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000845564 019__ $$a1048938276$$a1049849523
000845564 020__ $$a9783319975412$$q(electronic book)
000845564 020__ $$a3319975412$$q(electronic book)
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000845564 08204 $$a530.4/4$$223
000845564 1001_ $$aAllanson, Oliver,$$eauthor.
000845564 24510 $$aTheory of one-dimensional Vlasov-Maxwell equilibria :$$bwith applications to collisionless current sheets and flux tubes /$$cOliver Allanson.
000845564 264_1 $$aCham :$$bSpringer,$$c[2018]
000845564 264_4 $$c©2018
000845564 300__ $$a1 online resource :$$bcolor illustrations.
000845564 336__ $$atext$$btxt$$2rdacontent
000845564 337__ $$acomputer$$bc$$2rdamedia
000845564 338__ $$aonline resource$$bcr$$2rdacarrier
000845564 4901_ $$aSpringer theses
000845564 500__ $$a"Doctoral thesis accepted by the University of St. Andrews, St. Andrews, UK."
000845564 504__ $$aIncludes bibliographical references.
000845564 5050_ $$aIntro; Supervisor's Foreword; Abstract; Publications Related to this Thesis; Contents; Abbreviations; Some Important Notations; Physical Constants (SI Units); 1 Introduction; 1.1 The Hierarchy of Plasma Models; 1.1.1 Single Particle Motion; 1.1.2 Kinetic Theory; 1.1.3 Quasineutrality; 1.1.4 Fluid Models; 1.2 Collisions in Plasmas; 1.2.1 Collisional Plasmas; 1.2.2 Collisionless Plasmas; 1.3 Collisionless Plasma Equilibria; 1.3.1 The `Forward' and `Inverse' Approaches; 1.3.2 Motivating Translationally Invariant Vlasov-Maxwell (VM) Equilibria; 1.3.3 Magnetic Reconnection
000845564 5058_ $$a1.3.4 Forward Approach for One-Dimensional (1D) VM Equilibria1.3.5 Inverse Approach for 1D VM Equilibria; 1.3.6 Previous Work on VM Equilibria; 1.4 Thesis Motivation and Outline; 1.4.1 Outline of the Thesis; References; 2 The Use of Hermite Polynomials for the Inverse Problem in One-Dimensional Vlasov-Maxwell Equilibria; 2.1 Preamble; 2.2 Introduction; 2.2.1 Hermite Polynomials in Fluid Closure; 2.2.2 Hermite Polynomials in VM Plasma Theory; 2.2.3 Hermite Polynomials for Exact VM Equilibria; 2.3 Formal Solution by Hermite Polynomials; 2.3.1 Weierstrass Transform
000845564 5058_ $$a2.3.2 Two Interpretations with Respect to Our Equations2.3.3 Formal Inversion of the Weierstrass Transform; 2.4 Mathematical Validity of the Method; 2.4.1 Convergence of the Hermite Expansion; 2.5 Non-negativity of the Hermite Expansion; 2.5.1 Possible Negativity of the Hermite Expansion; 2.5.2 Detailed Arguments; 2.5.3 Summary; 2.6 Illustrative Case of the Use of the Method: Correspondence with the Fourier …; 2.7 Summary; References; 3 One-Dimensional Nonlinear Force-Free Current Sheets; 3.1 Preamble; 3.2 Introduction; 3.2.1 Force-Free Equilibria and the Plasma Beta
000845564 5058_ $$a4 One-Dimensional Asymmetric Current Sheets4.1 Preamble; 4.2 Introduction; 4.2.1 Asymmetric Current Sheets; 4.2.2 Modelling the Magnetopause Current Sheet; 4.3 Exact VM Equilibria for 1D Asymmetric Current Sheets; 4.3.1 Theoretical Obstacles; 4.3.2 Outline of Basic Method; 4.4 The Numerical/``tanh'' Equilibrium DF; 4.4.1 The Pressure Function; 4.4.2 Inverting the Weierstrass Transform; 4.5 The Analytical/``Exponential'' Equilibrium DF; 4.5.1 The Pressure Tensor; 4.5.2 The DF; 4.5.3 Plots of the DF; 4.6 Discussion; References; 5 Neutral and Non-neutral Flux Tube Equilibria; 5.1 Preamble
000845564 506__ $$aAccess limited to authorized users.
000845564 520__ $$aThis book describes and contextualises collisionless plasma theory, and in particular collisionless plasma equilibria. The Vlasov–Maxwell theory of collisionless plasmas is an increasingly important tool for modern plasma physics research: our ability to sustain plasma in a steady-state, and to mitigate instabilities, determines the success of thermonuclear fusion power plants on Earth; and our understanding of plasma aids in the prediction and mitigation of Space Weather effects on terrestrial environments and satellites. Further afield, magnetic reconnection is a ubiquitous energy release mechanism throughout the Universe, and modern satellites are now able to make in-situ measurements with kinetic scale resolution. To keep pace with these challenges and technological developments, a modern scientific discussion of plasma physics must enhance, and exploit, its ‘literacy’ in kinetic theory. For example, accurate analytical calculations and computer simulations of kinetic instabilities are predicated on a knowledge of Vlasov–Maxwell equilibria as an initial condition. This book highlights new fundamental work on Vlasov–Maxwell equilibria, of potential interest to mathematicians and physicists alike. Possible applications involve two of the most significant magnetic structures known to confine plasma and store energy: current sheets and flux tubes.
000845564 588__ $$aOnline resource ; title from PDF title page (viewed August 15, 2018).
000845564 650_0 $$aCollisionless plasmas.
000845564 650_0 $$aEquilibrium.
000845564 77608 $$iPrint version: $$z3319975404$$z9783319975405$$w(OCoLC)1042404845
000845564 830_0 $$aSpringer theses.
000845564 852__ $$bebk
000845564 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-97541-2$$zOnline Access$$91397441.1
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