This monograph is devoted to the derivation and research of fluid types taking place in plasma physics. It specializes in types related to quasi-neutrality approximation, difficulties concerning laser propagation in a plasma, and coupling plasma waves and electromagnetic waves. utilized mathematicians will discover a stimulating advent to the realm of plasma physics and some open difficulties which are mathematically wealthy. Physicists who will be crushed via the abundance of versions and unsure in their underlying assumptions will locate easy mathematical homes of the similar platforms of partial differential equations. A deliberate moment quantity may be dedicated to kinetic models.

First and most excellent, this ebook mathematically derives yes universal fluid versions from extra normal types. even though a few of these derivations can be popular to physicists, you will need to spotlight the assumptions underlying the derivations and to achieve that a few probably easy approximations turn into extra complex than they appear. Such approximations are justified utilizing asymptotic research at any place attainable. moreover, effective simulations of multi-dimensional types require certain statements of the similar structures of partial differential equations in addition to acceptable boundary stipulations. a few mathematical homes of those structures are provided which provide tricks to these utilizing numerical tools, even though numerics isn't the fundamental concentration of the book.

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Extra resources for Mathematical Models and Methods for Plasma Physics, Volume 1: Fluid Models (Modeling and Simulation in Science, Engineering and Technology)

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1 Asymptotic research within the Nonmagnetized Case . . . . . . . . . . . . 2. 2. 2 Asymptotic research within the Magnetized Case . . . . . . . . . . . . . . . . 2. 2. three Proofs of the Propositions of Sects. 2. 1 and a couple of. 2 .. . . . . . . . . . . . . 2. three Two-Temperature Euler types and Magneto-Hydrodynamics . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2. three. 1 The Two-Temperature Euler approach .. . . . .. . . . . . . . . . . . . . . . . . . . 2. three. 2 Electron Magneto-Hydrodynamics .. . . . . . .. . . . . . . . . . . . . . . . . . . . 2. four research of the Hyperbolic a part of platforms . E2T / and . MHD/ . . . 2. four. 1 at the Galilean alterations .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2. four. 2 Hyperbolic homes of either versions . . . .. . . . . . . . . . . . . . . . . . . . 2. four. three Proofs of the Propositions of the Section.. . . . . . . . . . . . . . . . . . . . eleven eleven 12 sixteen 24 24 27 29 37 38 forty seven sixty three sixty five sixty six sixty nine three Laser Propagation: Coupling with Ion Acoustic Waves . . . . . . . . . . . . . . . . . seventy three three. 1 Laser Propagation in a Plasma . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . seventy five three. 1. 1 at the Time Envelope versions . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . seventy five three. 1. 2 Geometrical Optics. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . ninety one three. 1. three The Paraxial Approximation .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . ninety nine three. 2 The Brillouin Instability in Laser–Plasma interplay .. . . . . . . . . . . . . . . 111 three. 2. 1 The changed Decay version in a Homogeneous Plasma . . . . . 114 three. 2. 2 the normal Decay approach in a Homogeneous Plasma.. . . . one hundred fifteen xi xii Contents three. 2. three version with a Nonhomogeneous Plasma . .. . . . . . . . . . . . . . . . . . . . 119 three. 2. four A Three-Wave Coupling method and Its Analysis.. . . . . . . . . . . a hundred and twenty four Langmuir Waves and Zakharov Equations . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . four. 1 Langmuir Waves with out Coupling with Ions .. . .. . . . . . . . . . . . . . . . . . . . four. 1. 1 Conductivity and Dispersion Relation . . . .. . . . . . . . . . . . . . . . . . . . four. 1. 2 Linear Langmuir Wave conception .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . four. 2 Coupling of Langmuir Waves with Acoustic Waves. . . . . . . . . . . . . . . . . . four. three The Zakharov Equations and Their homes .. . .. . . . . . . . . . . . . . . . . . . . one hundred thirty five 136 138 141 143 149 five Coupling Electron Waves and Laser Waves . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 1 Raman Instability .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 1. 1 version with fastened Ions .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 1. 2 aid of the version with mounted Ions . .. . . . . . . . . . . . . . . . . . . . five. 1. three The Raman version with an Ion Acoustic Wave .. . . . . . . . . . . . . . five. 2 The Euler–Maxwell version for brief Ultra-High depth Laser Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 2. 1 Well-Posedness of the version .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. 2. 2 Boundary stipulations . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . five. three Envelope versions for terribly brief High-Intensity Laser Pulses . . . . . . . 159 one hundred sixty 162 169 179 6 versions with a number of Species . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. 1 Two-Temperature Euler procedure for a blending of 2 Ion Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. 1. 1 The Three-Population complete version .. . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. 1. 2 Average-Species types . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6. 2 a few types for Weakly Ionized Plasmas . . . . . . .. . . . . . . . . . . . . . . . . . . . 6.

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