Plasma kinetic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla.
CRC Press
2008
|
| Series: | Series in plasma physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 323 S. |
| ISBN: | 9781420075809 |
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MARC
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| 100 | 1 | |a Swanson, Donald G. |d 1935- |e Verfasser |0 (DE-588)124291333 |4 aut | |
| 245 | 1 | 0 | |a Plasma kinetic theory |c D. G. Swanson |
| 264 | 1 | |a Boca Raton, Fla. |b CRC Press |c 2008 | |
| 300 | |a XIII, 323 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Series in plasma physics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Plasma dynamics | |
| 650 | 4 | |a Kinetic theory of gases | |
| 650 | 0 | 7 | |a Kinetische Theorie |0 (DE-588)4030669-0 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016663355 | ||
Record in the Search Index
| _version_ | 1804137907435339776 |
|---|---|
| adam_text | Contents
PREFACE
xi
AUTHOR
xiii
INTRODUCTION
1
1.1
Overview
............................. 1
1.2
Plasma frequency
......................... 2
1.3
Debye length
........................... 2
1.4
Plasma parameter
........................ 4
1.5
Distribution functions
...................... 5
1.5.1
Moments of the distribution function
.......... 6
1.5.2
Magnetic pressure
.................... 7
1.6
Cyclotron frequencies
....................... 7
1.7
Collisions
............................. 8
1.7.1
Binary Coulomb collisions
................ 8
1.7.2
Deflection by multiple Coulomb collisions
....... 11
1.7.3
Charge-neutral collisions
................. 13
1.7.4
Charge-exchange collisions
................ 14
1.8
Particle drifts
........................... 14
1.9
Waves
............................... 15
1.9.1
Sound waves
....................... 16
1.9.2
Electromagnetic waves
.................. 16
1.9.3
Alfvén
waves
....................... 17
1.9.4
Electrostatic waves
.................... 18
1.9.5
Plasma waves
....................... 18
1.9.6
Bernstein waves
...................... 18
1.9.7
Wave damping
...................... 18
1.9.8
Large amplitude waves
.................. 19
1.10
Plasma radiation
......................... 19
1.10.1 Bremsstrahlung...................... 19
1.10.2
Blackbody
radiation
................... 20
1.10.3
Impurity radiation
.................... 20
1.10.4
Cyclotron or synchrotron radiation
........... 20
1.10.5
Cherenkov radiation
................... 20
vi Plasma
Kinetic Theory
2
BASIC
KINETIC EQUATIONS
21
2.1
The Klimontovich equation
................... 21
2.1.1
Introduction
........................ 21
2.1.2
The density function
................... 21
2.1.3
The Klimontovich equation
............... 22
2.1.4
Kinetic equation
..................... 23
2.2
The Liouville equation
...................... 26
2.2.1
Introduction
........................ 26
2.2.2
Liouville equation
—
standard form
.......... 27
2.3
System ensembles
......................... 28
2.3.1
BBGKY hierarchy
.................... 29
2.3.2
Truncating the BBGKY hierarchy
........... 33
3
THE LENARD-BALESCU EQUATION
39
3.1
Bogolyubov s hypothesis
..................... 39
3.2
Solution via Fourier and Laplace transforms
.......... 41
3.2.1
Transforming the evolution equations
.......... 43
3.2.2
Inverting the operators
.................. 45
3.2.3
Integrating over
рг
.................... 46
3.2.4
Integrating over pi
.................... 48
3.2.5
Integrating over fc
.................... 51
3.3
The Fokker-Planck equation
................... 52
3.4
Dynamic friction and diffusion
................. 53
3.4.1
Runaway electrons in a steady electric field
...... 54
3.4.2
Resonant wave heating
.................. 58
4
THE VLASOV-MAXWELL EQUATIONS
69
4.1
Electrostatic waves in an unmagnetized plasma
........ 69
4.1.1
Vlasov
method
...................... 70
4.1.2
Landau solution
...................... 73
4.2
Effects of collisions on Landau damping
............ 79
4.3
The Debye potential
....................... 82
4.3.1
Potential of a stationary test charge
.......... 82
4.3.2
Average potential of thermal test charges
....... 84
5
WAVES IN A MAGNETIZED HOT PLASMA
89
5.1
The hot plasma dielectric tensor
