Session JO4: Basic: Plasma Theory and Computation

A structure-preserving scheme for the Landau-Fokker-Planck equation with the relativistic kernel

Recently, we published a paper of mass-momentum-energy-conserving scheme for the relativistic Landau-Fokker-Planck equation. The mass conservation is easily derived for any collision kernel, but the conservation laws of momentum and energy depend on the mathematical symmetries of the Beliaev-Budker kernel. Unlike the potential formulation, the momentum conservation is also derived simply in the Landau form. However, the discussion of energy conservation is more difficult than the others because one of the mathematical symmetries is coupled with the integration-by-parts. In this work, we developed a new method to calculate the Beliaev-Budker kernel in discrete form ensuring the conservation laws of mass, momentum and energy. Some constraints for conservation laws were derived with careful discussion of the integration-by-parts in discrete form, and the discrete kernel was obtained uniquely which can preserve these constraints. In a numerical experiment, the proposed scheme strictly maintains the conservation laws of mass, momentum and energy, and the growth rate of the entropy agrees well with a linear theory assuming the initial distribution.   

The Regionally Implicit Discontinuous Galerkin Method: Application to the Relativistic Vlasov-Maxwell system

The motivation of this work is to develop an efficient solver for models of collision-less high energy plasmas. These types of plasmas are studied in the context of, for example, a Wakefield Accelerator [Schlenvoigt 2008] where a laser causes plasma waves to accelerate electrons to nearly the speed of light. The relativistic Vlasov-Maxwell (RVM) system models such laser-plasma interactions and in particular, models the acceleration of electrons to relativistic energies. This system introduces numerical difficulties which are not present in the nonrelatisvistic limit, namely that operator splitting the Lorentz Force term leads to unphysical instabilities as explained in [Huot 2003]. We offer the Regionally Implicit Discontinuous Galerkin (RIDG) method [Guthrey & Rossmanith 2019] as an efficient alternative to operator splitting.   

Improved Particle Pusher Performance with Exponential Integrators

Simulating charged particle dynamics (particle pushing) has applications in plasma and accelerator physics and is a key component of particle-in-cell methods. In a magnetized plasma, fast oscillatory motion at the gyrofrequency imposes a severe restriction on the maximum allowable time step for standard numerical time integrators. For standard explicit methods the time steps must be smaller than the gyroperiod in order to be numerically stable. Standard implicit methods allow larger time steps but tend to dampen the oscillatory motion, thus they still need to take time steps at the scale of the gyroperiod or smaller if resolving the oscillatory gyromotion is required for accuracy. We developed a new approach to numerical time integration that has desirable numerical stability properties using exponential integrators to simulate charged particle trajectories in a strong magnetic field. Numerical experiments demonstrate accurate time integration at time steps larger than the gyroperiod with significant computational savings compared to standard numerical methods.   

On cutting off variable for Coulomb collision in plasma.

The correct cutting off variable for Coulomb collision in plasma is established in this presentation. The traditional cutting off variables, such as scattering angle $\theta $ and impact parameter b, are merely partial cutting off variables due to lacking the necessary cutting off on relative speed g of two particles. The correct cutting off variable should be introduced as velocity change before and after collision, which can correctly describe the singularity of the integrals. The difference of the partial cutting off variables and the correct one is compared through their contour lines in the b $-$ g plane here b is the impact parameter. With the correct cutting off, many physical results become more simplified and structured for Coulomb collisions. These physical results include the arbitrary higher order of Fokker-Planck coefficients, transition moments, and energy transfer rates for Coulomb collisions. All the physical results depending on velocity are expressed by a set of functions which associates with incomplete gamma functions. In particular, the so-called Coulomb logarithm ln$\Lambda $ should be replaced by the exact form -- the zeroth order incomplete Gamma function.   

Diffusion of Strongly Magnetized One-Component Plasma.

Charged particles in ultracold neutral plasmas or in non-neutral plasmas experiments with a strong magnetic field can have a gyroradius smaller than the Debye length but larger than the distance of closest approach. Particles with such characteristics are referred to as strongly magnetized. The transport properties of charged particles at these conditions have not been well described. Recent molecular dynamics (MD) simulations appear to observe Bohm scaling ($1/B$) of the diffusion coefficient perpendicular to the magnetic field when the plasma is strongly magnetized [1]. Here we extend the previous work to weaker coupling by calculating the perpendicular, parallel, and transverse diffusion coefficients from MD simulations of the one-component plasma in the strongly magnetized, weakly coupled regime ($\Gamma \approx 0.01$). The MD diffusion results show the perpendicular and parallel diffusion coefficients scaling with magnetic field strength do not agree with the traditional Braginskii transport theory or other leading theories. A new transport theory is needed to address these conditions. Also discussed are the requirements for the time step, simulation duration, and the number of particles needed for accurate MD simulations. [1] S.D.B. and J.D., Phys. Rev. E 96, 043202 (2017).   

