Alfvén spectra in a reversed-shear tokamak plasma with a population of energetic ions exhibit a quasiperiodic pattern of primarily upward frequency sweeping (Alfvén cascade). Presented here is an explanation for such asymmetric sweeping behavior which involves finding a new energetic particle mode localized around the point of zero magnetic shear.The presence of energetic particles in a plasma can alter its behavior from that predicted by conventional magnetohydrodynamics (MHD) theory in two ways. First these particles can perturbatively destabilize a basic MHD mode. Alternatively, a sufficient number of these particles can nonperturbatively alter the very structure of the MHD modes. This latter behavior is relevant to certain shear Alfvénic perturbations often called energetic particle modes (EPM) [1][2][3]. In addition, in recent years there has been a great deal of interest in plasmas with reversed magnetic shear profiles, where transport and MHD stability properties have been shown to improve [4,5]. It is important for fusion experiments in shear reversed fields to understand the collective properties associated with energetic particles. Experiments in JT-60U [6] and JET [7] have investigated reversed shear regimes and have produced energetic particles with ion cyclotron heating (ICRH) [8]. Alfvén modes emerge in these experiments but their spectrum is often puzzling. This paper presents an example of how a purely MHD description is incompatible with the data while a description which accounts for the nonperturbative energetic particle response explains a large part of the data. The interpretation suggests a sensitive method to experimentally determine q min (the minimum safety factor) in reversed magnetic shear tokamaks.The JET experiments exhibit upward frequency sweeping phenomena, named Alfvén wave cascades (ACs) [9] (see Fig. 1a). Each cascade consists of several modes with different toroidal mode numbers and different frequencies.The toroidal mode numbers vary from n 1 to n 6. The frequency starts from 20 40 kHz and increases up to 100 120 kHz which is the toroidal Alfvén eigenmode (TAE) gap frequency. Similar data were obtained some time ago on JT-60U [6]. In both the JET and JT-60U data, the modes with higher toroidal mode numbers exhibit a more rapid frequency sweeping, and the higher n modes re-occur more often than the lower n modes. It is striking that downward frequency sweeping either does not appear, or appears only rarely. In both JET and JT-60U experiments, the minimum value of q decreases in time and a population of energetic ions is created by ICRH heating.ACs resemble the global Alfvén eigenmode [10,11], whose frequency is close to the local value of the Alfvén wave frequency at the zero shear point in minor radius, r r 0 , i.e., 2pf AC ഠ v A ͑r 0 ͒ ϵ jk k ͑r 0 ͒jV A ͑r 0 ͒, where V A is Alfvén velocity and k k is the wave-vector component along the equilibrium magnetic field B 0 . To avoid strong damping, the frequency f AC needs to be somewhat larger than v A ͑r 0 ͒ if v A ͑r͒ has a maxi...

Persistent rapid up and down frequency chirping modes with a toroidal mode number of zero (n = 0) are observed in the JET tokamak when energetic ions, in the range of several hundred keV, are created by high field side ion cyclotron resonance frequency heating. Fokker-Planck calculations demonstrate that the heating method enables the formation of an energetically inverted ion distribution which supplies the free energy for the ions to excite a mode related to the geodesic acoustic mode. The large frequency shifts of this mode are attributed to the formation of phase space structures whose frequencies, which are locked to an ion orbit bounce resonance frequency, are forced to continually shift so that energetic particle energy can be released to counterbalance the energy dissipation present in the background plasma.

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Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfvén perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n=1 to n=6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfvén eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfvén cascades and the evolution of the Alfvén continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfvén continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfvén spectroscopy for studying q(r). Modeling shows that the Alfvén cascade occurs when the Alfvén continuum frequency has a maximum at the zero shear point. Interpretation of the Alfvén cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping.

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High fusion power experiments using DT mixtures in ELM-free H mode and optimized shear regimes in JET are reported. A fusion power of 16.1 MW has been produced in an ELM-free H mode at 4.2 MA/3.6 T. The transient value of the fusion amplification factor was 0.95±0.17, consistent with the high value of nDT(0)τEdiaTi(0) = 8.7 × 1020±20% m-3 s keV, and was maintained for about half an energy confinement time until excessive edge pressure gradients resulted in discharge termination by MHD instabilities. The ratio of DD to DT fusion powers (from separate but otherwise similar discharges) showed the expected factor of 210, validating DD projections of DT performance for similar pressure profiles and good plasma mixture control, which was achieved by loading the vessel walls with the appropriate DT mix. Magnetic fluctuation spectra showed no evidence of Alfvénic instabilities driven by alpha particles, in agreement with theoretical model calculations. Alpha particle heating has been unambiguously observed, its effect being separated successfully from possible isotope effects on energy confinement by varying the tritium concentration in otherwise similar discharges. The scan showed that there was no, or at most a very weak, isotope effect on the energy confinement time. The highest electron temperature was clearly correlated with the maximum alpha particle heating power and the optimum DT mixture; the maximum increase was 1.3±0.23 keV with 1.3 MW of alpha particle heating power, consistent with classical expectations for alpha particle confinement and heating. In the optimized shear regime, clear internal transport barriers were established for the first time in DT, with a power similar to that required in DD. The ion thermal conductivity in the plasma core approached neoclassical levels. Real time power control maintained the plasma core close to limits set by pressure gradient driven MHD instabilities, allowing 8.2 MW of DT fusion power with nDT(0)τEdiaTi(0) ≈ 1021 m-3 s keV, even though full optimization was not possible within the imposed neutron budget. In addition, quasi-steady-state discharges with simultaneous internal and edge transport barriers have been produced with high confinement and a fusion power of up to 7 MW; these double barrier discharges show a great potential for steady state operation. © 1999, Euratom