GYRO AND DRIFT KINETIC-EQUATIONS IN TOROIDAL PLASMAS

Some powerful mathematical tools, adapted to both the equilibrium and the stability theories of hot plasmas confined by strong toroidal magnetic fields, are introduced. The expected characteristics of the potentially most unstable modes are discussed on the basis of physical considerations and an adequate mode representation, fulfilling the obtained criteria, is presented. The gyro-kinetic equation, which describes the gyro-phase averaged kinetic behavior of ions along the magnetic field in 'low'' frequency (omega much less than OMEGA(i), ''finite'' perpendicular wave vector (k(perpendicular-to) a(i) approximately 1) oscillations, and the electron drift kinetic equation (k(perpendicular-to a(c) much less than 1), which similarly describes the averaged kinetic behavior of electrons, are then derived. Finally, the original ballooning mode description is related to our formalism.