Transverse Force Induced by a Magnetized Wake

This work considers the evolution of a charged test particle in a strongly magnetized plasma computed from linear response theory; a fundamental problem with direct application to plasma transport, confinement and energy deposition of fusion products, and runaway electron generation. The main result is the prediction of a transverse component of the force on the test particle that is perpendicular to its velocity, but in the plane formed by the velocity and magnetic field vectors. This component is in addition to the usual drag force opposing the velocity. The transverse force arises due to the manner in which the Lorentz force influences the dielectric polarization of the background plasma. This causes an asymmetry about the velocity vector in the induced charge distribution and electrostatic potential in the wake of the test charge. The transverse force is observed to change sign depending on the speed of the test charge. For fast projectiles it causes the angle between the velocity and magnetic field vectors to increase, while for slow projectiles it causes this angle to decrease.   

Space-charge limited current calculation using the minimum energy principle

Classical space-charge limited emission (SCLE) theory for cylindrical and spherical diodes were first formulated by Langmuir and Blodgett (LB) [1]. Recent studies improved LB results using analytical techniques [2]; however, they assume zero space-charge. This presentation applies variational calculus (VC) and the minimum energy principle to derive analytic solutions for the current-voltage behavior of these diodes. This yielded exact, closed-form solutions for SCLE from first principles and a second order differential equation valid for any geometry. VC agreed better with simulations than LB, particularly at extreme ratios of anode to cathode radius. We further report extensions of these calculations to include a crossed magnetic field to assess cycloidal flow stability$^{\mathrm{\thinspace }}$[3]. The application of this approach for other electron emission mechanisms and conditions will be discussed. [1] I. Langmuir and K. Blodgett, Phys. Rev. 24, 49-59 (1924). [2] Y. B. Zhu, P. Zhang, A. Valfells, L. K. Ang, and Y. Y. Lau, Phys. Rev. Lett. 110, 265007 (2013). [3] P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725-3727 (1994).   

Braking radiation of heterogeneous plasma of solid propellant combustion products in the radio frequency range

Heterogeneous plasma (HP), formed in the torch of the combustion products of rocket engines on solid metallic fuel, contains a significant proportion of particulate matter condensed dispersed phase. The self-consistent interaction of the gas of emission electrons and oppositely charged macro-particles leads to an accelerated movement of plasma charges, and to the presence of a field of electromagnetic braking radiation from the flame of the combustion products. A method for determining the parameters of the amplitude-frequency function of the braking radiation based on the statistical approach of quasineutral plasma cells and kinetic ideas about restoring local thermodynamic equilibrium is proposed. The contribution of a single charge to the integral power of braking radiation in the radio frequency range is determined by its acceleration in the electrostatic field of instantaneous plasma cells and the field of the dipole formed by the displaced particle and its electrostatic image. Model experiments carried out on the telediagnostics of plasma torch parameters of the products of combustion of Aluminium particles and the applicability of the proposed method for telediagnostics of HP by braking radiation in the radio frequency range are discussed.   

Sensitivity of the Convergence to Direct-Drive Cylindrical Implosion Parameters

To achieve efficient thermonuclear burn in Inertial Confinement Fusion (ICF) implosions, high convergence is needed to reduce the required amount of driver energy. Additionally, there is a well-known correlation between the convergence and hydrodynamic instabilities, such as the Rayleigh-Taylor (RT) instability, which have a deleterious effect on ICF. Thus, examining both the consequences of high convergence as well as the target parameters necessary for achieving this condition is essential to the development of robust target designs. 1D simulations of cylindrical targets produced by the Los Alamos Eulerian radiation-hydrodynamics code, \texttt{xRAGE}, have been used to search our target parameter space. Studying the topology of these spaces both informs our understanding of the sensitivity of the convergence to target design parameters, such as fill density, and provides insight into the exact extent to which instability growth can be attributed to convergence. We will present future plans for high convergence direct-drive cylindrical implosion experiments fielded at the National Ignition Facility (NIF). Experiments utilizing the NIF should be able to produce high quality measurements reaching convergences near 15; 4x greater than previous cylindrical implosions.   

