Passive cyclotron current drive efficiency for relativistic toroidal plasmas

In this paper we present results of analytical and numerical studies of the passive cyclotron current drive efficiency in mildly relativistic toroidal plasmas. The problem of linearization and separation of the electron and photon balance equations becomes nontrivial for high-temperature plasmas (e.g., D–3He) with low electron pressure (βe<0.1) due to the increased effect of radiation friction. The conditions under which this separation is possible is derived in this paper. The linearized problem for the electron distribution is formulated in the form of a standard variational principle, which includes both Coulomb collisions and ‘‘collisions’’ due to cyclotron radiation. The reduced variational principle for the current drive efficiency (generalized Spitzer–Härm function) is derived, as well as its bounce-averaged form for toroidal plasmas. Finally, a convenient form of the passive cyclotron current drive efficiency is introduced, which can be used for a self-consistent modeling of passive cyclotron current generation in tokamaks with the help of fish-scale structures [see the companion paper, W. Kernbichler and S. Kasilov, Phys. Plasmas 3, 4128 (1996)].