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E-raamat: Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma

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E.V. Chizhonkov (Lomonosov Moscow State University, Moscow, RU)

Formaat: 310 pages
Ilmumisaeg: 08-Apr-2019
Kirjastus: CRC Press
ISBN-13: 9781000012194

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Formaat: 310 pages
Ilmumisaeg: 08-Apr-2019
Kirjastus: CRC Press
ISBN-13: 9781000012194

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This book is devoted to research in the actual field of mathematical modeling in modern problems of plasma physics associated with vibrations and wake waves excited by a short high-power laser pulse. The author explores the hydrodynamic model of the wake wave in detail and from different points of view, within the framework of its regular propagation, a development suitable for accelerating electrons, and the final tipping effect resulting in unregulated energy transfer to plasma particles.

Key selling features:

Presents research directly related to the propagation of super-power short laser pulses (subject of the 2018 Nobel Prize in Physics).
Presents mathematical modeling of plasma physics associated with vibrations and wake waves excited by a short high-power laser pulse.
Includes studies of large-amplitude plasma oscillations.
Most of the presented results are of original nature and have not appeared in the domestic and foreign scientific literature
Written at a level accessible for researchers, academia, and engineers.

This book is devoted to research in the actual field of mathematical modeling in modern problems of plasma physics associated with vibrations and wake waves excited by a short high-power laser pulse.

Preface

Part I Free plasma oscillations

1 Introductory information

(22)

1.1 What is breaking?

(4)

1.2 Physical model and basic equations

(8)

1.3 About initial conditions

(3)

1.4 About boundary conditions

(2)

1.5 Bibliography and comments

(5)

2 Plane one-dimensional non-relativistic electron oscillations

(25)

2.1 Problem statement in Eulerian and Lagrangian variables

(2)

2.2 Axial solutions

(11)

2.3 `Triangular' solutions

(4)

2.3.1 Simple solutions

(1)

2.3.2 Composite solutions

(2)

2.4 Numerical--analytical method

(4)

2.5 Bibliography and comments

(4)

3 Plane one-dimensional relativistic electron oscillations

(28)

3.1 Problem statement in the Eulerian and Lagrangian variables

(2)

3.2 Theoretical background of breaking

(5)

3.2.1 Quadratic frequency shift

(3)

3.2.2 Violation of the property of invariance

(1)

3.3 Method in Lagrangian variables

(2)

3.4 Scenario of development and completion of oscillations

(5)

3.5 Method in the Eulerian variables

(3)

3.6 Artificial boundary conditions

(6)

3.6.1 Full damping of oscillations

(1)

3.6.2 Linearization of the original equations

(1)

3.6.3 Accounting for the weak nonlinearity of the original equations

(1)

3.6.4 Deterioration of the approximation at the boundary

(2)

3.7 Bibliography and comments

(5)

4 Cylindrical one-dimensional relativistic and non-relativistic electron oscillations

(56)

4.1 Problem statements in Eulerian and Lagrangian variables

(6)

4.2 Analytical studies

(7)

4.2.1 Axial solution

(5)

4.2.2 Perturbation method

(2)

4.3 Finite difference method

(14)

4.3.1 Auxiliary designs. Splitting into physical processes

(2)

4.3.2 Construction of difference schemes

(3)

4.3.3 Process scenario

(9)

4.5 Calculation of axial solutions

103

(15)

4.5.1 Free non-relativistic oscillations

103

(7)

4.5.2 Forced relativistic oscillations

110

(8)

4.6 About spherical oscillations

118

(11)

4.6.1 Problems formulation

118

(4)

4.6.2 Axial solution

122

(3)

4.6.3 Perturbation method

125

(2)

4.6.4 For numerical modelling

127

(2)

4.7 Bibliography and comments

129

(3)

5 Influence of ion dynamics on plane one-dimensional oscillations

132

(19)

5.1 Formulation of the problem

132

(4)

