It is shown in this paper that turbulence propagation can be due to toroidal or non-linear mode coupling. An analytical analysis indicates that the toroidal coupling acts through convection while the non-linear effects induce diffusion. Numerical simulations suggest that the toroidal propagation is usually the faster process, except perhaps in some highly turbulent regimes. A consequence is the possibility of non-local effects on the fluctuation level and the associated transport.
The fluid theory of electrostatic perturbations in a scrape-off layer (SOL) plasma is analysed. The main difficulty is that the edge is theoretically found to be stable, while experimentally it is unstable. A possible explanation relies on the fact that the commonly used ballooning representation is not correct in the SOL. An alternative representation is proposed which reproduces the instability of the edge in several simple configurations and explains many experimental features.
The question of heating a tokamak plasma by means of electromagnetic waves in the ion cyclotron range of frequencies (ICRF) is considered in the perspective of large rf powers and in the low collisionality regime. In such a case, the quasilinear theory (QLT) is validated by the Hamiltonian dynamics of the wave–particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows derivation of the rf diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker–Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. The Fokker–Planck equation is then given a variational form from which a solution is derived in the form of a semianalytical trial function of three parameters: the percentage of resonant particles contained in the tail, an isotropic width ΔT, and an anisotropic width ΔP. This solution is successfully tested against real experimental observations. It is shown that in the case of the JET tokamak [Plasma Phys. Controlled Fusion 30, 1467 (1988)] the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that from a bounce-averaged prediction. This may actually be an advantage for machines like JET [Plasma Phys. Controlled Fusion 30, 1467 (1988)] considering the energy range required to simulate the α-particle behavior in a relevant fusion reactor.
The electromagnetic perturbation produced through a set of antennas in a tokamak plasma is studied near the ion cyclotron resonances and the two-ion hybrid resonance. Using an appropriate variational principle, it is possible to derive ' the perturbed field (thecompressional wave and the converted torsional wave) with the help of relatively smooth test functions of the compressional type. The method produces conditions under which the variational functional L, an extremum with respect to the perturbation, can be written in a suitable manner for computer handling. Moreover, this functional provides an expression for the power damped by the thermal motion of particles, and in the two-ion hybrid regime it provides the power coupled to the converted wave. The ion cyclotron resonance leads to different regimes for the ratio of the parallel scalelength, X, of the field and the intrinsic parallel scale of the resonance, X £ , with X £ % l v |/V||W c l 1/2 . The usual WKB formulas used by previous authors appear to be limited to the case X < X c only, and new formulas are given for X > X . In the mode conversion case, the method generalizes Budden's results, with restrictions taking into account the non-uniformity effects along the resonance surface.
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