J. U. Brackbill

A continuum method for modeling surface tension

Abstract A new method for modeling surface tension effects on fluid motion has been developed. Interfaces between fluids of different properties, or “colors,” are represented as transition regions of finite thickness, across which the color variable varies continuously. At each point in the transition region, a force density is defined which is proportional to the curvature of the surface of constant color at that point. It is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero. The continuum method eliminates the need for interface reconstruction, simplifies the calculation of surface tension, enables accurate modeling of two- and three-dimensional fluid flows driven by surface forces, and does not impose any modeling restrictions on the number, complexity, or dynamic evolution of fluid interfaces having surface tension. Computational results for two-dimensional flows are given to illustrate the properties of the method.

Adaptive zoning for singular problems in two dimensions

Abstract Winslows method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh. Through simple analysis and numerical examples, the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems.

FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions

A method is presented for calculating fluid flow in two dimensions using a full particle-in-cell representation on an adaptively zoned grid. The method has many interesting properties, among them an almost total absence of numerical dissipation and the ability to represent large variations in the data. The method is described using a standard formalism and its properties are illustrated by supersonic flow over a step and the interaction of a shock with a thin foil.

An implicit method for electromagnetic plasma simulation in two dimensions

Abstract A new method for modeling low-frequency plasma phenomena is presented. The method uses an implicit formulation of the Vlasov-Maxwell equations to relax restrictions on the time-step and mesh spacing so that larger values which correspond to the frequencies and wavelengths of interest can be used. As a result, the range of length and time scales accessible to plasma simulation is increased by orders of magnitude. The algorithm, as embodied in a new code VENUS for electromagnetic plasmas in two dimensions, is described, its stability and accuracy analyzed through linear and nonlinear analysis, and its properties, including suppression of the finite grid instability, illustrated through its application to the Weibel instability.

Collisionless magnetic reconnection in the presence of a guide field

The results of kinetic simulations of magnetic reconnection in Harris current sheets are analyzed. A range of guide fields is considered to study reconnection in plasmas characterized by different β values, β>me/mi. Both an implicit particle-in-cell (PIC) simulation method and a parallel explicit PIC code are used. Simulations with mass ratios up to the physical value are performed. The simulations show that the reconnection rate decreases with the guide field and depends weakly on the mass ratio. The off-diagonal components of the electron pressure tensor break the frozen-in condition, even in low β plasmas. In high β plasmas, evidence is presented that whistler waves play a key role in the fast reconnection physics, while in low β plasmas the kinetic Alfven waves are important. The in-plane and the out-of-plane ion and electron motion are also considered, showing that they are influenced by the mass ratio and the plasma β.

Nonlinear evolution of the lower‐hybrid drift instability

The results of simulations of the lower‐hybrid drift instability in a neutral sheet configuration are described. The simulations use an implicit formulation to relax the usual time step limitations and thus extend previous explicit calculations to weaker gradients, larger mass ratios, and long times compared with the linear growth time. The numerical results give the scaling of the saturation level, heating rates, resistivity, and cross‐field diffusion and a demonstration by comparison with a fluid electron model that dissipation in the lower‐hybrid drift instability is caused by electron kinetic effects.

A kinetic theory for the drift-kink instability

We have developed a linear two-dimensional kinetic theory, which is motivated by recent results for the drift-kink instability. The theory predicts plasma instability for large values of ion-electron temperature ratios, Ti/Te, moderate drift speeds, and large ion-electron mass ratios, mi/me, corresponding to conditions in the near-Earth region of the magnetotail neutral sheet. The growth rate predicted by the theory is in good agreement with nonlinear plasma simulations (but the mode structure is not), including linear growth rates obtained with an implicit, electromagnetic simulation with realistic ion-electron mass ratio.

Influence of the lower hybrid drift instability on the onset of magnetic reconnection

Two-dimensional and three-dimensional kinetic simulation results reveal the importance of the lower-hybrid drift instability (LHDI) to the onset of magnetic reconnection. Both explicit and implicit kinetic simulations show that the LHDI heats electrons anisotropically and increases the peak current density. Linear theory predicts these modifications can increase the growth rate of the tearing instability by almost two orders of magnitude and shift the fastest growing modes to significantly shorter wavelengths. These predictions are confirmed by nonlinear kinetic simulations in which the growth and coalescence of small scale magnetic islands leads to a rapid onset of large scale reconnection.

Nonlinear evolution of the lower hybrid drift instability: Current sheet thinning and kinking

Through numerical plasma simulations using the implicit code CELESTE3D [G. Lapenta and J. U. Brackbill, Nonlinear Processes Geophys. 7, 151 (2000)], the development of kink modes in a Harris current sheet is investigated, and their possible nonlinear interaction with the lower hybrid drift instability (LHDI) is considered. Consistent with earlier work, the rapid development of a short wavelength LHDI is observed, followed by the slow development of long wavelength current sheet kinking. The growth of kink modes is in agreement with the linear theory for the drift kink instability only at very small mass ratios (mi/me=16). At more realistic mass ratios, the growth rate exceeds that predicted by linear theory. A thorough investigation of the dependence of current sheet kinking on ion/electron mass and temperature ratios, and current sheet thickness reveals that the growth of kink modes is unaffected by current sheet thinning, but is strongly dependent on the ion/electron temperature ratio. The saturation am...

Kinetic approach to microscopic-macroscopic coupling in space and laboratory plasmas

Kinetic plasma simulation typically requires to handle a multiplicity of space and time scales. The implicit moment particle in cell (PIC) method provides a possible route to address the presence of multiple scales effectively. Here, a new implementation of the implicit moment method is described. The present paper has two goals. First, the most modern implementation of the implicit moment method is described. While many of the algorithms involved have been developed in the past, the present paper reports for the first time how the implicit moment method is currently implemented and what specific algorithms have been found to work best. Second, we present the CELESTE3D code, a fully electromagnetic and fully kinetic PIC code, based on the implicit moment method. The code has been in use for a number of years but no previous complete description of its implementation has been provided. The present work fills this gap and introduces a number of new methods not previously presented: a new implementation of t...