Searcharxiv⌕ Search

arXiv subjects

I H Hutchinson

Publications and source records attributed to I H Hutchinson.

At least 19 recordsLinked to original sources
arXiv2024

Coherent Structures in One-dimensional Buneman Instability Nonlinear Simulations

Long-duration one-dimensional PIC simulations are presented of Buneman-unstable, initially Maxwellian, electron and ion distributions shifted with respect to one another, providing detailed phase-space videos of the time-dependence. The final state of high initial ion temperature cases is dominated by fast electron holes, but when initial ion temperature is less than approximately four times the electron temperature, ion density modulation produces potential perturbations of approximately ion-acoustic character, modified by the electron distribution shift. Early in the nonlinear phase, they often have electron holes trapped in them ("coupled hole-solitons": CHS). In high-available-energy cases, when major broadening of the electron distribution occurs, both electron holes and coupled hole-solitons can be reflected, giving persistent counter-propagating potential peaks. Analytical theory is presented of steady nonlinear potential structures in model nonlinear particle distribution plasmas with Buneman unstable parameters. It compares favorably in some respects with the nonlinear simulations, but not with the later phases when the electron velocity distributions are greatly modified.

physics.plasm-ph↗
arXiv2024

Kinetic Solitary Electrostatic Structures in Collisionless Plasma: Phase-Space Holes

The physics of isolated plasma potential structures sustained by a deficit of phase-space density on trapped orbits, commonly known as electron or ion holes, is reviewed. The principles of their equilibria are explained and illustrated, and contrasted with solitons. A literature review mostly prior to 2016 highlights the key historical developments of the field. Progress since, especially in hole acceleration, stability, and multi-dimensional effects, is summarized in more detail.

physics.plasm-ph↗
arXiv2023

Ion Hole Equilibrium and Dynamics in One Dimension

Electrostatic solitary waves with negative potential (ion holes) are analyzed theoretically using a generalization of the treatment recently developed for slow electron holes. It is shown that an often-cited criterion for their existence is mistaken and they can in fact exist for a wide range of ion to electron temperature ratios. Shifts of the hole velocity $v_h$ relative to the ion distributions systematically decrease the permitted hole depths, which become extremely small by $v_h/v_{ti}\sim 2$. Ion holes are usually unstably accelerated by electron reflection forces which are calculated numerically and analytically for the resulting asymmetric potential structure. The timescale of this acceleration is proportional to the ion plasma period, and generally longer than the ion bounce time in the potential well. Thus, ion holes behave like approximately rigid entities and even when unstable can survive much longer than the typical transit time of a satellite, so as to be observable.

physics.plasm-ph↗
arXiv2022

Multimode theory of electron hole transverse instability

We present Vlasov-Poisson 3-D linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain PIC simulations that observe instability up to $\sim20$\% beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.

physics.plasm-ph↗
arXiv2022

An Assessment Of Full-Wave Effects On Maxwellian Lower-Hybrid Wave Damping

Lower-hybrid current drive (LHCD) actuators are important components of modern day fusion experiments as well as proposed fusion reactors. However, simulations of LHCD often differ substantially from experimental results, and from each other, especially in the inferred power deposition profile shape. Here we investigate some possible causes of this discrepancy; "full-wave" effects such as interference and diffraction, which are omitted from standard raytracing simulations and the breakdown of the raytracing near reflections and caustics. We compare raytracing simulations to state-of-the-art full-wave simulations using matched hot-plasma dielectric tensors in realistic tokamak scenarios for the first time. We show that differences between full-wave simulations and raytracing in previous work were primarily due to numerical and physical inconsistencies in the simulations, and we demonstrate that good agreement between raytracing and converged full-wave simulations can be obtained in reactor relevant-scenarios with large ray caustics and in situations with weak damping.

physics.plasm-ph↗
arXiv2021

Overstability of Plasma Slow Electron Holes

Sufficient conditions are found on the ion velocity distribution $f_i$ and potential amplitude for stability of steady electron holes moving at slow speeds, coinciding with the bulk of $f_i$. Fully establishing stability requires calculation of the ion response to shift potential perturbations having an entire range of oscillatory frequencies, because under some conditions real frequencies intermediate between the ion and electron responses prove to be unstable even when the extremes are not. The mechanism of this overstability is explained and calculated in detail. Electron holes of peak potential $ψ$ less than approximately 0.01 times the background temperature ($ψ\lesssim 0.01T_0/e$) avoid the oscillatory instability entirely. For them, the \emph{necessary} condition that there be a local minimum in $f_i$ in which the hole resides is also \emph{sufficient}, unless the magnetic field $B$ is low enough to permit the transverse instability having finite wavenumber $k$ perpendicular to $B$.

