Beta-induced temperature gradient eigenmodes in tokamaks II. Kinetic theory
Kinetic theory of unstable beta-induced temperature-gradient (BTG) eigenmodes in a tokamak is developed. These eigenmodes with eigenfrequencies omega of the order of the ion transit frequency V(Ti)/qR (V(Ti) is the ion thermal velocity, q the safety factor and R the major radius of tokamak) are shown to be driven by the contribution of the inverse ion Landau damping into the geodesic current (current due to the geodesic curvature of the equilibrium magnetic field). To derive the mode equation the Vlasov ion kinetic equation with the geodesic magnetic drift is used. The kinetic equation is simplified by expansion in the small parameter omega/omega(Bi) (omega(Bi) is the ion cyclotron frequency) and solved then by expansion in a series in the small parameter rho(i)/X(*) (rho(i)=V(Ti)/omega(Bi) is the ion Larmor radius, X(*) is the characteristic radial scale of the mode). The dispersion relation and the localization condition of the kinetic BTG eigenmodes are given. It is shown that, similarly to the BTG eigenmodes in the magnetohydrodynamics (MHD) model, the BTG eigenmodes in the kinetic approach are unstable for a positive relative ion temperature gradient, if the ion beta exceeds a critical value.
Bibliographic Reference: Report: JET-P(98)12 EN 16pp.
Availability: Available from the Publications Officer, JET Joint Undertaking, Abingdon, Oxon, OX14 3EA (GB)
Record Number: 199810646 / Last updated on: 1998-05-26
Original language: en
Available languages: en