. The temperature gradient threshold, the frequency ω and the increment γ of the instability have been obtained as functions of shear, ratio Tsub(i)Tsub(e) and of the azimuthal wave number. The values ω and γ turned out to be much less than the ion temperature drift frequency. Unlike the local theory, the instability threshold in temperature gradient increases drastically with increasing Tsub(i)Tsub(e), which may elucidate the experiment when the instability threshold of the local theory is surpassed, but no essential effects connected with the temperature drift instability have been not likely to be observed. The smallness of increment and oscillation frequency may lead to a situation when taking into account toroidal effects (such as particles trapping and magnetic drift) may change the conditions of existence of the instability under consideration