................ 89
5.1.1
The evolution of the distribution function
....... 89
5.1.2
Integrating along the unperturbed orbits
........ 91
5.1.3
General fo(vj_,vz)
.................... 93
5.1.4
Maxwellian distributions
................. 96
5.1.5
The dielectric tensor
................... 100
5.1.6
The hot plasma dispersion relation
........... 103
5.1.7
Examples of hot plasma wave effects
.......... 103
5.2
Electrostatic waves
........................ 107
Table of Contents
vii
5.2.1
Electrostatic dispersion relation
.............107
5.2.2
Perpendicular propagation
-
Bernstein modes
.....109
5.3
Velocity space instabilities
....................110
5.3.1 Anisotropie
temperature
.................110
5.3.2
Bump-on-the-tail instability
...............112
5.4
Conservation of energy and power flow
.............114
5.4.1
Poynting s theorem for kinetic waves
..........114
5.4.2
Group velocity and kinetic flux
.............116
5.5
Collisional effects
.........................119
5.5.1
Collisions via the Krook model
.............119
5.5.2
Collisions via a Fokker-Planck model
..........119
5.6
Relativistic plasma effects
....................120
5.6.1
The relativistic dielectric tensor
.............121
5.6.2
The relativistic dielectric tensor without sums
.....124
5.6.3
The weakly relativistic dielectric tensor
........125
5.6.4
Moderately relativistic expressions
...........128
5.6.5
Exact expressions with
пц
= 0..............130
5.6.6
The relativistic X-wave
.................134
6
MOMENT EQUATIONS AND FLUID PLASMAS
137
6.1
Moments of the distribution function
..............138
6.1.1
The simple moment equations
..............138
6.1.2
Plasma oscillations
....................140
6.1.3
The kinetic moment equations
.............143
6.2
The fluid equations
........................146
6.3
Low frequency waves
.......................147
6.3.1
The low frequency dispersion relation
.........147
6.3.2
Stringer diagrams
.....................150
6.4
High frequency waves
.......................151
6.4.1
Warm plasma dispersion relation
............151
6.4.2
Electrostatic dispersion relation
.............157
6.4.3
Parallel and perpendicular propagation
.........162
6.4.4
Summary of fluid waves
.................162
7
TRANSPORT IN
A
NONUNIFORM GAS
165
7.1
Boltzmann equation
.......................165
7.2
Collision symmetries
.......................167
7.3
Collision theorems
........................170
7.4
The equilibrium state
......................171
7.5
The mean free time theory
....................176
7.6
The formal theory of kinetic processes
.............181
7.7
Results of the variational procedure
...............189
via Plasma Kinetic Theory
8
TRANSPORT IN
A
NONUNIFORM
BINARY GAS
197
8.1
The Boltzmann equations
....................197
8.2
The equations of hydrodynamics
................198
8.3
The collision terms
........................202
8.4
The equilibrium state
......................205
8.5
The formal theory of kinetic processes
.............207
8.6
The variation method
......................219
8.6.1
Definition of {G; H}
...................221
8.6.2
The Davison function
..................222
8.7
Results
...............................223
8.7.1
Viscosity
..........................223
8.7.2
Diffusion and electrical conductivity
..........225
8.7.3
Thermal conduction
...................229
9
TRANSPORT WITH A FINITE MAGNETIC FIELD
233
9.1
Boltzmann equations
.......................233
9.2
The magnetohydrodynamic
(MHD)
equations
.........234
9.3
The formal theory of kinetic processes
.............236
9.4
Solutions for the electrical conductivity
.............251
9.4.1
Solving for the ef
....................253
9.5
Thermal conductivity and diffusion
...............258
9.5.1
Variational results
....................258
9.5.2
The transport coefficients
................260
9.5.3
Convergence and accuracy
................262
9.6
The pressure tensor
........................262
9.6.1
Solving for G,
.......................270
9.6.2
The pressure tensor elements
..............271
9.7
Summary of results
........................276
A MATHEMATICAL FUNCTIONS
283
A.I The plasma dispersion function
.................283
A.
