Stochastic diffusion of ions due to a finite set of lower hybrid waves

Abstract

In this paper we generalize the discussion on stochastic diffusion of energetic ions by lower hybrid waves by considering a case where a set of waves with similar frequencies is present in the system. In the particular case of a finite number of coherent waves, we show that the threshold for stochastic diffusion is reduced in comparison with the threshold in the one-wave case, and that the ensuing particle diffusion in velocity space occurs in periodic bursts along the time evolution. In the more general case of a set of waves with random phases, we have obtained even more efficient long-term diffusion in velocity space, for the same number of waves, although the initial diffusion rate can be smaller than in the case of coherent waves.

Chaotic particle heating due to an obliquely propagating wave in a magnetized plasma

“…There are several applications in which the wave-particle interaction arises, like in particle accelerators [1][2][3], free-electron devices [2,4], and heating and current generation in fusion devices [5,6], among others. While in some cases the phenomena can be described and understood by modeling the wave as a single monochromatic mode [3,[5][6][7], more generally the particle may interact with a spectrum of waves [8][9][10]. In particular, when the spectrum is broad and the group velocity is large, the wave can be well approximated by a series of periodic pulses [11].…”

“…Along the years many generalizations of the standard map have been proposed to include important effects, such as the relativistic mass variation of the particles as they gain energies comparable to their rest mass [11,15]. However, despite the fact that the wave-particle interaction in a vast number of systems takes place in the presence of an external magnetic field [2,3,[5][6][7][8][9][10], there was no map to describe such cases. The difficulty in deriving such maps is that while in the absence of a background magnetic field the canonical variables appear separately in different parts of the Hamiltonian-the momentum in the kinetic part only and the coordinate in the interacting part only-the presence of the magnetic field mixes the variables in the different parts * thalestr@gmail.com of the Hamiltonian, making the integration along one wave period more cumbersome.…”

Stochastic diffusion of energetic ions due to incoherent lower hybrid waves

“…In a recent paper we have investigated the transition between cases in which one coherent LH wave is present in the system, with amplitude below the stochasticity threshold, and cases with the presence of several LH waves of close frequencies, studying the appearance of stochasticity along this transition [8]. We have employed a generalization of Karney's approach, assuming that a finite number of waves is present in the system, forming a sufficiently narrow wave packet in k space [8].…”

“…We have employed a generalization of Karney's approach, assuming that a finite number of waves is present in the system, forming a sufficiently narrow wave packet in k space [8]. Despite the relative simplicity of the Hamiltonian obtained, the system dynamics has been shown to be complicated, originating interesting behavior which had not until quite recently been widely studied in the literature [9].…”

“…[8] has shown that in the particular case of a set of coherent waves the threshold for stochastic diffusion is reduced in comparison with the threshold in the one wave case, with the ensuing particle diffusion in velocity space occurring in periodic bursts along the time evolution. For a set of waves with random phases, the results appearing in Ref.…”