Modified negative mass instability in the A.S. device

Stabilization of the Alfvén wave instability in a two-component tokamak

“…In connection with theoretical investigations of Alfven wave excitation by fast ions in a tokamak plasma, and especially in connection with Refs [3,9], Timofeev [14] has drawn attention to the analogy between the problem of Alfven waves in an inhomogeneous plasma and the problem of the stability of the inhomogeneous flows of a plasma and a liquid. On the basis of this analogy, Timofeev pointed out that the rising eigenoscillations found in Ref.…”

“…[9], and representing a combination of long-wave and small-scale oscillations, were formally similar to Poiseuille flow instability [15]. Moreover, Timofeev [14] has established that the equations for small oscillations derived in Ref. [9] also permit solutions of the Van Kampen-Case wave type [16], the frequency being determined by the "local" dispersion equation used in Ref.…”

“…According to Ref. [14], the spatial scale of these non-natural perturbations, which occur at some initial moment of time, decreases, as a result of which the "viscosity" effect associated with trapped electrons and leading to their damping enters into play. According to Timofeev, waves of the Van Kampen-Case type should be considered unstable if they grow to such large amplitudes before "viscosity" begins to have an influence that non-linear effects intervene in their evolution.…”

“…On the whole, from Timofeev's analysis [ 14] it follows that in the problem of Alfven wave excitation by fast ions both "local" perturbations, of the type considered in Ref. [3] and subsequently [4][5][6][7][8], and perturbations of the "eigenoscillation" type, considered in Ref.…”

“…It is therefore necessary to consider, along the lines indicated in Ref. [14], the evolution of the initial perturbations growing as a result of the "local" instability. This is done in Section 6, and the results are discussed in Section 7.…”