Waves and Wave Interaction in Plasmas

379 Pages·2022·14.562 MB·English

by  Prasanta Chatterjee, Kaushik Roy, Uday Narayan Ghosh

Waves
and Wave
Interaction
in Plasmas
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orl Slowly Varying Oscillations and Waves: From Basics to Modernity
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Waves
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Interaction
in Plasmas
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orl Prasanta Chatterjee
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w Visva Bharati University, India
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a Beluti M K M High School, India
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Uday Narayan Ghosh
K K M College (A Constituent Unit of
Munger University), India
World Scientific
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Library of Congress Control Number: 2022052897
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
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ds WAVES AND WAVE INTERACTION IN PLASMAS
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w Copyright © 2023 by World Scientific Publishing Co. Pte. Ltd.
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w All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
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Preface
Waves and wave interactions in plasmas is written in a lucid and system-
atic way to serve as a special book for advanced post graduate students
andresearchersinApplied Mathematics, PlasmaPhysics, Nonlineardiffer-
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o ential equations, Nonlinear Optics, and other Engineering branches where
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ntifi nonlinear wave phenomena is studied. The first chapter deals with basic
e plasma with elementary definitions of magnetized and unmagnetized plas-
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ds mas, plasma modeling, dusty plasma, and quantum plasma. In Chapter 2,
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w we deal with linear and nonlinear waves, solitons and shocks, and other
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w wave phenomena.
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m In Chapter 3, solution of some nonlinear wave equations is discussed
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d fr by using some standard technique. Chapter 4 starts with elementary
de knowledgeofperturbationandnonperturbationmethods. Severalevolution
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Do solitons in those environments are discussed. In Chapter 5, Higher-order

correction to those equations and the improvement of the solution is are
discussed. In Chapter 6, evolution equations in nonplanar geometry are
obtained and the wave solution for such equation is also obtained. In
Chapter 7, different type collisions of solitons in a plasma environment
is discussed. The phenomena of soliton turbulence are also discussed as
a consequence of multi soliton interactions. In Chapter 8, the properties
of large amplitude solitary wavesare obtained by using a non perturbative
approach called Sagdeev’s Pseudopotential Approach. Speed and shape of
solitons are also discussed in this chapter. Possiblefuture developments of
research in this area are explained in brief in Chapter 9.
Prasanta Chatterjee, Kaushik Roy
Uday Narayan Ghosh
India
April 2022
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Acknowledgments
We are greatly delighted to publish a book on Waves and Wave Interac-
tion in Plasma. During writing this book, we have got help from many of
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o our seniors and friends. We are highly obliged by the guidance we have
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entific. rKeocelkivaetad.fDrorm. SPanrotof.BRaanjekrujemeaarnRdoDycr.hoAumdhaurrPy,raEsmaderMituissraPhroavfeesssourppoforItSeId,
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ds and motivated us in our endeavor. We are also grateful to Dr. Malay
worl Gorui, Dr. Asit Saha, Dr. Pankaj Kumar Mandal, Dr. Ganesh Mandal,
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w Dr. Rustam Ali, and Laxmikanta Mandi. Last but not the least, we are
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Contents
Preface v
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orld 1.1 Introduction ................................................................. 1
w 1.2 Saha Equation and Plasma Temperature . . . . . . . . . .
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m 1.3 Basic Concepts of Plasma . . . . . . . . . . . . . . . . . .
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d 1.3.1 Basic dimensionless parameters. . . . . . . . . . .
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Do 1.3.2 Debye length and Debye shielding . . . . . . . . .

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1.3.3 Quasineutrality . . . . . . . . . . . . . . . . . . .
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1.3.4 Response time 7
1.3.5 Plasma frequency . . . . . . . . . . . . . . . . . .
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1.3.6 Collisions and coupling limit . . . . . . . . . . . .
9
1.4 Criteria for Plasma 10
1.5 High-Temperature Plasmas . . . . . . . . . . . . . . . . . 10
1.6 Mathematical Description . . . . . . . . . . . . . . . . . . 10
1.7 Magnetized Plasmas 11
1.8 Single Particle Motion in Uniform Electric and
Magnetic Field 14
1.9 Fluid Approach 15
1.10 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . 18
ix
1.11 Electromagnetic Wave Equation in Free Space . . . . . . . 20
1.12 Plasma Kinetic Theory . . . . . . . . . . . . . . . . . . . . 21
1.12.1 Distribution function . . . . . . . . . . . . . . . . 21
1.12.2 Macroscopic variables. . . . . . . . . . . . . . . . 22