In FY80 we have developed a scientific program to study this beammagnetosphere interaction problem for realistic plasma distributions on a dipolar magnetic field. These aspects of the problem are very important because the plasma density and magnetic field strength along a plasmaspheric field line vary by orders of magnitude. Consequently, the simple constant density and magnetic field considerations of Scholer (1970) do not apply. Numerical calculations verify that the momentum transfer process has a time constant of < 20 sec, so the argon beam has a length of < 2000 km. To formulate the problem we use the coordinate system of Fig. 1 and assume the following magnetohydrodynamic equations: (a) We assume the frozen-field condition that the displacement [[spi:math]] of the plasma (displacement of the beam and the ambient plasma) coincides with the displacement of the magnetic field [[spi:math]] , i.e., [[spi:math]] (11) In this calculation, we shall always assume that [[spi:math]] and [[spi:math]]. Eq. (11) can be integrated over time t, yielding [[spi:math]] (12) b) In our case of inhomogeneous magnetic field and plasma distributions, the equations of momentum conservation must be expressed in terms of the energy component of the Maxwell stress tensor [[spi:math]] [[spi:math]] (13) 20
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