arXiv subjects

S. D. Baalrud

Publications and source records attributed to S. D. Baalrud.

10 recordsLinked to original sources

arXiv2026

Numerical thermalization in $n$-D particle-in-cell simulations

The particle-in-cell (PIC) simulation method is often understood to solve the collisionless Vlasov equation due to the finite shape of its macroparticles. In reality, it can suffer from artificially high collisionality due to the underresolution of particle number; i.e., the use of a large macroparticle weight. The degree to which particle shape effects compensate for a large macroparticle weight in 1D, 2D, and 3D is presented. The collision time is calculated from PIC simulations based on the decay rate of the velocity autocorrelation function and compared directly with the kinetic theory of Okuda, Birdsall, and Langdon. The theory is found to accurately predict the simulated collision time with varied grid spacings, plasma conditions, and simulation dimensionalities. The result is a means to predict the timescale of self-consistent Coulomb interactions in the PIC simulation and thus characterize the relevance and implications of numerical thermalization as a function of grid spacing and macroparticle weight. It is determined that reaching the physical thermalization time, let alone approximating the collisionless Vlasov limit, may often be intractable in 3D for macroparticle sizes that resolve the Debye length.

physics.plasm-ph↗

arXiv2024

When should PIC simulations be applied to atmospheric pressure plasmas? Impact of correlation heating

Molecular dynamics simulations are used to test when the particle-in-cell (PIC) method applies to atmospheric pressure plasmas. It is found that PIC applies only when the plasma density and macroparticle weight are sufficiently small because of two effects associated with correlation heating. The first is the physical effect of disorder-induced heating (DIH). This occurs if the plasma density is large enough that a species (typically ions) is strongly correlated in the sense that the Coulomb coupling parameter exceeds one. In this situation, DIH causes ions to rapidly heat following ionization. PIC is not well suited to capture DIH because doing so requires using a macroparticle weight of one and a grid that well resolves the physical interparticle spacing. These criteria render PIC intractable for macroscale domains. The second effect is a numerical error due to Artificial Correlation Heating (ACH). ACH is like DIH in that it is caused by the Coulomb repulsion between particles, but differs in that it is a numerical effect caused by a macroparticle weight larger than one. Like DIH, it is associated with strong correlations. However, here the macroparticle coupling strength is found to scale as $Γw^{2/3}$, where $Γ$ is the physical coupling strength and $w$ is the macroparticle weight. So even if the physical coupling strength of a species is small, as is expected for electrons in atmospheric pressure plasmas, a sufficiently large macroparticle weight can cause the macroparticles to be strongly coupled and therefore heat due to ACH. Furthermore, it is shown that simulations in reduced dimensions exacerbate these issues.

physics.plasm-ph↗

arXiv2022

Strong Coulomb Coupling Influences Ion and Neutral Temperatures in Atmospheric Pressure Plasmas

Molecular dynamics simulations are used to model ion and neutral temperature evolution in partially-ionized atmospheric pressure plasma at different ionization fractions. Results show that ion-ion interactions are strongly coupled at ionization fractions as low as 10^-5 and that the temperature evolution is influenced by effects associated with the strong coupling. Specifically, disorder-induced heating is found to rapidly heat ions on a timescale of the ion plasma period (~10s ps) after an ionization pulse. This is followed by the collisional relaxation of ions and neutrals, which cools ions and heats neutrals on a longer (~ns) timescale. Slight heating then occurs over a much longer (~ 100s ns) timescale due to ion-neutral three-body recombination. An analytic model of the temperature evolution is developed that agrees with the simulation results. A conclusion is that strong coupling effects are important in atmospheric pressure plasmas.

physics.plasm-ph↗

arXiv2021

A Kinetic Model for Electron-Ion Transport in Warm Dense Matter

We present a model for electron-ion transport in Warm Dense Matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although this model has been derived rigorously in the classical limit [S.D. Baalrud and J. Daligault, Physics of Plasmas 26, 8, 082106 (2019)], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. By solving the Uehling-Uhlenbeck equation for electron-ion relaxation rates, we predict the momentum and temperature relaxation time and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.

physics.plasm-ph↗

arXiv2020

Review of the First Charged-Particle Transport Coefficient Comparison Workshop

We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4-6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron-ion coupling, inter-ion diffusion, ion viscosity, and charged particle stopping powers. Here, we give general background on Coulomb coupling and computational expense, review where some transport coefficients appear in hydrodynamic equations, and present the submitted data. Large variations are found when either the relevant Coulomb coupling parameter is large or computational expense causes difficulties. Understanding the general accuracy and uncertainty associated with such transport coefficients is important for quantifying errors in hydrodynamic simulations of inertial confinement fusion and high-energy density experiments.

