The effect of a magnetic field on the transition layer between a plasma and an absorbing wall is studied. A numerical model is used which simulates the motion of plasma particles in the electric and magnetic fields for a prescribed particle influx at the plasma boundary. Bohm’s condition for the existence of a monotonic profile of the layer is generalized. The transition layer proves to have a double structure comprising a quasineutral magnetic presheath preceding the electrostatic Debye sheath. The magnetic presheath scales with the ion gyroradius at the sound speed and with the angle of the magnetic field. The total electric potential drop between plasma and wall proves to be fairly insensitive to the magnitude and angle of the magnetic field.

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Turbulent heating and stabilization of the ion sound instability is investigated by twodimensional computer simulation. Quasilinear rather than nonlinear effects determine the evolution of the instability. The instability is quenched by flattening of the electron distribution and the formation of a high-energy ion tail.Numerous stabilization mechanisms have been proposed for the current-driven ion sound instability. 1 "* 5 We have done extensive simulation studies in order to provide a test for these basic predictions. 6 The two-dimensional code has been described previously. 7 Specifically for the purpose of testing nonlinear theories of stabilization, we have made runs in which the ratio between drift velocity and electron thermal velocity was kept constant, in addition to runs with constant current. In the same vein we discuss the case of a current perpendicular to a weak magnetic field (fy/o> e = 0.04). The magnetic field (perpendicular to the plane of computation) has a very small effect on wave dispersion, but keeps the electron distribution isotropic. (In the case of a current along a magnetic field, further complicated dynamical effects are added by the formation of an electron runaway tail.)We find that for a wide range of initial parameters the growth phase of the instability is followed by the decay of the wave energy W , the return of the fluctuation level W/nT e to the thermal level, 8 and termination of heating in typically (100-200)a) i " 1 . Clearly, in the case of constant current, the growth phase of the instability must terminate at the latest when the phase velocity reaches the drift velocity, w«c s = (T e /M) 1/2 , The runs with constant u/c s , however, show quench-ing in much the same way; see Fig. 1. It is seen that in this case the plasma enters a regime in which the macroscopic parameters remain constant.Nonlinear theories of stabilization generally determine a quasisteady fluctuation level W/nT e as a function of m/M, u/v ey and T e /T t from the condition that the nonlinear damping just balances the linear growth rate, y = y L + y NL = 0. Actually, for (*/dt)ln(W/nT e ) = W/W-T e /T, = 0 9 W/W=2y must be balanced by the electron heat-FIG. 1. Wave energy W, fluctuation level W/nT e , T e , and T i /T e for a typical run. M/m=100, (T^T^ = 0.02, w/v e = 0.75. 1231

The scrape off layer (SOL) of a confined plasma (Fig. la) is in many respects in a state far from thermodynamic equilibrium: -The energy diffusing outward from the plasma core across the separatrix is condensed in the thin SOL to a strong energy flux along the magnetic field.-The recycling of cold neutrals from the limiter or divertor target gives rise to a strong temperature gradient from the hot midplane region to the relatively cold recycling zone.-For long mean free path length in the plasma relative to the extension of the recycling zone the thermalization in the recycling zone may be incomplete.-The potential gradient length in the sheath in front of the target is small as compared to the mean free path length; the velocity distributions of ions and electrons as determined by the electric field are far from being Maxwellians there.Thus the follwing topics will be discussed in this paper:-Parallel transport (electron heat flow, ion viscosity) -Recycling -Sheath structure (grazing incidence of magnetic field, secondary electrons).-Boundary conditions for fluid models Numerical illustrations for these kinetic effects are given from a Id particle-in-cell code including In studying kinetic effects in the SOL one is interested in basic features in velocity space rather than in an exact modelling of the spatial situation. The higher dimensionality due to inclusion of v-space is achieved on the expense of a simplified geometry in configuration space: The axially symmetric SOL is straightened to a prism limited by two target plates a3 shown in Fig. lb

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