A new spherical tokamak TST-2 was constructed at the University of Tokyo and started operation in September 1999. Reliable plasma initiation is achieved with typically 1 kW of ECH power at 2.45 GHz. Plasma currents of up to 90 kA and toroidal fields of up to 0.2 T have been achieved during the initial experimental campaign. The ion temperature is typically 100 eV. Internal reconnection events (IREs) are often observed. The internal magnetic field measured at r/a = 2/3 indicated growth of fluctuations up to the 4 th harmonic, suggesting the existence of modes with several different mode numbers. In the presence of a toroidal field and a vertically oriented mirror field, noninductively driven currents of order 1 kA were observed with 1 kW of ECH power. The driven current increased with decreasing filling pressure, down to 3 × 10 −6 torr. A study of high harmonic fast wave (HHFW) excitation and propagation has begun. Initial results indicate highly efficient wave launching.

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.

In the present paper we consider the interaction between energetic ions and lower hybrid waves in tokamak plasmas and study the parametric dependence of the threshold condition for stochastic ion di usion. It is shown that the threshold condition as obtained in the work by Karney C. F. F. Karney, P h ys. Fluids 22, 2188 1979 may be not easily satis ed in present d a y large tokamaks, but can attained in small tokamaks with relatively modest levels of wave p o wer. I IntroductionIn a series of two papers published in 1978 and 1979, it has been shown that the movement of an ion in a uniform magnetic eld becomes stochastic in the presence of a perpendicularly propagating coherent electrostatic wave, if the wave amplitude exceeds a threshold 1, 2 . Due to the stochasticity the ion di uses in velocity space, and this di usion may be described by a di usion equation which also applies to the case of lower hybrid waves in the slow mode non-vanishing k k k ? , propagating in a weakly inhomogeneous magnetic eld 2 . The possibility of this di usion mechanism raised important questions related to the e ciency of proposed RF current drive s c hemes using lower hybrid LH waves 3, 4, 5 . In particular, it has been argued that in fusion reactors the presence of particles originated from fusion reactions would contribute to decrease the e ciency of the lower hybrid current drive, since part of the energy of the LH waves would be absorbed by the particles 1 . The potential importance of this interaction between LH waves and particles has motivated subsequent i n vestigations, and many examples may be found in the recent literature 6, 7 , 8 , 9 , 1 0 , 11, 12, 13 . Investigations have also been made by considering other kind of possible interactions, as the interaction between LH waves and a population of energetic ions generated by neutral beam injection 14, 1 5 , 16, 17 , and the interaction between LH waves and fast ions generated by I C w aves utilized for ion heating. Some experimental results on this subject are available, as those originated from relatively recent experiments conducted in the JET tokamak Joint European Torus 18, 1 9 . The results of these experiments provide evidence of signi cant absorption of LH waves by fast ions, and therefore con rm the convenience of further investigations on this important issue concerning the dynamics of particles or other energetic ions in the environment of a reactor, and the e ciency of the LH waves for radio frequency current drive.In the present paper we study particular features of the subject, considering the threshold condition for stochastic di usion of energetic ions, in a tokamak environment modelated by a plasma slab. We utilize the formalism proposed by Karney 2 , discussing the dependence of the threshold condition on some wave and plasma parameters, for large present d a y tokamaks and for small scale tokamaks, and compare the value of the electric eld predicted by the threshold condition with the wave electric eld inside the tokamak.

This paper discusses the interaction between energetic ions and lower hybrid waves in tokamak plasmas, presenting a numerical analysis which employs a quasilinear formalism appropriated for the situation in which ion stochastic di usion occurs. The results show that signi cant w ave-particle interaction may take place when a population of energetic ions is present in the plasma, in partial agreement with evidence from experimental results available in the literature.

In the present paper we discuss stochastic diffusion of energetic ions by a set of lower hybrid waves with frequencies close to each other and random phases which change along the time evolution of the system. We obtain efficient long term diffusion in velocity space, which is more representative of the diffusion produced by a continuous wave packet than the diffusion produced by a set of waves with random phases which are constant along the time evolution.