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Summary form only given. A new type of "smart PIC" algorithm, intended to bridge the gap between Eulerian fluid and kinetic regimes, is now being used for a variety of applications in ICF and weapon effects. The CPK method (complex particle kinetic) concept [Hewett, 2003] uses an ensemble of small, fluid-like macro-particles to represent particle distributions in phase space. These macro-particles are Gaussian-shaped in both position and velocity with internal parameters such as width, thermal velocity, total mass and charge in addition to the traditional PIC like Lagrangian location and drift velocity. Time evolution is modeled by a combination of Lagrangian motion and internal evolution within each individual macro-particle. In regions of "high activity", macro-particles are aggressively fragmented in phase space to probe for emerging kinetic features and aggressively merged, for economy, if interesting features fail to materialize. Exploiting the shape of the CPK particle, fragmentation in both position and velocity space can be accomplished without loss of significant phase space information. Fragmentation preserves the kinetic capabilities of PIC; merging dramatically shrinks the number of particles in non-kinetic or collisional regions. In collision-dominated regimes, merging naturally produces a few Lagrangian particles that act much as nodes in free-Lagrangian hydrodynamics. Recent improvements [Larson, 2003], allow inter-particle interactions between those particles within a mean-free-path, thus naturally including partially-collisional effects that go over to collision-dominated physics, as the mean-free-path becomes less that the particle width. Applications relevant to our principal applications will be presented

A novel HIF code, FOCI, combines the capabilities of several codes: (1) the x,y envelope equations are integrated in the axial direction, (2) an optimizer varies selected transport system parameters to make the envelope satisfy weighted constraints, (3) transverse particle motion can be followed simultaneously, (4) the E field used for the particle advance is computed from Poisson's equation using the local beam charge density, as input, and (5) longitudinal velocity variations can be included in the particle description. >

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 stable lifetimes of many field-reversed configuration (FRC) experiments have been observed to be limited by the onset of the m = 2 rotational instability. The origin of the rotation which drives this instability is investigated with the aid of hybrid simulation methods. The loss of particles with guiding centres on open field lines is found to lead to localized rotation near the separatrix and this effect is found to be enhanced by end-shorting of the radial electric field outside the separatrix. In simulations allowing azimuthal variation the velocity shear is eventually relaxed so that the bulk of the plasma begins to rotate. These simulations also show that the m = 2 instability does not appear as long as rotation is localized near the separatrix. It is found that by increasing the separatrix radius it is possible to significantly delay the transfer of rotation from the separatrix, hence delaying the onset of the m = 2 instability.

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.