Physics:Quantum Magnetohydrodynamics

← Back to Book:Quantum Collection Book I

← Back to Plasma and kinetic methods Book III

Magnetohydrodynamics (MHD) describes the behavior of conducting fluids such as plasmas.

It is derived as a macroscopic limit of kinetic theory.

File:Not found

Fundamental equations

Magnetohydrodynamics is described by a set of coupled equations:

Continuity equation (mass conservation):

$\frac{\partial \rho }{\partial t}+\mathrm{\nabla }\cdot (\rho 𝐮)=0$

Momentum equation:

$\rho (\frac{\partial 𝐮}{\partial t}+𝐮\cdot \mathrm{\nabla }𝐮)=-\mathrm{\nabla }p+𝐉\times 𝐁$

Induction equation:

$\frac{\partial 𝐁}{\partial t}=\mathrm{\nabla }\times (𝐮\times 𝐁)$

Magnetic constraint:

$\mathrm{\nabla }\cdot 𝐁=0$

Limitations

MHD does not include effects described by transport theory or drift physics.

Index

Core theory

1. Foundations

2. Conceptual and interpretations

3. Mathematical structure and systems

4. Atomic and spectroscopy

5. Wavefunctions and modes

6. Quantum dynamics and evolution

7. Measurement and information

8. Quantum information and computing

Applications and extensions

9. Quantum optics and experiments

10. Open quantum systems

11. Quantum field theory

12. Statistical mechanics and kinetic theory

13. Condensed matter and solid-state physics

14. Plasma and fusion physics

15. Timeline

16. Advanced and frontier topics

Book II

• Matter by scale

Book III

• Methods and tools

Book IV

• Data Analysis Techniques

Full contents

1. Foundations (14) Back to index

1. Physics:Quantum basics

2. Physics:Quantum photoelectric effect

3. Physics:Quantum black-body radiation

4. Physics:Quantum Planck constant

5. Physics:Quantum Postulates

6. Physics:Quantum Hilbert space

7. Physics:Quantum Observables and operators

8. Physics:Quantum mechanics

9. Physics:Quantum mechanics measurements

10. Physics:Quantum state

11. Physics:Quantum system

12. Physics:Quantum superposition

13. Physics:Quantum probability

14. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (14) Back to index

15. Physics:Quantum Interpretations of quantum mechanics

16. Physics:Quantum Wave–particle duality

17. Physics:Quantum Complementarity principle

18. Physics:Quantum Uncertainty principle

19. Physics:Quantum Measurement problem

20. Physics:Quantum Bell's theorem

21. Physics:Quantum Hidden variable theory

22. Physics:Quantum nonlocality

23. Physics:Quantum contextuality

24. Physics:Quantum Darwinism

25. Physics:Quantum A Spooky Action at a Distance

26. Physics:Quantum A Walk Through the Universe

27. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

28. Physics:Quantum measurement problem

3. Mathematical structure and systems (15) Back to index

29. Physics:Quantum Density matrix

30. Physics:Quantum Exactly solvable quantum systems

31. Physics:Quantum many-body problem

32. Physics:Quantum Formulas Collection

33. Physics:Quantum A Matter Of Size

34. Physics:Quantum Symmetry in quantum mechanics

35. Physics:Quantum Noether theorem

36. Physics:Quantum Angular momentum operator

37. Physics:Quantum Runge–Lenz vector

38. Physics:Quantum Approximation Methods

39. Physics:Quantum Matter Elements and Particles

40. Physics:Quantum Dirac equation

41. Physics:Quantum Klein–Gordon equation

42. Physics:Quantum pendulum

43. Physics:Quantum configuration space

4. Atomic and spectroscopy (14) Back to index

44. Physics:Quantum Atomic structure and spectroscopy

45. Physics:Quantum Hydrogen atom

46. Physics:Quantum number

47. Physics:Quantum Multi-electron atoms

48. Physics:Quantum Fine structure

49. Physics:Quantum Hyperfine structure

50. Physics:Quantum Isotopic shift

51. Physics:Quantum defect

52. Physics:Quantum Zeeman effect

53. Physics:Quantum Stark effect