1.1
Definition of the plasma dispersion function
......283
A.I.
2
Relation to the error function for complex argument
. 284
A.1.3 Relation to the
Y
function
................287
A.
1.4
Relation to the
W
function
...............287
A.
2
Relativistic plasma dispersion functions
............288
A.
2.1
Weakly relativistic dispersion function
.........288
A.2.2 Generalized relativistic dispersion function
.......289
A.3 Gamma Function,
Γ(ζ)
.....................290
A.3.1 Definition
.........................290
A.3.
2
Incomplete gamma function
...............291
A.
4
Generalized hypergeometric functions
..............292
A.4.1 Hypergeometric function integrals
—
first type
.... 292
A.4.2 Hypergeometric function integrals
—
second type
. . . 293
A.
5
Vector identities
.........................293
Table of Contents
ix
A.
5.1
Products of three vectors
................293
A.
5.2
Vector identities with the V operator
..........294
В
COLLISION INTEGRALS
295
B.I Rutherford scattering
.......................295
B.2 Collision integrals
.........................299
С
NOTATION AND LIST OP SYMBOLS
309
C.I Mathematical notation
......................309
C.2 List of symbols
..........................310
Bibliography
315
Index
319
|
| adam_txt |
Contents
PREFACE
xi
AUTHOR
xiii
INTRODUCTION
1
1.1
Overview
. 1
1.2
Plasma frequency
. 2
1.3
Debye length
. 2
1.4
Plasma parameter
. 4
1.5
Distribution functions
. 5
1.5.1
Moments of the distribution function
. 6
1.5.2
Magnetic pressure
. 7
1.6
Cyclotron frequencies
. 7
1.7
Collisions
. 8
1.7.1
Binary Coulomb collisions
. 8
1.7.2
Deflection by multiple Coulomb collisions
. 11
1.7.3
Charge-neutral collisions
. 13
1.7.4
Charge-exchange collisions
. 14
1.8
Particle drifts
. 14
1.9
Waves
. 15
1.9.1
Sound waves
. 16
1.9.2
Electromagnetic waves
. 16
1.9.3
Alfvén
waves
. 17
1.9.4
Electrostatic waves
. 18
1.9.5
Plasma waves
. 18
1.9.6
Bernstein waves
. 18
1.9.7
Wave damping
. 18
1.9.8
Large amplitude waves
. 19
1.10
Plasma radiation
. 19
1.10.1 Bremsstrahlung. 19
1.10.2
Blackbody
radiation
. 20
1.10.3
Impurity radiation
. 20
1.10.4
Cyclotron or synchrotron radiation
. 20
1.10.5
Cherenkov radiation
. 20
vi Plasma
Kinetic Theory
2
BASIC
KINETIC EQUATIONS
21
2.1
The Klimontovich equation
. 21
2.1.1
Introduction
. 21
2.1.2
The density function
. 21
2.1.3
The Klimontovich equation
. 22
2.1.4
Kinetic equation
. 23
2.2
The Liouville equation
. 26
2.2.1
Introduction
. 26
2.2.2
Liouville equation
—
standard form
. 27
2.3
System ensembles
. 28
2.3.1
BBGKY hierarchy
. 29
2.3.2
Truncating the BBGKY hierarchy
. 33
3
THE LENARD-BALESCU EQUATION
39
3.1
Bogolyubov's hypothesis
. 39
3.2
Solution via Fourier and Laplace transforms
. 41
3.2.1
Transforming the evolution equations
. 43
3.2.2
Inverting the operators
. 45
3.2.3
Integrating over
рг
. 46
3.2.4
Integrating over pi
. 48
3.2.5
Integrating over fc
. 51
3.3
The Fokker-Planck equation
. 52
3.4
Dynamic friction and diffusion
. 53
3.4.1
Runaway electrons in a steady electric field
. 54
3.4.2
Resonant wave heating
. 58
4
THE VLASOV-MAXWELL EQUATIONS
69
4.1
Electrostatic waves in an unmagnetized plasma
. 69
4.1.1
Vlasov
method
. 70
4.1.2
Landau solution
. 73
4.2
Effects of collisions on Landau damping
. 79
4.3
