About the cyclotron resonance conditions in magnetized current-carrying plasmas

The resonant cyclotron wave-particle interactions in a cylindrical current-carrying plasma and in two-dimensional axisymmetric toroidal plasma models for tokamaks with D-shaped, elliptic and circular magnetic surfaces are discussed. The corresponding phase resonance conditions are derived by solving the linearized Vlasov equations as a boundary-value problem for perturbed plasma particle distribution functions, accounting for the geometry of a confinement magnetic field in the zero-order over magnetization parameters. It is shown that the Doppler shifts under the cyclotron resonance conditions in the current-carrying plasmas differ from those for a plasma in a uniform magnetic field due to the rotational transformation (including the shear-effects) of the helical magnetic field lines. As for elongated tokamaks, the cyclotron wave-particle resonance conditions in the general case, along with helicity-corrections, involve the bounce-resonances of the untrapped (circulating, passing) and two groups of so-called t-trapped and d-trapped particles.