54. Physics:Quantum Spectral lines and series

55. Physics:Quantum Selection rules

56. Physics:Quantum Fermi's golden rule

57. Physics:Quantum beats

5. Wavefunctions and modes (9) Back to index

58. Physics:Quantum Wavefunction

59. Physics:Quantum Superposition principle

60. Physics:Quantum Eigenstates and eigenvalues

61. Physics:Quantum Boundary conditions and quantization

62. Physics:Quantum Standing waves and modes

63. Physics:Quantum Normal modes and field quantization

64. Physics:Number of independent spatial modes in a spherical volume

65. Physics:Quantum Density of states

66. Physics:Quantum carpet

6. Quantum dynamics and evolution (21) Back to index

67. Physics:Quantum Time evolution

68. Physics:Quantum Schrödinger equation

69. Physics:Quantum Time-dependent Schrödinger equation

70. Physics:Quantum Stationary states

71. Physics:Quantum Perturbation theory

72. Physics:Quantum Time-dependent perturbation theory

73. Physics:Quantum Adiabatic theorem

74. Physics:Quantum Berry phase

75. Physics:Quantum Aharonov-Bohm effect

76. Physics:Quantum Aharonov-Casher effect

77. Physics:Quantum Scattering theory

78. Physics:Quantum Scattering matrix

79. Physics:Quantum S-matrix

80. Physics:Quantum tunnelling

81. Physics:Quantum speed limit

82. Physics:Quantum revival

83. Physics:Quantum reflection

84. Physics:Quantum oscillations

85. Physics:Quantum jump

86. Physics:Quantum boomerang effect

87. Physics:Quantum chaos

7. Measurement and information (9) Back to index

88. Physics:Quantum Measurement theory

89. Physics:Quantum Measurement operators

90. Physics:Quantum Projective measurement

91. Physics:Quantum POVM

92. Physics:Quantum Weak measurement

93. Physics:Quantum Measurement collapse

94. Physics:Quantum entanglement

95. Physics:Quantum Zeno effect

96. Physics:Quantum limit

8. Quantum information and computing (15) Back to index

97. Physics:Quantum information theory

98. Physics:Quantum Qubit

99. Physics:Quantum Entanglement

100. Physics:Quantum Bell state

101. Physics:Quantum Gates and circuits

102. Physics:Quantum BB84

103. Physics:Quantum No-cloning theorem

104. Physics:Quantum Computing Algorithms in the NISQ Era

105. Physics:Quantum Noisy Qubits

106. Physics:Quantum error correction

107. Physics:Quantum Boson sampling

108. Physics:Quantum random access code

109. Physics:Quantum pseudo-telepathy

110. Physics:Quantum network

111. Physics:Quantum money

9. Quantum optics and experiments (10) Back to index

112. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

113. Physics:Quantum Stern-Gerlach experiment

114. Physics:Quantum Experimental quantum physics

115. Physics:Quantum optics

116. Physics:Quantum optics beam splitter experiments

117. Physics:Quantum Mach-Zehnder interferometer

118. Physics:Quantum Hong-Ou-Mandel effect

119. Physics:Quantum eraser experiment

120. Physics:Quantum delayed-choice quantum eraser

121. Physics:Quantum Ultra fast lasers

122. Template:Quantum optics operators

10. Open quantum systems (15) Back to index

123. Physics:Quantum Open systems

124. Physics:Quantum channel

125. Physics:Quantum Kraus operators

126. Physics:Quantum Amplitude damping

127. Physics:Quantum Phase damping

128. Physics:Quantum Depolarizing channel

129. Physics:Quantum Master equation

130. Physics:Quantum Lindblad equation

131. Physics:Quantum Decoherence

132. Physics:Quantum Dynamical decoupling

133. Physics:Quantum dissipation

134. Physics:Quantum Markov semigroup

135. Physics:Quantum Markovian dynamics

136. Physics:Quantum Non-Markovian dynamics

137. Physics:Quantum Trajectories

11. Quantum field theory (23) Back to index

138. Physics:Quantum field theory (QFT) basics

139. Physics:Quantum field theory (QFT) core

140. Physics:Quantum Fields and Particles

