E. Alec Johnson: References for Plasma Computation

Plasma modeling

• Balance laws (derivations)
  • A book-keeping derivation of multi-fluid equations from a kinetic description of a plasma (written in my beginnings) [.dvi] [.pdf]
  • A book-keeping derivation of 1-fluid equations from multi-fluid equations (written in my beginnings) [.dvi] [.pdf] [.tex]
  • A compact elementary derivation of Magnetohydrodynamics (MHD) and two-fluid plasma equations.
    In five pages: [.dvi] , [.pdf] , [.tex] .
    On two sides of one sheet: [.ps], [.pdf].
    Makefile to produce this stuff: Makefile
  • A brief derivation of Ohm's law and extended MHD starting from nondimensionalized two-fluid equations. [.pdf]
    (Invokes simplifying assumptions such as quasineutrality right away to get to specific results.)
  • A careful derivation of Ohm's law and extended MHD starting from statistical mechanics. [.pdf]
  • General moment evolution. [.pdf]
• Closure
  • The Gaussian (ten-moment entropy-maximizing) distribution
  • 10-moment (and 5-moment) closure [.pdf]
  • Ten-moment two-fluid Hall MHD [.htm]

Plasma analysis

• Waves in Plasmas (eigenstructure)
  • waves in MHD (in primitive variables only) [.pdf]
  • waves in Maxwell's equations (including correction potentials) [.pdf]
  • waves in 10-moment gas-dynamics (assuming Gaussian pressure tensor) [.pdf]
• Source term
  • Exact solution of two-fluid source term ODE (for five and ten moments) [.pdf]
• Problems
  • The Geospace Environmental Modeling (GEM) magnetic reconnection challenge problem [.pdf]
  • Steady reconnection problems [.pdf]
  • X-point analysis [.pdf]

Numerical methods for plasma

• Discontinuous Galerkin (DG) methods
  • brief summary of quadrature rules for rectangles
  • overview of the DG method (hand-out of an old talk)
  • proof of consistency of DG method (hand-out of a talk)
• Handling weak diffusive terms explictly with the discontinuous Galerkin method
• Constrained Transport (old)
  • PIC algorithm for collisionless plasma (includes description of multi-dimensional Yee scheme). [.pdf]
  • Yee scheme (old; 1 dimension) [.pdf]
  • Projection onto given divergence (old) [.dvi] [.pdf]