Instabilities, anomalous transport, and nonlinear structures in partially and fully magnetized plasmas.

Plasmas behavior, to a large extent, is determined by collective phenomena such as waves. Wave excitation, turbulence, and formation of quasi-coherent nonlinear structures are defining features of nonlinear multi-scale plasma dynamics. In this thesis, instabilities, anomalous transport, and structures in partially and fully magnetized plasmas were studied with a combination of analytical and numerical tools. The phenomena studied in this thesis are of interest for many applications, e.g., plasma reactors for material processing, electric propulsion, magnetic plasma confinement, and space plasma physics. Large equilibrium flows of ions and electrons exist in many devices with partially magnetized plasmas in crossed electric and magnetic fields. Such flows result in various instabilities and turbulence that produce anomalous electron transport across the magnetic field. We present first principle, self-consistent, nonlinear fluid simulations that predict the level of anomalous current generally consistent with experimental data. We also show that drift waves in partially magnetized plasmas (which we called Hall drift waves), destabilized by the electron drift along with density gradients, tend to form (via inverse energy cascade) shear flows similar to zonal flows in fully magnetized plasmas. These flows become unstable due to a secondary instability (similar to Kelvin–Helmholtz instability) and produce large-scale quasi-stationary vortices. Then, it was shown that in nonlinear regimes, the axial mode instability due to electron and ion flows (along the electric field) forms large-amplitude cnoidal type waves. At the same time, the strong electric field produced by axial modes affects Hall drift waves stability and provides a feedback mechanism on density gradient driven turbulence, creating a complex picture of interacting anomalous transport, zonal flows, vortices, and streamers. In the case where axial modes are destabilized by boundary effects, the nonlinear dynamics result in a new nonlinear equilibrium or standing oscillating waves. The formation of shear flows (zonal flows) was also studied in the framework of the Hasegawa-Mima equation and it was established that zonal flows can saturate due to nonlinear self-interactions. Lastly, a novel approach for high-fidelity numerical simulations of multi-scale nonlinear plasma dynamics is developed which is illustrated with the example of an unmagnetized plasma

EQUADIFF 15

Equadiff 15 – Conference on Differential Equations and Their Applications – is an international conference in the world famous series Equadiff running since 70 years ago. This booklet contains conference materials related with the 15th Equadiff conference in the Czech and Slovak series, which was held in Brno in July 2022. It includes also a brief history of the East and West branches of Equadiff, abstracts of the plenary and invited talks, a detailed program of the conference, the list of participants, and portraits of four Czech and Slovak outstanding mathematicians

Meromorphy and topology of localized solutions in the Thomas–MHD model

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas

Plasma Dynamics

Contains reports on seven research projects.U.S. Air Force - Office of Scientific Research (Grant AFOSR 84-0026)National Science Foundation (Grant ECS 85-14517)U.S. Department of Energy (Contract DE-FGO5-84ER 13272)Lawrence Livermore National Laboratory (Subcontract 6264005)National Science Foundation (Grant ECS 82-13430)U.S. Department of Energy (Contract DE-ACO2-78-ET-51013

Quasilinear theory of laser-plasma interactions

The interaction of a high intensity laser beam with a plasma is generally susceptible to the filamentation instability due to nonuniformities in the laser profile. In ponderomotive filamentation high intensity spots in the beam expell plasma by ponderomotive force, lowering the local density, causing even more light to be focused into the already high intensity region. The result--the beam is broken up into a filamentary structure.;Several optical smoothing techniques have been proposed to eliminate this problem. In the Random Phase Plates (RPS) approach, the beam is split into a very fine scale, time-stationary interference pattern. The irregularities in this pattern are small enough that thermal diffusion is then responsible for smoothing the illumination. In the Induced Spatial Incoherence (ISI) approach the beam is broken up into a larger scale but non-time-stationary interference pattern. In this dissertation we propose that the photons in an ISI beam resonantly interact with the sound waves in the wake of the beam. Such a resonant interaction induces diffusion in the velocity space of the photons. The diffusion will tend to spread the distribution of photons, thus if the diffusion time is much shorter than the e-folding time of the filamentation instability, the instability will be suppressed.;Using a wave-kinetic description of laser-plasma interactions we have applied quasilinear theory to model the resonant interaction of the photons in an ISI beam with the beam\u27s wake field. We have derived an analytic expression for the transverse diffusion coefficient. The quasilinear hypothesis was tested numerically and shown to yield an underestimate of the diffusion rate. By comparing the quasilinear diffusion rate, {dollar}\gamma\sb{lcub}D{rcub}{dollar}, with the maximum growth rate for the ponderomotive filamentation of a uniform beam, {dollar}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}{dollar}, we have derived a worst case criterion for stability against ponderomotive filamentation: {dollar}{dollar}{lcub}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}\over \gamma\sb D{rcub} \sim .5 {lcub}\tilde f\sp5/\tilde D\sp5\over \vert \tilde E\vert\sp2 \tilde\omega\sbsp{lcub}0{rcub}{lcub}2{rcub}\tilde N\sp6{rcub}\ll 1.{dollar}{dollar}The tildaed quantities are scaled to the following fusion relevant reference values; laser intensity: {dollar}\vert E\vert\sp2{dollar} = 10{dollar}\sp{lcub}15{rcub}\vert\tilde E\vert{dollar} Watts cm,{dollar}\sp{lcub}-2{rcub}{dollar} focal length: {dollar}f = 30\tilde f{dollar}m, width of each ISI echelon: {dollar}D = .75\tilde D{dollar} cm, laser carrier frequency: {dollar}\omega\sb{lcub}0{rcub} = 7.5 \times 10\sp{lcub}15{rcub}\tilde\omega\sb0{dollar} s{dollar}\sp{lcub}-1{rcub}{dollar}, and the number of ISI echelons: {dollar}N = 20\tilde N{dollar}