physics.plasm-ph↗

arXiv2020

Diffusion coefficients in the envelopes of white dwarfs

The diffusion of elements is a key process in understanding the unusual surface composition of white dwarfs stars and their spectral evolution. The diffusion coefficients of Paquette et al. (1986) have been widely used to model diffusion in white dwarfs. We perform new calculations of the coefficients of inter-diffusion and ionic thermal diffusion with 1) a more advanced model that uses a recent modification of the calculation of the collision integrals that is more suitable for the partially ionized, partially degenerate and moderately coupled plasma, and 2) classical molecular dynamics. The coefficients are evaluated for silicon and calcium in white dwarf envelopes of hydrogen and helium. A comparison of our results with Paquette et al. shows that the latter systematically underestimates the coefficient of inter-diffusion yet provides reliable estimates for the relatively weakly coupled plasmas found in nearly all types of stars as well as in white dwarfs with hydrogen envelopes. In white dwarfs with cool helium envelopes (Teff < 15000K), the difference grows to more than a factor of two. We also explored the effect of the ionization model used to determine the charges of the ions and found that it can be a substantial source of discrepancy between different calculations. Finally, we consider the relative diffusion time scales of Si and Ca in the context of the pollution of white dwarf photospheres by accreted planetesimals and find factor of > 3 differences between calculations based on Paquette et al. and our model.

astro-ph.SR↗

arXiv2013

Kinetic Theory of the Presheath and the Bohm Criterion

A kinetic theory of the Bohm criterion is developed that is based on positive-exponent velocity moments of the plasma kinetic equation. This result is contrasted with the conventional kinetic Bohm criterion that is based on a v^{-1} moment of the Vlasov equation. The salient difference between the two results is that low velocity particles dominate in the conventional theory, but are essentially unimportant in the new theory. It is shown that the derivation of the conventional kinetic Bohm criterion is flawed. Low velocity particles can cause unphysical divergences in the conventional theory. These divergent contributions are avoided with this new approach. The two theories are compared using example distribution functions from previous presheath models. The importance of ion-ion and electron-electron collisions to determining the particle distribution functions throughout the presheath is also discussed. A kinetic equation that accounts for wave-particle scattering by convective instabilities is used to show that ion-acoustic instabilities in the presheath of low temperature plasmas (where T_e \gg T_i) can cause both ions and electrons to obtain Maxwellian distribution functions near the sheath.

physics.plasm-ph↗

arXiv2013

Particle-in-cell simulations of a current-free double layer

Current-free double layers of the type reported in plasmas in the presence of an expanding magnetic field [C. Charles and R. W. Boswell, Appl. Phys. Lett. 82, 1356 (2003)] are modeled theoretically and with particle-in-cell/Monte Carlo simulations. Emphasis is placed on determining what mechanisms affect the electron velocity distribution function (EVDF) and how the EVDF influences the double layer. A theoretical model is developed based on depletion of electrons in certain velocity intervals due to wall losses and repletion of these intervals due to ionization and elastic electron scattering. This model is used to predict the range of neutral pressures over which a double layer can form and the electrostatic potential drop of the double layer. These predictions are shown to compare well with simulation results.

physics.plasm-ph↗

arXiv2011

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by $\vc{B}_o = B_{po} \tanh (x/λ) \hat{y} + B_{zo} \hat{z}$, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the polodial field $B_{yo} (x) = B_{po} \tanh (x/λ)$, which is the only resonant surface in 2D or in the absence of a guide field. Here $B_{po}$ is the asymptotic value of the equilibrium poloidal field, $B_{zo}$ is the constant equilibrium guide field, and $λ$ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity $θ\equiv \arctan(k_z/k_y)$. The resonant surface location for angle $θ$ is $x_s = - λ\arctanh (\tan θB_{zo}/B_{po})$, and the existence of a resonant surface requires $|θ| < \arctan (B_{po} / B_{zo})$. The most unstable angle is oblique, i.e. $θ\neq 0$ and $x_s \neq 0$, in the constant-$ψ$ regime, but parallel, i.e. $θ= 0$ and $x_s = 0$, in the nonconstant-$ψ$ regime. For a fixed angle of obliquity, the most unstable wavenumber lies at the intersection of the constant-$ψ$ and nonconstant-$ψ$ regimes. The growth rate of this mode is $γ_{\textrm{max}}/Γ_o \simeq S_L^{1/4} (1-μ^4)^{1/2}$, in which $Γ_o = V_A/L$, $V_A$ is the Alfvén speed, $L$ is the current sheet length, and $S_L$ is the Lundquist number. The number of plasmoids scales as $N \sim S_L^{3/8} (1-μ^2)^{-1/4} (1 + μ^2)^{3/4}$.

physics.plasm-ph↗

arXiv2011

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth $d_η\equiv S_L^{-1/2} \sqrt{L v_A/γ}$, where $S_L$ is the Lundquist number, $L$ the length of the current sheet, $v_A$ the Alfvén speed, and $γ$ the growth rate. Modifications to a recent resistive MHD analysis [N.\ F.\ Loureiro, A.\ A.\ Schekochihin, and S.\ C. Cowley, Phys.\ Plasmas {\bf 14}, 100703 (2007)] arise when collisions are sufficiently weak that $d_η$ is shorter than the ion skin depth $d_i \equiv c/ω_{pi}$. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as $(d_i/L)^{6/13} S_L^{7/13} v_A/L$ and the number of plasmoids as $(d_i/L)^{1/13} S_L^{11/26}$, compared to $S_L^{1/4} v_A/L$ and $S^{3/8}$, respectively, in resistive MHD.

physics.plasm-ph↗