arXiv subjects

E. G. Evstatiev

Publications and source records attributed to E. G. Evstatiev.

8 recordsLinked to original sources

arXiv2025

Non-local, diamagnetic electromagnetic effects in magnetically insulated transmission lines

We identify the time-dependent physics responsible for the critical reduction of current losses in magnetically insulated transmission lines (MITLs) due to uninsulated space charge limited (SCL) currents of electrons emitted by field stress. A drive current of sufficiently short pulse length introduces a strong enough time dependence that steady state results alone become inadequate for the complete understanding of current losses. The time-dependent physics can be described as a non-local, diamagnetic electromagnetic response of space charge limited currents. As the pulse length is increased or equivalently, the MITL length reduced, these time-dependent effects diminish and current losses converge to those predicted by the well-known Child-Langmuir law in the external (vacuum) fields. We present a simple one-dimensional (1D) model that encapsulates the essence of this physics. We find excellent agreement with 2D particle-in-cell (PIC) simulations for two MITL geometries, Cartesian parallel plate and azimuthally symmetric straight coaxial. Based on the 1D model, we explore various scaling dependencies of MITL losses with relevant parameters, e.g., peak current, pulse length, geometrical dimensions, etc. We propose an improved physics model of magnetic insulation in the form of a Hull curve, which could also help improve predictions of current losses by common circuit element codes, such as BERTHA. Lastly, we describe how to calculate temperature rise due to electron impact within the 1D model.

physics.plasm-ph↗

arXiv2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

We analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We describe kernel density estimation for continuous values of the spatial variable, $x$, and compute the covariance matrix for uniform true density. The band width of the covariance matrix is related to the width of the kernel. We find the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step. The effect of these negative correlations on the electric field, computed by Gauss's law, is that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge. For non-constant density still with continuous $x$, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length $l$ and kernel width $h$, having too few particles within $h$ leads to too much variance; for $h$ large relative to $l$, there is too much smoothing of the density. The optimum between these two limits is found by BVO. We repeat the analysis for $x$ discretized on a grid, connecting particle shapes and estimation kernels. If the particle shape satisfies a sum rule, the charge deposited on the grid is conserved exactly. Particle shapes expressed as the convolution of a kernel with another kernel that satisfies the sum rule also obey the sum rule. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. We show good agreement with numerical computations.

physics.plasm-ph↗

arXiv2014

Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation

We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low's Lagrangian or on a Hamiltonian with a non-canonical Poisson bracket. The useful property of this variational principle is that it allows independent transformations of particle coordinates and velocities, i.e., transformations in particle phase space. With such transformations, a finite degree-of-freedom drift-kinetic action is obtained through time-averaging of the finite degree-of-freedom fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads to a self-consistent, macro-particles and fields numerical model. Since the computational particles utilize only guiding center coordinates and velocities, there is a large computational advantage in the time integration part of the algorithm. Numerical comparison between the time-averaged fully-kinetic and drift-kinetic charge and current, deposited on a computational grid, offers insight into the range of validity of the model. Being based on a variational principle, the algorithm respects the energy conserving property of the underlying continuous system. The development in this paper serves to further emphasize the advantages of using variational approaches in plasma particle simulations.

physics.plasm-ph↗

arXiv2014

Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398, 2013], the discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macro-particles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with both 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. Additionally, 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 1-1/2 dimensional case (one coordinate and two momenta). Simulations are performed with the new models and demonstrate energy conservation and low noise.

physics.comp-ph↗

arXiv2012

Variational formulation of particle algorithms for kinetic plasma simulations

Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not conserve total energy, which may lead to spurious numerical heating (grid heating). Its overall accuracy is at most second due to the nature of the force interpolation between grid and particle position. Energy-conserving algorithms do not exhibit grid heating, but because their formulation uses potentials, computationally undesirable matrix inversions may be necessary. In addition, compared to PIC algorithms for the same accuracy, these algorithms have higher numerical noise due to the restricted choice of particle shapes. Here we formulate time-explicit, finite-size particle algorithms using particular reductions of the particle distribution function. These reductions are used in two variational principles, a Lagrangian-based and a Hamiltonian-based in conjunction with a non-canonical Poisson bracket. The Lagrangian formulations here generalize previous such formulations. The Hamiltonian formulation is presented here for the first time. Many drawbacks of the two classes of particle methods are mitigated. For example, restrictions on particle shapes are relaxed in energy conserving algorithms, which allows to decrease the numerical noise in these methods. The Hamiltonian formulation of particle algorithms is done in terms of fields instead of potentials, thus avoiding solving Poisson's equation. An algorithm that conserves both energy and momentum is presented. Other features of the algorithms include a natural way to perform coordinate transformations, the use of various time integrating methods, and the ability to increase the overall accuracy beyond second order, including all generalizations.

physics.plasm-ph↗

arXiv1999

The complex Toda chains and the simple Lie algebras - solutions and large time asymptotics -- II

We propose a compact and explicit expression for the solutions of the complex Toda chains related to the classical series of simple Lie algebras g. The solutions are parametrized by a minimal set of scattering data for the corresponding Lax matrix. They are expressed as sums over the weight systems of the fundamental representations of g and are explicitly covariant under the corresponding Weyl group action. In deriving these results we start from the Moser formula for the A_r series and obtain the results for the other classical series of Lie algebras by imposing appropriate involutions on the scattering data. Thus we also show how Moser's solution goes into the one of Olshanetsky and Perelomov. The results for the large-time asymptotics of the A_r -CTC solutions are extended to the other classical series B_r - D_r. We exhibit also some `irregular' solutions for the D_{2n+1} algebras whose asymptotic regimes at t ->\pm\infty are qualitatively different. Interesting examples of bounded and periodic solutions are presented and the relations between the solutions for the algebras D_4, B_3 and G_2 $ are analyzed.

solv-int↗

arXiv1998

The Complex Toda Chains and the Simple Lie Algebras - Solutions and Large Time Asymptotics

The asymptotic regimes of the N-site complex Toda chain (CTC) with fixed ends related to the classical series of simple Lie algebras are classified. It is shown that the CTC models have much richer variety of asymptotic regimes than the real Toda chain (RTC). Besides asymptotically free propagation (the only possible regime for the RTC), CTC allow bound state regimes, various intermediate regimes when one (or several) group(s) of particles form bound state(s), singular and degenerate solutions. These results can be used e.g., in describing the soliton interactions of the nonlinear Schroedinger equation. Explicit expressions for the solutions in terms of minimal sets of scattering data are proposed for all classical series B_r - D_r.

solv-int↗

arXiv1997

Criterion and Regions of Stability for Quasi-Equidistant Soliton Trains

Using the complex Toda chain (CTC) as a model for the propagation of the N-soliton pulse trains of the nonlinear Schrodinger (NLS) equation, we predict the asymptotic behavior of these trains. The following asymptotic regimes are stable: (i)~asymptotically free propagation of all N solitons; (ii)~bound state regime where the N solitons may move quasi-equidistantly (QED); and (iii)~various different combinations of (i) and (ii). For N=2 and 3 we determine analytically the set of initial soliton parameters corresponding to each of these regimes. We find excellent agreement between the solutions of CTC and NLS for all regimes and propose realistic choices for the sets of amplitudes, for which the solitons propagate QED to very large run lengths. This is of importance for optical fiber communication.

solv-int↗