Alfven Hybrid Simulation

\[ P_{parp} = |P_{xx} \cdot B_x + P_{yy} \cdot B_y + P_{zz} \cdot B_z| / |B| \]

Compare $ v_A ?= v_i $ first
One step back, how the RD evolve after generation?
Velocity distribution function
Omidi (1992) Zotero
- Title:: Rotational discontinuities in anisotropic plasmas
Vasquez and Hollweg (1999)
- Title:: Nonlinear evolution of Alfvén waves and RDs-hybrid simulations

BUGS

beta and ion temperature

Ion dynamics in the rotational discontinuities

Formation of rotational discontinuities from oblique linearly polarized Alfven wave trains And ion dynamics in the vicinity of the rotational discontinuities => Hybrid Simulation

Generally speaking the hybrid model approach has difficulty with Whistler waves that are included in the model physics but because their dispersion runs to the electron cyclotron frequency there is a point where the chosen grid and timestep resolution no longer properly resolves these waves (unless you use a very small timestep in which case the value of the hybrid approach is lost).

Numerical dispersion by whistler waves (up to electron cyclotron frequency)

The ponderomotive force (o(OB_l/Ox) exerted by the first-order wave generates waves with twice its wavenumber which have a compressional component and a wave magnetic field in the z-direction.

References

Omidi, N. 1992. “Rotational Discontinuities in Anisotropic Plasmas.” Geophysical Research Letters 19 (13): 1335–38. https://doi.org/10.1029/92GL01127.

Vasquez, Bernard J., and Joseph V. Hollweg. 1999. “Nonlinear Evolution of Alfvén Waves and RDs-hybrid Simulations.” AIP Conference Proceedings 471 (1): 167–72. https://doi.org/10.1063/1.58745.