5.2 Scaling equations and difference scheme

136

(4)

5.3 Axial solution

140

(4)

5.4 Calculation results

144

(4)

5.5 Bibliography and comments

148

(3)

6 Plane two-dimensional relativistic electron oscillations

151

(31)

6.1 Formulation of the problem

151

(2)

6.2 Asymptotic theory

153

(4)

6.3 Difference scheme

157

(6)

6.3.1 Difference equations in the internal nodes of the grid

159

(2)

6.3.2 Implementation of the artificial boundary conditions

161

(2)

6.4 Numerical experiments

163

(17)

6.4.1 General remarks

163

(2)

6.4.2 Calculations with circular symmetry

165

(3)

6.4.3 Quasi-one-dimensional model

168

(5)

6.4.4 Small deviation from circular symmetry

173

(3)

6.4.5 Significant difference from circular symmetry

176

(4)

6.5 Bibliography and comments

180

(2)

Part II Plasma wake waves

7 Introductory information

182

(26)

7.1 Source equations

182

(4)

7.2 The case of an arbitrary pulse velocity

186

(6)

7.2.1 Equations in scalar form

186

(1)

7.2.2 New coordinates and quasistatics

187

(1)

7.2.3 Equations in dimensionless variables

188

(1)

7.2.4 Equations in convenient variables

189

(3)

7.3 The basic formulation of the problem

192

(4)

7.3.1 Nonlinear statement

192

(2)

7.3.2 Linearized formulation

194

(2)

7.4 `Slow' pulse

196

(7)

7.4.1 Linearized equations

196

(1)

7.4.2 Auxiliary Cauchy problem

197

(4)

7.4.3 Numerical---asymptotic method

201

(2)

7.5 Bibliography and comments

203

(5)

8 Numerical algorithms for the basic problem

208

(38)

8.1 Difference method I

208

(8)

8.1.1 Construction of a difference scheme

208

(3)

8.1.2 Study of schemes in variations

211

(3)

8.1.3 The algorithm for implementing the difference scheme I

214

(2)

8.2 Difference method II

216

(5)

8.2.1 Construction of a difference scheme

216

(2)

8.2.2 Study of schemes in variations

218

(1)

8.2.3 Algorithm for the implementation of difference scheme II

219

(2)

8.3 Difference method III (Linearization method)

221

(7)

8.3.1 Setting the task in a convenient form

221

(2)

8.3.2 Preliminary transformations

223

(2)

8.3.3 Difference method III in the linear case

225

(1)

8.3.4 Difference method III in the nonlinear case

226

(2)

8.4 Projection method

228

(5)

8.4.1 Setting the problem in a convenient form

228

(1)

8.4.2 Description of the projection method

229

(3)

8.4.3 Numerical implementation of the projection method

232

(1)

8.5 Numerical experiments and comparison methods

233

(6)

8.6 Bibliography and comments

239

(7)

9 Additional research

246

(35)

9.1 Axial wake wave solution

246

(11)

9.1.1 Formulation of the `truncated' problem

246

(4)

9.1.2 Numerical algorithm for solving the `truncated' problem

250

(1)

9.1.3 Calculation results

251

(6)

9.2 Accounting for the dynamics of ions in the wake wave

257

(11)

9.2.1 Problem statement in physical variables

257

(3)

9.2.2 Statement of the problem in convenient variables

260

(2)

9.2.3 Solution method

262

(4)

9.2.4 Calculation results

266

(2)

9.3 Elliptical pulse

268

(11)

9.3.1 Formulation of the problem

268

(5)

9.3.2 Difference scheme and solution method

273

(4)

9.3.3 Calculation results

277

(2)

9.4 Bibliography and comments

279

(2)

Conclusion

281

(3)

References

284

(7)

Index

291

E.V. Chizhonkov, Lomonosov Moscow State University, Moscow, RU

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E-raamat: Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma

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