No abstract

The review is devoted to the discussion of the role of trapped particles for equilibrium, diffusion and stability of plamas in toroidal magnetic devices. The motion of single particles in a toroidal magnetic field, the neoclassical transport processes due to the trapping of particles and trapped-particle instabilities in toroidal geometry are discussed. The correspondence between the neoclassical theory of diffusion, the turbulent transport processes due to the instabilities and the existing experimental Tokamak data is discussed.

We give an analytical consideration of the relaxation of the distribution function for systems of particles with Coulomb interaction. It takes into account two-particle corre-1ations which correspond to formation of some macropartlcles~l.e~coherently moving regions. It is argued that such relaxation leads to the Lynden-BeQ distribution with an additional high-energy tail.Recently Lynden-Bell' has ax gued that relaxation of collisionless systems of charged particles or stellar systems shouM be some kind of chRotlc interchange of elements in phase spRce. The e1ements in phase space cannot overlap and therefore follow an exclusion px inciple. This leads to statistics of the Fermi-Dirac type. For the special case where the initial distribution function f is equal to unity over certain regions of phase space Rnd is zero outside these regions, the equilibrium distribution function is exactly equal to the Permi-Dix ac function.To check the Lynden-Bell theox'y, numex ical calculations were carried out' with a one-dimensional model. These calculations have shown that for simple initial conditions the quasiequilibrium 8tRte which ls x'eRched Rfter seve1 al plasma periods is close to the Fermi di. stribution with an additional high-enexgy tail. Por more com-pllcRted lnltlal coxldltloI18 the final d18trlbutlon deviates from the Fermi distribution.We shall discuss this problem analytically from the point of view suggested recently by Dupree's' and the authors'~idea on the formation of~acroparticles in a plasma. The relationship between this approach and quasilinear theory mill also be discussed.Fox' simplicity we consider an electron plasma which is homogeneous on the average except for some small initial perturbations. The evolution of these perturbations is described by the Vlasov equation -+v-VE =-E-= 9f SZ 8V Bf~e~Bfo -+v Vf = -E' Bt Vl 8V (4) In Pourier representation, neglecting slow variation of fo with time, we can write (4) in the form Bf (m-k v)f =yk. (5) Pl BV wllel e p ls tile potelltlal. We find fl'olll (5) e I -Bfowhel'e f2 ls all arbitrary solutloll of Eq. (5) witll zero on the right-band side. In fact, f, corresponds to some initial perturbati. on of the electron distribution function. The substitution of (6) into (2) gives us! where e is the weil-known dielectric constant:with self-consistent electric fieM E =-V'y, divE =-4we( JFd'v-n, ), whex e n = const is the density of heavy ions and I' is the distribution function. It is natural to suppose that after several plasma periods the evolution of electrons may be considered to be stochastic. We introduce the average value f, = {P) so that E = f, +f, where (f ) = 0. We find by averaging Eq. (I) Bf, e Bf~t (fo)B t teal 8Vwhere St(f,) denotes the collision termAssuming that perturbation f is not very large, we use for f an equation of the quasilinear type:4we' " P . Bfo iw5(&u k-v) k-Bv ikey from (7) in Eq. (3). It is convenient to separate the wave [h &m /v, h, where v, h is some average "thermal" velocity and no=(4 nwe/ )0' r'n] and nonwave (k&~/ o, v)1 region...

This paper presents the results of JET experiments aimed at studying the operational space of plasmas with a Type III ELMy edge, in terms of both local and global plasma parameters. In JET, the Type III ELMy regime has a wide operational space in the pedestal n e-T e diagram, and Type III ELMs are observed in standard ELMy H-modes as well as in plasmas with an internal transport barrier (ITB). The transition from an H-mode with Type III ELMs to a steady state Type I ELMy H-mode requires a minimum loss power, P TypeI. P TypeI decreases with increasing plasma triangularity. In the pedestal n e-T e diagram, the critical pedestal temperature for the transition to Type I ELMs is found to be inversely proportional to the pedestal density (T crit ∝ 1/n) at a low density. In contrast, at a high density, T crit , does not depend strongly on density. In the density range where T crit ∝ 1/n, the critical power required for the transition to Type I ELMs decreases with increasing density. Experimental results are presented suggesting a common mechanism for Type III ELMs at low and high collisionality. A single model for the critical temperature for the transition from Type III to Type I ELMs, based on the resistive interchange instability with magnetic flutter, fits well the density and toroidal field dependence of the JET experimental data. On the other hand, this model fails to describe the variation of the Type III n e-T e operational space with isotopic mass and q 95. Other results are instead suggestive of a different physics for Type III ELMs. At low collisionality, plasma current ramp