physics.plasm-ph↗
arXiv2021

Asymmetric One-Dimensional Slow Electron Holes

Slow solitary positive-potential peaks sustained by trapped electron deficit in a plasma with asymmetric ion velocity distributions are in principle asymmetric, involving a potential change across the hole. It is shown theoretically how to construct such asymmetric electron holes, thus providing fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a wide variety of prescribed background ion velocity distributions. Because of ion reflection forces experienced by the hole, there is generally only one discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is unstable unless there is a local minimum in the ion velocity distribution, in which the hole velocity then resides. For stable equilibria with Maxwellian electrons, the potential drop across the hole is shown to be $Δϕ\simeq{2\over 9}f'''{T_e\over e}({eψ\over m_i})^2$, where $ψ$ is the hole peak potential, $f'''$ is the third derivative of the background ion velocity distribution function at the hole velocity, and $T_e$ the electron temperature. Potential asymmetry is small for holes of the amplitudes usually observed, $ψ\lesssim 0.5T_e/e$.

physics.plasm-ph↗
arXiv2021

How can slow plasma electron holes exist?

One dimensional analysis is presented of solitary positive potential plasma structures whose velocity lies within the range of ion distribution velocities that are strongly populated: so called "slow" electron holes. It is shown that to avoid the self-acceleration of the hole velocity away from ion velocities it must lie within a local minimum in the ion velocity distribution. Quantitative criteria for the existence of stable equilibria are obtained. The background ion distributions required are generally stable to ion-ion modes unless the electron temperature is much higher than the ion temperature. Since slow positive potential solitons are shown not to be possible without a significant contribution from trapped electrons, it seems highly likely that such observed slow potential structures are indeed electron holes.

physics.plasm-ph↗
arXiv2021

Finite gyro-radius multidimensional electron hole equilibria

Finite electron gyro-radius influences on the trapping and charge density distribution of electron holes of limited transverse extent are calculated analytically and explored by numerical orbit integration in low to moderate magnetic fields. Parallel trapping is shown to depend upon the gyro-averaged potential energy and to give rise to gyro-averaged charge deficit. Both types of average are expressible as convolutions with perpendicular Gaussians of width equal to the thermal gyro-radius. Orbit-following confirms these phenomena but also confirms for the first time in self-consistent potential profiles the importance of gyro-bounce-resonance detrapping and consequent velocity diffusion on stochastic orbits. The averaging strongly reduces the trapped electron deficit that can be sustained by any potential profile whose transverse width is comparable to the gyro-radius $r_g$. It effectively prevents equilibrium widths smaller than $\sim r_g$ for times longer than a quarter parallel-bounce-period. Avoiding gyro-bounce resonance detrapping is even more restrictive, except for very small potential amplitudes, but it takes multiple bounce-periods to act. Quantitative criteria are given for both types of orbit loss.

physics.plasm-ph↗
arXiv2021

Synthetic Multidimensional Plasma Electron Hole Equilibria

Methods for constructing synthetic multidimensional electron hole equilibria without using particle simulation are investigated. Previous approaches have various limitations and approximations that make them unsuitable within the context of expected velocity diffusion near the trapped-passing boundary. An adjustable model of the distribution function is introduced that avoids unphysical singularities there, and yet is sufficiently tractable analytically to enable prescription of the potential spatial profiles. It is shown why simple models of the charge density as being a function only of potential cannot give solitary multidimensional electron holes, in contradiction of prior suppositions. Fully self-consistent axisymmetric electron holes in the drift-kinetic limit of electron motion (negligible gyro-radius) are constructed and their properties relevant to observational interpretation and finite-gyro-radius theory are discussed.

physics.plasm-ph↗
arXiv2020

Oblate Electron Holes are not attributable to Anisotropic Shielding

Shielding mechanisms' influence on the ratio of perpendicular to parallel scale lengths of multidimensional plasma electron hole equilibria are analyzed theoretically and computationally. It is shown that the ``gyrokinetic'' model, invoking perpendicular polarization, is based on a misunderstanding and cannot explain the observational trend that greater transverse extent accompanies lower magnetic field. Instead, the potential in the wings of the hole, outside the region of trapped-electron depletion, has isotropic shielding giving $ϕ\propto {\rm e}^{-r/L}/r$, with the shielding length $L$ equal to the Debye length for holes much slower than the electron thermal speed. Particle in cell simulations confirm the analysis.