The Debye potential
. 82
4.3.1
Potential of a stationary test charge
. 82
4.3.2
Average potential of thermal test charges
. 84
5
WAVES IN A MAGNETIZED HOT PLASMA
89
5.1
The hot plasma dielectric tensor
. 89
5.1.1
The evolution of the distribution function
. 89
5.1.2
Integrating along the unperturbed orbits
. 91
5.1.3
General fo(vj_,vz)
. 93
5.1.4
Maxwellian distributions
. 96
5.1.5
The dielectric tensor
. 100
5.1.6
The hot plasma dispersion relation
. 103
5.1.7
Examples of hot plasma wave effects
. 103
5.2
Electrostatic waves
. 107
Table of Contents
vii
5.2.1
Electrostatic dispersion relation
.107
5.2.2
Perpendicular propagation
-
Bernstein modes
.109
5.3
Velocity space instabilities
.110
5.3.1 Anisotropie
temperature
.110
5.3.2
Bump-on-the-tail instability
.112
5.4
Conservation of energy and power flow
.114
5.4.1
Poynting's theorem for kinetic waves
.114
5.4.2
Group velocity and kinetic flux
.116
5.5
Collisional effects
.119
5.5.1
Collisions via the Krook model
.119
5.5.2
Collisions via a Fokker-Planck model
.119
5.6
Relativistic plasma effects
.120
5.6.1
The relativistic dielectric tensor
.121
5.6.2
The relativistic dielectric tensor without sums
.124
5.6.3
The weakly relativistic dielectric tensor
.125
5.6.4
Moderately relativistic expressions
.128
5.6.5
Exact expressions with
пц
= 0.130
5.6.6
The relativistic X-wave
.134
6
MOMENT EQUATIONS AND FLUID PLASMAS
137
6.1
Moments of the distribution function
.138
6.1.1
The simple moment equations
.138
6.1.2
Plasma oscillations
.140
6.1.3
The kinetic moment equations
.143
6.2
The fluid equations
.146
6.3
Low frequency waves
.147
6.3.1
The low frequency dispersion relation
.147
6.3.2
Stringer diagrams
.150
6.4
High frequency waves
.151
6.4.1
Warm plasma dispersion relation
.151
6.4.2
Electrostatic dispersion relation
.157
6.4.3
Parallel and perpendicular propagation
.162
6.4.4
Summary of fluid waves
.162
7
TRANSPORT IN
A
NONUNIFORM GAS
165
7.1
Boltzmann equation
.165
7.2
Collision symmetries
.167
7.3
Collision theorems
.170
7.4
The equilibrium state
.171
7.5
The mean free time theory
.176
7.6
The formal theory of kinetic processes
.181
7.7
Results of the variational procedure
.189
via Plasma Kinetic Theory
8
TRANSPORT IN
A
NONUNIFORM
BINARY GAS
197
8.1
The Boltzmann equations
.197
8.2
The equations of hydrodynamics
.198
8.3
The collision terms
.202
8.4
The equilibrium state
.205
8.5
The formal theory of kinetic processes
.207
8.6
The variation method
.219
8.6.1
Definition of {G; H}
.221
8.6.2
The Davison function
.222
8.7
Results
.223
8.7.1
Viscosity
.223
8.7.2
Diffusion and electrical conductivity
.225
8.7.3
Thermal conduction
.229
9
TRANSPORT WITH A FINITE MAGNETIC FIELD
233
9.1
Boltzmann equations
.233
9.2
The magnetohydrodynamic
(MHD)
equations
.234
9.3
The formal theory of kinetic processes
.236
9.4
Solutions for the electrical conductivity
.251
9.4.1
Solving for the ef
.253
9.5
Thermal conductivity and diffusion
.258
9.5.1
Variational results
.258
9.5.2
The transport coefficients
.260
9.5.3
Convergence and accuracy
.262
9.6
The pressure tensor
.262
9.6.1
Solving for G,
.270
9.6.2
The pressure tensor elements
.271
9.7
Summary of results
.276
A MATHEMATICAL FUNCTIONS
283
A.I The plasma dispersion function
.283
A.
