2. Stationary equilibrium state
We consider a plasma configuration consisting of two semi-infinite homogeneous regions, separated by a nonuniform layer. The axis in a Cartesian coordinate system is perpendicular to the boundaries of the nonuniform plasma layer that are located at and . The basic state quantities depend on the variable z only.
The magnetic field is assumed homogeneous throughout the whole space while the plasma flow with the velocity parallel to the magnetic field, exists for only:
The flow speed is discontinuous at while the other physical quantities, such as the density and the temperature , have smooth profiles within the layer.
Since the effect of gravity is ignored in our treatment, the statics of the basic state is simply given by:
This means that the thermal pressure is uniform due to the assumption const, and that we can freely specify either the plasma density or the temperature . For analytical and numerical reasons, we prescribe the dependence of the cusp speed instead, and express the other basic state quantities in terms of .
with . Clearly, const in our model.
The basic state profiles (3) are prescribed by the values of and in Eq. (4) for the cusp speed. However, the speeds and are not convenient from a practical point of view as they cannot be estimated in a straightforward way. For this reason, we express them in terms of and the temperature ratio of the two uniform regions as follows:
In our model, we assume i.e. and . Region 1 () is thus warmer but less dense than region 2 ().
© European Southern Observatory (ESO) 1998
Online publication: September 30, 1998