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MHD/Shocks: MHD Wave Graphs

Magnetohydrodynamic (MHD) waves, are low-frequency waves (f ≪ ion gyrofrequency) in the plasma. In this module, we examine small amplitude waves propagating in a homogeneous, isotropic, and uniformly magnetized plasma. The program solves for the phase velocity and group velocity of the waves based on the properties of the plasma. The velocities for three MHD wave modes, fast, intermediate, and slow, are calculated by the program. A fourth mode is sometimes discussed, called the entropy fluctuation. This mode does not propagate.

Enter the parameters of the plasma on the left-hand side of the window. The defaults correspond to typical values in the solar wind. These parameters include: the magnetic field strength in nT, number density of the plasma in #/cm3, electron and ion γ (the ratio of specific heats) and temperature in K, and the ion mass in units of the mass of a proton. The electrons and ions are handled separately to allow different ratios of specific heat in the calculation of the sound speed. Click Calculate to update the graphs.

The left graph shows the wave phase velocities of the three MHD modes in km/s. The magnetic field direction is vertical. The polar plot shows the propagation velocities of the phase fronts of the three modes and their dependence on the angle between k (the wave vector) and B (the magnetic field).

The right graph shows the group velocities of the three MHD modes in km/s. The magnetic field direction is also vertical. The plot shows the direction of the energy propagation relative to the magnetic field. Thus it shows how strictly the energy is constrained to follow the magnetic field. It should not be interpreted as the group velocity dependence on the direction of the phase velocity to the magnetic field, which may be quite different. To explore this, use the MHD/Shocks: MHD Wave Case Studies module.