Evstati Evstatiev

Variational formulation of macro-particle plasma simulation algorithms

A variation formulation of macro-particle kinetic plasma models is discussed. In the electrostatic case, the use of symplectic integrators is investigated and found to offer advantages over typical generic methods. For the electromagnetic case, gauge invariance and momentum conservation are considered in detail. It is shown that, while the symmetries responsible for these conservation laws are broken in the presence of a spatial grid, the conservation laws hold in an average sense. The requirements for exact invariance are explored and it is shown that one viable option is to represent the potentials with a truncated Fourier basis.

A new method for analyzing line-tied kink modes in cylindrical geometry

A new method for studying linear stability of the m=1 (kink) mode in a cylinder with line-tied boundary conditions is presented. The method is applicable to both resistive and ideal MHD. It is based on expansion in one-dimensional eigenfunctions depending on the radius, satisfying boundary conditions on the cylindrical axis and radial wall. The boundary conditions at the end plates are satisfied by a sum of such radial eigenfunctions. The spectrum of possibly complex axial eigenvalues k is studied and is shown to consist of a continuum part and a discrete part in ideal MHD. Only the discrete part is used to give an approximation to the complete two-dimensional eigenfunction. The method is applied to a special equilibrium magnetic field with constant field line pitch. The role of the individual radial eigenfunctions is explained. It is shown that our method reproduces previously found values of the critical pitch (at marginal stability) for a plasma column in vacuum. The method also suggests important diff...

Variational Formulation of Macroparticle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macroparticle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work, discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macroparticles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with lab frame coordinates or moving window coordinates; the latter can greatly improve computational efficiency for studying some types of laser-plasma interactions. The primary advantage of the variational approach is the preservation of Lagrangian symmetries, which in our case leads to energy conservation and thus avoids difficulties with grid heating. In addition, this approach decouples particle size from grid spacing and relaxes restrictions on particle shape, leading to low numerical noise. The variational approach also guarantees consistent approximations in the equations of motion and is amenable to higher order methods in both space and time. We restrict our attention to the 1.5-D case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.

Line-tied kink modes in cylindrical equilibria with magnetic shear

The method described by Evstatiev et al. [Phys. Plasmas 13, 072902 (2006)] to study the linear stability of line-tied modes in cylindrical geometry is applied to screw pinch equilibria with magnetic shear. The method is based on an expansion in eigenfunctions which depend on radius, and for ideal magnetohydrodynamics (MHD) the inclusion in the expansion of singular eigenfunctions (originating from a continuum) is necessary. The method is also applied to study scaling laws for large cylinder lengths L. It is found that the width of the internal layer of the radial displacement for the line-tied mode scales asymptotically as L−2, consistent with the so-called two-mode approximation. This result is valid in the context of both ideal and resistive MHD and is obtained both analytically and numerically.

Resistive effects on line-tied magnetohydrodynamic modes in cylindrical geometry

An investigation of the effect of resistivity on the linear stability of line-tied magnetohydrodynamic (MHD) modes is presented in cylindrical geometry, based on the method recently developed in the paper by Evstatiev et al. [Phys. Plasmas 13, 072902 (2006)]. The method uses an expansion of the full solution of the problem in one-dimensional radial eigenfunctions. This method is applied to study sausage modes (m=0, m being the poloidal wavenumber), kink modes (m=1), and m=2 modes. All these modes can be resistively unstable. It is found that m≠0 modes can be unstable below the ideal MHD threshold due to resistive diffusion of the field lines, with growth rates proportional to resistivity. For these resistive modes, there is no indication of tearing, i.e., current sheets or boundary layers due to ideal MHD singularities. That is, resistivity acts globally on the whole plasma column and not in layers. Modes with m=0, on the other hand, can exist as tearing modes if the equilibrium axial magnetic field rever...

The role of resistivity on line-tied kink modes in cylindrical geometry

An investigation of the effect of resistivity on linear line-tied kink modes is presented in cylindrical geometry. A region near marginal stability, where the line-tied system is stable in ideal magnetohydrodynamics but unstable with resistivity, is shown. In this region, the growth rate is found to be proportional to resistivity. There is no signature of the tearing-like scaling, which occurs in the corresponding system with periodic boundary conditions, or of the formation of boundary layers near the end plates. Instead, the resistive scaling is due to global resistivity, leading to imperfect line-tying. This feature is common to equilibrium pitch profiles that increase or decrease monotonically with radius and is not influenced by viscosity.

Space charge neutralization in inertial electrostatic confinement plasmas

A major issue for electron injected inertial electrostatic confinement (IEC) devices is space charge neutralization. A new formalism is developed that will allow this neutralization to occur for both oscillating and steady-state IEC plasmas. Results indicate that there are limits on the amount of compression that can be achieved by oscillating plasmas while simultaneously maintaining space charge neutralization and parabolic background potential. For steady-state plasmas, there are no such limits and space charge neutralization can be achieved even when the plasma becomes quasineutral.

Analytical and numerical modeling of radio frequency electron cyclotron resonance power absorption within the cold plasma picturea)

We present a one dimensional model of radio frequency (RF) power absorption in electron cyclotron resonance (ECR) ion sources based on a modified cold plasma dielectric description. The absorption is modeled by an imaginary collision frequency (damping coefficient) whose value is related to physical parameters such as magnetic field and its spatial derivative, electron temperature, and RF frequency and power. Properties and scaling laws of ECR power absorption are discussed within this model. Numerical benchmarking against a more accurate kinetic plasma code shows very good agreement.

Two-dimensional electron-electron two-stream instability of an inertial electrostatic confinement device

Theoretical works by Barnes and Nebel [D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998); R. A. Nebel and D. C. Barnes, Fusion Technol. 38, 28 (1998)] have suggested that a tiny oscillating ion cloud (referred to as the periodically oscillating plasma sphere or POPS) may undergo a self-similar collapse in a harmonic oscillator potential formed by a uniform electron background. A major uncertainty in this oscillating plasma scheme is the stability of the virtual cathode that forms the harmonic oscillator potential. The electron-electron two-stream stability of the virtual cathode has previously been studied with a fluid model, a slab kinetic model, a spherically symmetric kinetic model, and experimentally [R. A. Nebel and J. M. Finn, Phys. Plasmas 8, 1505 (2001); R. A. Nebel et al., Phys. Plasmas 12, 040501 (2005)]. Here the mode is studied with a two-dimensional particle-in-cell code. Results indicate stability limits near those of the previously spherically symmetric case.

A particle-in-cell Monte Carlo code for electron beam ion source simulation

FAR-TECH, Inc., has developed a particle-in-cell Monte Carlo code (EBIS-PIC) to model ion motions in an electron beam ion source (EBIS). First, a steady state electron beam is simulated by the PBGUNS code (see http://far-tech.com/pbguns/index.html). Then, the injected primary ions and the ions from the background neutral gas are tracked in the trapping region using Monte Carlo method. Atomic collisions and Coulomb collisions are included in the EBIS-PIC model. The space charge potential is updated by solving the Poisson equation each time step. The preliminary simulation results are presented and compared with BNL electron beam test stand (EBTS) fast trapping experiments.