Enhanced lower-hybrid heating caused by frequency modulation

Abstract

The effect of frequency modulation during stochastic ion heating induced by lower-hybrid waves is examined. The modulation occurs either in the ion-cyclotron frequency because of the variation of the magnetic field in toroidal devices, or it can be externally imposed on the frequency of the lower-hybrid waves. It has already been observed numerically [Phys. Fluids 27, 184 (1984)] that a small variation in the ion-cyclotron frequency can induce velocity diffusion for wave amplitudes well below the stochasticity threshold in a uniform magnetic field. Here a detailed study reveals that to the lowest order in the small parameters, the modulational effects can be incorporated in a two-dimensional Hamiltonian. This allows the derivation of the new stochasticity thresholds. It is found that a small amount of modulation, Δω/ω≲1%, produces an order of magnitude reduction in the stochasticity threshold relative to the constant frequency case. The stochastic regime in velocity space also grows in size, resulting in a considerable increase of number of heated particles in the case of devices with modest aspect ratio. Both ion-cyclotron and wave-frequency modulation lead to similar results. The modulation of the wave frequency offers the ability to control and optimize the modulation parameters and is proposed as a method to enhance radio frequency (rf) heating.