Fundamental ion-cyclotron frequency heating in tokamaks

The interaction of ions with waves at the fundamental ion-cyclotron frequency in tokamaks is studied without the assumption of geometrical optics. Instead, two small parameters, ε1=ρ/λ and ε2=BP/BT, are introduced, where ρ is the Larmor radius, λ is the wavelength, and BP and BT are the poloidal and toroidal magnetic fields. The heating at the resonance surface is studied for a given incoming wave without considering the problem of accessibility. The case ε2≫ε1 is studied in detail and a boundary layer analysis is performed at the resonance surface. The cold plasma theory is not valid at the resonance surface and the currents and fields are found by solving the Vlasov–Maxwell equations. The current is of nonlocal form, so that an integrodifferential equation is derived and solved numerically. Unlike the case of mirror geometry, in the tokamak the electric field is not constant across the boundary layer. The profiles of the electric field and energy flux are presented. It is shown that all the incoming flux is absorbed, and for these particular values of parameters (ε2≫ε1), there is strong heating at the fundamental resonance. In addition, the case when ε2 is not much larger than ε1 is discussed and it is shown that there is not much heating.