The Magnetized Plasma Sheath.

The sheath formed between a magnetized plasma and a particle absorbing wall is examined for the case in which the magnetic field intercepts the wall with a small angle 0^circ<epsilon<10 ^circ, where rm sin epsilon = {vec Bcdot nover | B |}, and n is the unit normal to the wall. The ions are modeled by a Maxwellian distribution which is modified by the condition that ions which hit the wall are absent. For the electrons it is sufficient to use a fluid description, including the effects of electron-neutral collisions. The transport of particles due to turbulent electrostatic fluctuations is modeled by a constant electric field which is perpendicular to both vec B and n. We have found that in the range of angles under consideration, there are two distinct regimes of sheath formation. If epsilon~| nu=nu/Omega_{e}, (i.e. grazing incidence) where nu is the electron neutral collision frequency and Omega_{e} is the electron cyclotron frequency, then the properties of the sheath are determined by the parameterlambda = {r_{it ci}v _{E{it y}}over D _epsilon[epsilon^2 + |nu]},where rm V_{rm E{it y}} is the cross field flow velocity due to the "turbulent" E times B drift, and D_{e} = T _{e}/mnu is the usual unmagnetized diffusion coefficient. If lambda < 1, the wall potential is negative and the sheath scales as an ion gyroradius. If lambda> 1, the wall potential is positive and the sheath is characterized by two scale lengths; a Debye length region adjacent to the wall, followed by an ion gyroradius region in the plasma interior. For epsilongg|nu, (i.e. oblique incidence) the potential at the wall is only weakly dependent on epsilon and is negative with respect to the plasma interior, with a magnitude close to that of the unmagnetized plasma. In addition, for this case, the sheath scale length is on the order of an ion gyroradius and is weakly dependent on epsilon; larger values of epsilon resulting in a slightly shorter scale length. The general techniques developed for describing the sheath have been used to estimate the floating potential of a small electrode in a magnetized plasma, and to determine the effects of boundaries on nonneutral plasma equilibria.