1.1
Definition of the plasma dispersion function
.283
A.I.
2
Relation to the error function for complex argument
. 284
A.1.3 Relation to the
Y
function
.287
A.
1.4
Relation to the
W
function
.287
A.
2
Relativistic plasma dispersion functions
.288
A.
2.1
Weakly relativistic dispersion function
.288
A.2.2 Generalized relativistic dispersion function
.289
A.3 Gamma Function,
Γ(ζ)
.290
A.3.1 Definition
.290
A.3.
2
Incomplete gamma function
.291
A.
4
Generalized hypergeometric functions
.292
A.4.1 Hypergeometric function integrals
—
first type
. 292
A.4.2 Hypergeometric function integrals
—
second type
. . . 293
A.
5
Vector identities
.293
Table of Contents
ix
A.
5.1
Products of three vectors
.293
A.
5.2
Vector identities with the V operator
.294
В
COLLISION INTEGRALS
295
B.I Rutherford scattering
.295
B.2 Collision integrals
.299
С
NOTATION AND LIST OP SYMBOLS
309
C.I Mathematical notation
.309
C.2 List of symbols
.310
Bibliography
315
Index
319 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Swanson, Donald G. 1935- |
| author_GND | (DE-588)124291333 |
| author_facet | Swanson, Donald G. 1935- |
| author_role | aut |
| author_sort | Swanson, Donald G. 1935- |
| author_variant | d g s dg dgs |
| building | Verbundindex |
| bvnumber | BV023481218 |
| callnumber-first | Q - Science |
| callnumber-label | QC718 |
| callnumber-raw | QC718.5.T5 |
| callnumber-search | QC718.5.T5 |
| callnumber-sort | QC 3718.5 T5 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 1300 |
| ctrlnum | (OCoLC)181142683 (DE-599)BVBBV023481218 |
| dewey-full | 530.4/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/4 |
| dewey-search | 530.4/4 |
| dewey-sort | 3530.4 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV023481218 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:38:00Z |
| indexdate | 2024-07-09T21:19:45Z |
| institution | BVB |
| isbn | 9781420075809 |
| language | English |
| lccn | 2008009175 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016663355 |
| oclc_num | 181142683 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XIII, 323 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Series in plasma physics |
| spelling | Swanson, Donald G. 1935- Verfasser (DE-588)124291333 aut Plasma kinetic theory D. G. Swanson Boca Raton, Fla. CRC Press 2008 XIII, 323 S. txt rdacontent n rdamedia nc rdacarrier Series in plasma physics Includes bibliographical references and index Plasma dynamics Kinetic theory of gases Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Plasmadynamik (DE-588)4123952-0 gnd rswk-swf Plasmadynamik (DE-588)4123952-0 s Kinetische Theorie (DE-588)4030669-0 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swanson, Donald G. 1935- Plasma kinetic theory Plasma dynamics Kinetic theory of gases Kinetische Theorie (DE-588)4030669-0 gnd Plasmadynamik (DE-588)4123952-0 gnd |
| subject_GND | (DE-588)4030669-0 (DE-588)4123952-0 |
| title | Plasma kinetic theory |
| title_auth | Plasma kinetic theory |
| title_exact_search | Plasma kinetic theory |
| title_exact_search_txtP | Plasma kinetic theory |
| title_full | Plasma kinetic theory D. G. Swanson |
| title_fullStr | Plasma kinetic theory D. G. Swanson |
| title_full_unstemmed | Plasma kinetic theory D. G. Swanson |
| title_short | Plasma kinetic theory |
| title_sort | plasma kinetic theory |
| topic | Plasma dynamics Kinetic theory of gases Kinetische Theorie (DE-588)4030669-0 gnd Plasmadynamik (DE-588)4123952-0 gnd |
| topic_facet | Plasma dynamics Kinetic theory of gases Kinetische Theorie Plasmadynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT swansondonaldg plasmakinetictheory |