where A is the vector-potential of the magnetic field. It has been shown that in this case the disturbance of the initial equilibrium state results in a rapid (with the Alfven velocity ua) establishment of a certain new quasi-equilibrium state through a shift across the force lines; the system will run a number of quasi-equilibrium states determined by the Eq. 4.17.4.
The picture of the shift of the plasma and the frozen-in magnetic field shown in Fig. 4.17.4 may be obtained by treating the above mentioned problem for the region with a neutral point appearing between two parallel currents located on the x-axis and shifted by a small distance ~ It follows from the calculations of the Jacobean of transition from non-shifted to shifted coordinates that the regions with strong rarefaction and compression of the plasma are formed in the region r >> rs (rs is the distance at which the Alfven velocity equals the sonic velocity) during the shift.
The nontrivial region x < 4s also comprises a strong-compression region where the characteristic ratio of the field gradient to plasma concentration is
s where h and ho are the magnetic field gradients.
The value determined by Eq. 4.17.6 defines the criterion of violation of the frozenness in this region since in virtue of the quasi-stationary equation
the ratio h/N cannot exceed the evident limit (since V < c):
where N is the concentration of the charges of both signs in the plasma.
Violation of Eq. 4.17.8 means that the charge concentration becomes insufficient to balance the increased gradient of the magnetic field. This gives rise to the induced electric field E which is directed along the current J and positively affects the particles, thereby increasing their energy. It is this process that provides the magnetic energy conversion into the particle energy, i.e. the dynamic dissipation of the magnetic field. It is characteristic that the process examined is not associated with the Joule dissipation, the current density is saturated when the frozenness condition is violated, and the field energy is lost to increase the total energy of the
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