141. Physics:Quantum Second quantization

142. Physics:Quantum Fock space

143. Physics:Quantum Harmonic Oscillator field modes

144. Physics:Quantum Creation and annihilation operators

145. Physics:Quantum vacuum fluctuations

146. Physics:Quantum Casimir effect

147. Physics:Quantum Propagators in quantum field theory

148. Physics:Quantum Feynman diagrams

149. Physics:Quantum Path integral formulation

150. Physics:Quantum Renormalization in field theory

151. Physics:Quantum Renormalization group

152. Physics:Quantum Field Theory Gauge symmetry

153. Physics:Quantum Spontaneous symmetry breaking

154. Physics:Quantum Non-Abelian gauge theory

155. Physics:Quantum Electrodynamics (QED)

156. Physics:Quantum chromodynamics (QCD)

157. Physics:Quantum Electroweak theory

158. Physics:Quantum Standard Model

159. Physics:Quantum triviality

160. Physics:Quantum confinement problem

12. Statistical mechanics and kinetic theory (9) Back to index

161. Physics:Quantum Statistical mechanics

162. Physics:Quantum Partition function

163. Physics:Quantum Distribution functions

164. Physics:Quantum Liouville equation

165. Physics:Quantum Kinetic theory

166. Physics:Quantum Boltzmann equation

167. Physics:Quantum BBGKY hierarchy

168. Physics:Quantum Relaxation and thermalization

169. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (17) Back to index

170. Physics:Quantum Band structure

171. Physics:Quantum Fermi surfaces

172. Physics:Quantum Landau levels

173. Physics:Quantum fractional Hall effect

174. Physics:Quantum Semiconductor physics

175. Physics:Quantum Phonons

176. Physics:Quantum Electron-phonon interaction

177. Physics:Quantum Exchange interaction

178. Physics:Quantum Superconductivity

179. Physics:Quantum Topological phases of matter

180. Physics:Quantum anyon

181. Physics:Quantum well

182. Physics:Quantum spin liquid

183. Physics:Quantum spin Hall effect

184. Physics:Quantum phase transition

185. Physics:Quantum critical point

186. Physics:Quantum dot

14. Plasma and fusion physics (8) Back to index

187. Physics:Quantum Fusion reactions and Lawson criterion

188. Physics:Quantum Plasma (fusion context)

189. Physics:Quantum Magnetic confinement fusion

190. Physics:Quantum Inertial confinement fusion

191. Physics:Quantum Plasma instabilities and turbulence

192. Physics:Quantum Tokamak core plasma

193. Physics:Quantum Tokamak edge physics and recycling asymmetries

194. Physics:Quantum Stellarator

15. Timeline (8) Back to index

195. Physics:Quantum mechanics/Timeline

196. Physics:Quantum mechanics/Timeline/Pre-quantum era

197. Physics:Quantum mechanics/Timeline/Old quantum theory

198. Physics:Quantum mechanics/Timeline/Modern quantum mechanics

199. Physics:Quantum mechanics/Timeline/Quantum field theory era

200. Physics:Quantum mechanics/Timeline/Quantum information era

201. Physics:Quantum mechanics/Timeline/Quantum technology era

202. Physics:Quantum mechanics/Timeline/Quiz

16. Advanced and frontier topics (16) Back to index

203. Physics:Quantum topology

204. Physics:Quantum battery

205. Physics:Quantum Supersymmetry

206. Physics:Quantum Black hole thermodynamics

207. Physics:Quantum Holographic principle

208. Physics:Quantum gravity

209. Physics:Quantum De Sitter invariant special relativity

210. Physics:Quantum Doubly special relativity

211. Physics:Quantum arithmetic geometry

212. Physics:Quantum unsolved problems

213. Physics:Quantum Yang-Mills mass gap

214. Physics:Quantum gravity problem

215. Physics:Quantum black hole information paradox

216. Physics:Quantum dark matter problem

217. Physics:Quantum neutrino mass problem

218. Physics:Quantum matter-antimatter asymmetry problem

References

Author: Harold Foppele

Source attribution: Magnetohydrodynamics