Action Principles and Conservation Laws
- Introduction
- The Model**
- The MHD Equations
- Energy Conservation
- Faraday’s Equation and Flux Conservation
- Field Line or Vortex Line Preservation
- Incompressible Fluid and MHD Limit
- Reduced MHD
- Solar and Heliospheric Physics Applications
- Helicity in Fluids and MHD**
- Helicity in Fluid Dynamics
- Helicity in MHD
- Magnetic Field Line Flow
- Magnetic Helicity Conservation Law
- Cross Helicity
- Nonlocal Conservation Laws
- Noether’s Theorems and the DirectMethod.
- Advected Invariants
- Topological Invariants.
- Euler-Poincaré Equation Approach
- Hamiltonian Approach
- Multi-Symplectic Clebsch Approach
- The Lagrangian Map.
- Symmetries and Noether’s Theorem in MHD.
- MHD Stability
- Appendix A Lie Derivatives .
- Appendix B Weber Transformations
- Appendix C Cauchy Invariant b = B/Rho
- Appendix D Magnetosonic N-Waves
- Appendix E Aharonov Bohm Effects in MHD
- Appendix F Equivalence Transformations
- Appendix G Covariant, Non-relativistic MHD**