Cross-code Validation for Simulations of a Planar MITL

For the planning of future pulsed-power devices such as Z-Next at Sandia National Labs, it is essential to have reliable predictive capability for modeling power-flow in the proposed designs of these devices. An important component of this predictive capability is to have results that can be closely reproduced between multiple codes for systems of progressively higher fidelity and increasing complexity. As a first step, we perform this cross-validation for the problem of power-flow along a Magnetically-Insulated Transmission Line (MITL) in planar (slab) geometry. We present a comparison of simulation results between the PERSEUS extended-MHD, EMPIRE-Fluid, and EMPIRE-PIC codes, first for the one-dimensional interaction of an electromagnetic wave with a layer of plasma, followed by an extension to a two-dimensional MITL. In this latter case, we vary the initial density of the plasma layer, seeking to identify a transition between quasi-neutral regimes that can be modeled with Hall physics, and non-quasi-neutral regimes that require space-charge-limiting in a fully two-fluid model.~ A close comparison between these codes provides the basis for cross-validation of power-flow simulations in more complex three-dimensional MITL geometries. SAND2019-7455 A   

Simulating Flux Ropes as Systems of Current Carrying Wires

A new model is developed to model flux ropes as plasma systems of thin current paths in a 3D space. This model is shown to be useful for reproducing experimental flux rope evolution, testing new experimental configurations, evaluating and interpreting the magnetic fields of complex 3D current paths, and testing the robustness of analytic flux rope models. The model is computationally inexpensive and can run parameter scans of flux rope experiments on a personal laptop computer.   

100X Speed-up of Particle-In-Cell (PIC) Langmuir Probe Simulation

Interpreting Langmuir probe data in real-world conditions can be very difficult---e.g., with non-ideal geometries, space charge and non-zero electric field (in the absence of the probe), collisionality, secondary emission, etc. With enough computational power, PIC simulation can precisely characterize probe responses to various plasma conditions, self-consistently including non-ideal effects, thus helping to interpret real probe data. Unfortunately, PIC simulation can be prohibitively expensive, partly because the cost scales with the square root of the ion/electron mass ratio, $\sqrt{m_i/m_e}$. Fortunately, the steady-state Vlasov-Poisson system scales trivially with ion mass, so probes in electron-ion plasma can be equivalently simulated in electron-positron plasma, speeding up computation by $\sqrt{m_i/m_e}$, e.g., by more than 100$\times$ for argon ions. The resulting solution yields the correct self-consistent charge density and electric potential for the electron-ion system. This approach is equivalent to the speed-limited PIC (SLPIC) method with a particularly simple speed-limiting function; moreover, SLPIC provides a systematic treatment for speeding up simulation by $\sqrt{m_i/m_e}$ while accurately treating collisionality, secondary emission, and magnetic fields.   

Nonlinear Alfven waves and recurrences in 3D Magnetohydrodynamics

Within the framework of MagnetoHydroDynamics, a strong interplay exists between flow and magnetic fields. This interplay is known to lead to several interesting phenomena such as mean-field and fluctuation (or small scale) dynamos, magnetic re-connection and recurrence phenomena, to name a few. Using a set of chaotic flow fields (eg, Arnold-Beltrami-Childress, Taylor-Green etc) driven at certain scales, we numerically integrate a self-consistent set of driven, 3D, weakly compressible MHD equations to study two fundamental processes, namely, the generation of mean magnetic field from the flow fields and the magnetic recurrence phenomena mediated by a dynamical exchange between magnetic and velocity fields via a reconnection process. After demonstrating the numerical convergence, we attempt possible explanation using Hamiltonian field models.   

Computational Study of Nanosecond Electric Pulse Parameters on Plasma Species Generation

Nanosecond pulsed plasmas (NPPs) can efficiently generate ionized/excited species from vacuum to atmospheric pressure [1]. While studies have elucidated the impact of voltage on local flow fields [2], the influence of pulse parameters, such as pulse duration and rise- and fall-times, and the species generated by the discharges remains incomplete. We examine the effect of pulse conditions on the electric field and generated plasma species by coupling a quasi-one dimensional model for a parallel plate geometry [1] to BOLSIG$+$ to improve plasma species characterization [3]. The long-term incorporation of this model into a high fidelity computational fluid dynamics (CFD) model and comparison to spectroscopic results under quiescent and flowing conditions will be discussed. 1. T. Piskin, V. Podolsky, S. Macheret, and J. Poggie, J. Phys. D. Appl. Phys. 52, 304002 (2019). 2. A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, Phys. Plasmas 14, 073501 (2007). 3. G. J. M. Hagelaar and L. C. Pitchford, Plasma Sources Sci. Technol$.$ 14, 722--733 (2005).