Inertial Alfven waves, mode conversion, resonance cones

Below: Proposed model showing inertial Alfven resonance cones excited by magnetic reconnection in Earth's magnetotail [from P. Bellan, Geophys. Res. Letters, 23,1717(1996)].

An investigation of non-MHD Alfven phenomena has been underway for the last six years.

Here is a summary of the main results (see publications for details).

Comparison to traditional models: Low frequency magnetized plasma phenomena have traditionally been modeled using ideal magnetohydrodynamics (MHD) where the plasma is assumed to behave as if it is fluid with no electrical resistance, i.e., is like a superconductor. This assumption is based on the idea that the rapid collisionless motion of light-weight electrons `shorts out' electric fields in the plasma frame. MHD predicts that an accumulation of wave energy (resonance) occurs whenever the parallel phase velocity of a wave matches the local Alfven velocity.

Inertial Alfven modes: Two fluid models take into account finite electron inertia and show that electrons do not `short out' the electric field in the plasma frame. This removes the singularity predicted by MHD discussed above. It also gives structure to the shear Alfven wave in the direction perpendicular to the magnetic field.

Magnetic Reconnection: Evolving MHD systems often develop strong spatial gradients of magnetic field at the interface between two topologically distinct regions; typically these  involve a  nearly discontinuous change in the direction of the magnetic field across the interface. An example would be the interface between two adjacent twisted magnetic flux tubes. The abrupt change in field angle corresponds to a thin sheet of intense current at the interface. If the current sheet becomes sufficiently thin, the electrons constituting the current will move so fast as to destabilize Alfven waves by inverse Landau damping (analogous to a Cerenkov instability). The destabilized waves carry energy away from the current sheet and so constitute an effective resistive load on the current. Depletion of the current sheet will change the magnetic topology and lead to magnetic reconnection.

Mode conversion: The two fluid theory shows when the parallel wave phase velocity matches the local Alfven velocity, there is a mode conversion from compressional Alfven wave to inertial shear Alfven wave. The total wave energy flux is conserved throughout, so that contrary to ideal MHD, there is no accumulation of wave energy anywhere.

Resonance cones: It has recently been realized that inertial Alfven waves have a resonance cone structure. This means that a spatially localized source at fixed frequency excites a cone of radiation with axis along the magnetic field passing through the source, apex at the source, and cone angle determined by the frequency. One recent publication shows how a localized temporal pulse will excite a pattern consisting of a superposition of resonance cones having a range of cone angles and postulates that certain auroral oscillations are manifestations of this pattern.

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