Kim Molvig

Realization of Fluid Boundary Conditions via Discrete Boltzmann Dynamics

We describe a novel way based on lattice-Boltzmann representation for realizing hydrodynamic boundary conditions at a solid surface. It is shown that using this approach the resulting physics properties are independent of the position and the orientation of the surface with respect to the lattice mesh. The fluxes of mass, energy as well as both normal and tangential momenta can be accurately controlled to correspond to various fluid dynamics situations.

Digital Physics Approach to Computational Fluid Dynamics: Some Basic Theoretical Features

We present an outline description of some fundamental theoretical properties in the Digital Physics lattice-gas algorithm.

Kinetic and collisional effects on the linear evolution of fast ignition relevant beam instabilities

The fast ignition scheme will involve the generation and transport of a relativistic electron beam, which may be subject to a number of instabilities that act to inhibit energy transport. This study will address the effects of collisions and the initial electron beam distribution on the linear evolution of these instabilities for theoretical distributions including the relativistic waterbag, the relativistic Maxwellian (Juttner), and the saddle point (low temperature) approximation of the relativistic Maxwellian. It will then be shown that a more physical distribution obtained from a 2D explicit particle-in-cell simulation of the laser-plasma interaction can be best modeled with a Juttner distribution, but well-approximated with a relativistic waterbag distribution. In sum, for all distributions of interest, collisions were found to have the ability to both suppress and enhance growth for the filamentary instability, while they only suppress growth for the two-stream instability.

Revised Knudsen-layer reduction of fusion reactivity

Recent work by Molvig et al. [Phys. Rev. Lett. 109, 095001 (2012)] examined how fusion reactivity may be reduced from losses of fast ions in finite assemblies of fuel. In this paper, this problem is revisited with the addition of an asymptotic boundary-layer treatment of ion kinetic losses. This boundary solution, reminiscent of the classical Milne problem from linear transport theory, obtains a free-streaming limit of fast ion losses near the boundary, where the diffusion approximation is invalid. Thermonuclear reaction rates have been obtained for the ion distribution functions predicted by this improved model. It is found that while Molvigs “Knudsen distribution function” bounds from above the magnitude of the reactivity reduction, this more accurate treatment leads to less dramatic losses of tail ions and associated reduction of thermonuclear reaction rates for finite fuel volumes.

Collisional damping for ion temperature gradient mode driven zonal flow

Zonal flow helps reduce and control the level of ion temperature gradient turbulence in a tokamak. The collisional damping of zonal flow has been estimated by Hinton and Rosenbluth (HR) in the large radial wavelength limit. Their calculation shows that the damping of zonal flow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, HR calculated the neoclassical polarization in the low and high collisionality limits. A new approach, based on an eigenfunction expansion of the collision operator, is employed to evaluate the neoclassical polarization and the zonal flow residual for arbitrary collisionality. An analytical expression for the temporal behavior of the zonal flow is also given showing that the damping rate tends to be somewhat slower than previously thought. These results are expected to be useful extensions of the original HR collisional work that can provide an effective benchmark for numerical codes for all regimes of collisionality.

Approximate models for the ion-kinetic regime in inertial-confinement-fusion capsule implosions

“Reduced” (i.e., simplified or approximate) ion-kinetic (RIK) models in radiation-hydrodynamic simulations permit a useful description of inertial-confinement-fusion (ICF) implosions where kinetic deviations from hydrodynamic behavior are important. For implosions in or near the kinetic regime (i.e., when ion mean free paths are comparable to the capsule size), simulations using a RIK model give a detailed picture of the time- and space-dependent structure of imploding capsules, allow an assessment of the relative importance of various kinetic processes during the implosion, enable explanations of past and current observations, and permit predictions of the results of future experiments. The RIK simulation method described here uses moment-based reduced kinetic models for transport of mass, momentum, and energy by long-mean-free-path ions, a model for the decrease of fusion reactivity owing to the associated modification of the ion distribution function, and a model of hydrodynamic turbulent mixing. The t...

Tail-ion transport and Knudsen layer formation in the presence of magnetic fields

Knudsen layer losses of tail fuel ions could reduce significantly the fusion reactivity of highly compressed cylindrical and spherical targets in inertial confinement fusion (ICF). With the class of magnetized ICF targets in mind, the effect of embedded magnetic fields on Knudsen layer formation is investigated for the first time. The modified energy scaling of ion diffusivity in magnetized hot spots is found to suppress the preferential losses of tail-ions perpendicular to the magnetic field lines to a degree that the tail distribution can be at least partially, if not fully, restored. Two simple threshold conditions are identified leading to the restoration of fusion reactivity in magnetized hot spots. A kinetic equation for tail-ion transport in the presence of a magnetic field is derived, and solutions to the equation are obtained numerically in simulations. Numerical results confirm the validity of the threshold conditions for restored reactivity and identify two different asymptotic regimes of the fusion fuel. While Knudsen layer formation is shown to be suppressed entirely in strongly magnetized cylindrical hot spot cavities, uniformly magnetized spherical cavities demonstrate remnant, albeit reduced, levels of tail-ion depletion.

Electron transport in a collisional plasma with multiple ion species

A generalization of the Braginskii electron fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. A description of the plasma ions with disparate masses is also discussed.

Photon coupling theory for plasmas with strong Compton scattering: Four temperature theory

When an equimolar mixture of deuterium (D) and tritium (T) at high density undergoes fusion burn, the system becomes extremely nonequilibrium. The ion temperature rises much higher than the electron temperature which, in turn, is much higher than the radiation temperature. Accurately simulating this nonequilibrium burn process has previously required a multigroup representation of the radiation field. Although simulating this D–T burn with a simple three temperature model (3T) also results in significant departures from thermal equilibrium, the ion and electron temperature histories from the 3T simulations are much lower than from the multigroup simulations. In this paper, a theory that overcomes the deficiencies of the 3T model in simulating burn of high density D–T is developed. The primary deficiency of the 3T model for this physical system is with the treatment of the Compton scattering energy exchange. The theory here developed culminates in a four temperature model (4T) which describes the radiation...

KINETIC MODEL OF A HELICON PLASMA SOURCE FOR VASIMR

Plasma kinetic model for the analysis of composition of partially ionized hydrogen gas in the helicon plasma source used in the VASIMR thruster is developed. Zero dimensional model provides a calculation of the main parameters of the helicon hydrogen discharge. It solves a set of 14 coupled non-linear plasma chemistry equations with relevant boundary conditions. To calculate mean velocity of the gas flow we use hybrid mixed-collisional pipe flow model. Numerical results are benchmarked against current VX-1 data for hydrogen, deuterium and helium discharges. They also used to explain some of the experimental observations. Next the model is used to predict helicon plasma source performance in space, including next step VF-10 configuration. The following effects are analyzed: gas pre-heating, catalytic break of molecules, role of vacuum chamber pressure and baffles to retain gas. We discuss a possibility of fully kinetic simulation of multidimensional gas flow in a channel and relative importance of various gas-plasma collisions.