arXiv subjects

William D. Dorland

Publications and source records attributed to William D. Dorland.

5 recordsLinked to original sources

arXiv2026

Counter-streaming heat-flux closure for electron-only collisionless magnetic reconnection

In electron-only collisionless magnetic reconnection (MR), a regime of growing importance in turbulent space plasmas, electrons develop strongly non-Maxwellian distributions that invalidate conventional fluid closures based on assumptions of near local thermodynamic equilibrium. Using particle-in-cell (PIC) simulations, we identify the physical origin of the electron heat-flux: counter-streaming between electron sub-populations originating from opposite sides of the current sheet, with each sub-population remaining approximately adiabatic. This insight yields a novel fluid closure, which we implement in fluid simulations using two adiabatic electron fluids initialized on opposite sides of the current sheet. The fluid simulations capture the heat-flux, reconnecting current density, thermal pressure, and bulk flows as observed in PIC, within a reduced fluid description that conventional single-electron-fluid models fundamentally cannot reproduce. The closure is most accurate at low $β_{\text{Reconn.}}$ and $B_{\text{Guide}}/B_{\text{Reconn.}}$, regimes relevant to Earth's magnetotail, where it establishes counter-streaming as the physical origin of heat-flux in electron-only collisionless MR and enables its computationally efficient fluid modeling.

physics.plasm-ph↗

arXiv2024

Omnigenous stellarator equilibria with enhanced stability

To build an economically viable stellarator, it is essential to find a configuration that satisfies a set of favorable properties to achieve efficient steady-state nuclear fusion. One such property is omnigenity, which ensures confinement of trapped particles. After creating an omnigenous equilibrium, one must also ensure reduced transport resulting from kinetic and magnetohydrodynamic (MHD) instabilities. This study introduces and leverages the GPU-accelerated DESC optimization suite, which is used to design stable high-$β$ omnigenous equilibria, achieving Mercier, ideal ballooning, and enhanced kinetic ballooning stability. We explain the link between ideal and kinetic ballooning modes and discover stellarators with second stability, a regime of large pressure gradient where an equilibria becomes ideal ballooning stable.

physics.plasm-ph↗

arXiv2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of `test particles' in 1D-1V, stirred by an externally imposed stochastic electric field. The mean effect on the particle distribution function is stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant $C_2 \propto \iint dx dv \, \langle f^2 \rangle$. We find that $C_2$ is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of $C_2$ in Fourier space, with $k$ and $s$ denoting spatial and velocity wavenumbers, respectively. Whereas even the linear phase mixing alone would lead to a constant flux of $C_2$ to high $s$ (towards the collisional dissipation range) at every $k$, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of $C_2$ is to both high $k$ and high $s$ simultaneously. Integrating over velocity (spatial) wavenumbers, the $k$-space ($s$-space) flux of $C_2$ is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the $(k,s)$ plane, with power-law asymptotics at large $k$ and $s$. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

physics.plasm-ph↗

arXiv2023

An adjoint-based method for optimizing MHD equilibria against the infinite-n, ideal ballooning mode

We demonstrate a fast adjoint-based method to optimize tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-$n$ ideal ballooning mode. We present three finite-$β$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal MHD, we construct a technique to rapidly calculate the change in the growth rate, a measure of ideal ballooning instability. Using the~\texttt{SIMSOPT} framework, we then implement our fast adjoint gradient-based optimizer to minimize the growth rate and find stable equilibria for each of the three initially unstable equilibria.

physics.plasm-ph↗

arXiv2022

Microstability of $β\sim 1$ tokamak equilibria

High-power-density tokamaks offer a potential solution to design cost-effective fusion devices. One way to achieve high power density is to operate at a high $β$ value (the ratio of thermal to magnetic pressure), i.e., $β\sim 1$. However, a $β\sim 1$ state may be unstable to various pressure- and current-driven instabilities or have unfavorable microstability properties. To explore these possibilities, we generate $β\sim 1$ equilibria and investigate their stability. Initially, we study an analytical technique that was used in the past to generate $β\sim 1$ equilibria and outline its limitations. Hence, we demonstrate the generation of high-$β$ equilibria with the computer code $\texttt{VMEC}$. We then analyze these equilibria to determine their stability against the infinite-$n$ ideal ballooning mode. We follow that by engaging in a detailed microstability study, beginning with assessments of electrostatic ITG and TEM instabilities. We observe interesting behavior for the high-$β$ equilibria -- stabilization of these modes through two distinct mechanisms. Finally, we perform electromagnetic gyrokinetic simulations and again observe stabilizing trends in the equilibria at high $β$. These trends are different from their lower $β$ counterparts and offer an alternative, potentially favorable regime of tokamak operation.

physics.plasm-ph↗