physics.plasm-ph↗
arXiv2020

Particle Trapping in Axisymmetric Electron Holes

Electron orbits are calculated in solitary two-dimensional axisymmetric electrostatic potential structures, typical of plasma electron holes, in order to establish the conditions for the particles to remain trapped. Analytic calculations of the evolution of the parallel energy caused by the perturbing radial electric field are shown to agree well with full numerical orbit integration Poincaré plots. The predominant mechanism of detrapping is resonance between the gyro frequency in the parallel magnetic field and harmonics of the parallel bounce frequency. A region of phase-space adjacent to the trapped-passing boundary in parallel energy is generally stochastic because of island overlap of different harmonics, but except for very strong radial electric field perturbation, more deeply trapped orbits have well-defined islands and are permanently confined. A simple universal quantitative algorithm is given, and its results plotted as a function of magnetic field strength and hole radial scale-length, determining the phase space volume available to sustain the electron hole by depression of the permanently trapped distribution function.

physics.space-ph↗
arXiv2019

Electron phase-space hole transverse instability at high magnetic field

Analytic treatment is presented of the electrostatic instability of an initially planar electron hole in a plasma of effectively infinite particle magnetization. It is shown that there is an unstable mode consisting of a rigid shift of the hole in the trapping direction. Its low frequency is determined by the real part of the force balance between the Maxwell stress arising from the tranverse wavenumber $k$ and the kinematic jetting from the hole's acceleration. The very low growth rate arises from a delicate balance in the imaginary part of the force between the passing-particle jetting, which is destabilizing, and the resonant response of the trapped particles, which is stabilizing. Nearly universal scalings of the complex frequency and $k$ with hole depth are derived. Particle in cell simulations show that the slow-growing instabilities previously investigated as coupled hole-wave phenomena occur at the predicted frequency, but with growth rates 2 to 4 times greater than the analytic prediction. This higher rate may be caused by a reduced resonant stabilization because of numerical phase-space diffusion in the simulations.

physics.plasm-ph↗
arXiv2019

Transverse instability magnetic field thresholds of electron phase-space holes

A detailed comparison is presented of analytical and particle-in-cell (PIC) simulation investigation of the transverse instability, in two dimensions, of initially one-dimensional electron phase-space hole equilibria. Good quantitative agreement is found between the shift-mode analysis and the simulations for the magnetic field ($B$) threshold at which the instability becomes overstable (time-oscillatory) and for the real and imaginary parts of the frequency. The simulation $B$-threshold for full stabilization exceeds the predictions of shift-mode analysis by 20 to 30\%, because the mode becomes substantially narrower in spatial extent than a pure shift. This threshold shift is qualitatively explained by the kinematic mechanism of instability.

physics.plasm-ph↗
arXiv2018

Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas

The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov-Poisson system consists of a shift-mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as integrals of equilibrium parameters over the hole and is shown at low frequency to be exactly equal to what has recently been found (by different analysis) to express `kinematic' hole momentum conservation. The mechanism of instability has nothing to do with the previously hypothesized transverse electron focusing. The unmagnetized growth rate $γ(k)$ is found numerically and is in excellent agreement with recent kinematic estimates. Magnetic field stabilization of the transverse mode is also evaluated. The resulting stability boundary for Maxwellian holes is in reasonable agreement with previously published criteria based on particle simulation. It arises from a change of trapped force sign across the resonance between bounce and cyclotron frequencies.

physics.plasm-ph↗
arXiv2016

Plasma electron-hole kinematics: momentum conservation

We analyse the kinematic properties of a plasma electron hole: a non-linear self-sustained localized positive electric potential perturbation, trapping electrons, that behaves as a coherent entity. When a hole accelerates or grows in depth, ion and electron plasma momentum is changed both within the hole and outside it, by an energization process we call jetting. We present a comprehensive analytic calculation of the momentum changes of an isolated general one-dimensional hole. The conservation of the total momentum gives the hole's kinematics, determining its velocity evolution. Our results explain many features of the behavior of hole speed observed in numerical simulations, including self-acceleration at formation, and hole pushing and trapping by ion streams.

physics.plasm-ph↗
arXiv2013

Particle in cell calculation of plasma force on a small grain in a non-uniform collisional sheath

The plasma force on grains of specified charge and height in a collisional DC plasma sheath are calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed sheath vary substantially with collisionality. The grain force is found to agree quite well with a combination of background electric field force plus ion drag force. However, the drag force must take account of the non-Maxwellian (and spatially varying) ion distribution function, and the collisional drag enhancement. It is shown how to translate the dimensionless results into practical equilibrium including other forces such as gravity.

physics.plasm-ph↗