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A multidimensional hybrid simulation model has been developed for use in studying plasma phenomena on extended time and distance scales. The model makes fundamental use of the small Debye length or quasineutrality assumption. The ions are modeled by particle-in-cell techniques, while the electrons are considered a collision-dominated fluid. Some electron inertial effects are retained. The fields are calculated in the nonradiative Darwin limit. The quasineutral counterpart of Poisson's equation is obtained by first summing the electron and ion momentum equations and then taking the quasineutral limit. The resulting elliptic equation correctly includes those electrostatic potentials which occur in sheath or ambipolar phenomena while neglecting the short-range electrostatic fields which give rise to plasma oscillations. This model has been implemented in a two-dimensional code QN2. A lower hybrid drift unstable equilibrium with parameters accessible to both hybrid and full-particle simulation has been selected as a test of the code and a demonstration of the model. Initial results indicate quite good agreement between the two simulation methods in linear growth rate and wave number.

A formulation of the electron momentum equation and Maxwell's field equations suitable for global solution in an r-z hybrid plasma simulation code has been derived. The assumption of zero electron inertia is made in the electron momentum equation and Maxwell's equations are used in the radiation-free or Darwin limit. These techniques make explicit use of the axisymmetric properties of the model to decouple the components of the model equations. Equations to self-consistently advance the electron temperature are not presently included in this scheme. The model equations which result from these considerations are two coupled, nonlinear, second order partial differential equations. These two equations are integrated in time by a noniterative ADI procedure along with the explicit particle-in-cell ion time integration procedure. The resulting nearly implicit electron-field algorithm treats wide variations in the local signal velocity without instability; this consideration is most important since pure vacuum regions are allowed. The global nature of the solution requires boundary conditions only on the boundaries of the simulation region; arbitrary intermixing of plasma vacuum regions requires only the simple detection of low density cells and does not require monitoring of plasma vacuum interfaces.

The numerical time integration of an initial value problem based upon the nonlinear Vlasov equation as applied to an axisymmetric, inhomogeneous plasma column has been developed. All six components of the electric and magnetic fields are advanced self-consistently in time. An assumption has been made which neglects purely electromagnetic modes. Each field contains a contribution from plasma source terms calculated by a Green's function technique as well as a boundary value contribution which may be time dependent. The Vlasov equation has been reduced to a convenient numerical form by an extension of the standard Fourier-Hermite expansion. Radial dependence is discretized. Results are presented on the streaming instability of the electrostatic column.