lines show schematically earth’s magnetic field lines at various times. The condition [[spi:math]] means that these lines are frozen into the plasma beam at the equator; their distortion is an Alfven wave (t = 1, in Figure 8). At t = 2, the wave reaches the ionosphere, where the foot of the field line slips, because of the ionosphere’s finite conductivity; the wave then reflects back to the beam (t = 3,4). The field lines act somewhat like rubber bands, tending to retard the cloud. The physical mechanism is that the polarization charges responsible for [[spi:math]] move along the field lines at the Alfven speed vA, accelerating magnetospheric plasma and transferring momentum out of the beam. Ultimately, the Alfven wave reaches the ionosphere and drives dissipative Pedersen currents (in the absence of dissipation, the argon beam would oscillate like a mass on a rubber band field line). Let MAbe the mass density of the argon beam, integrated along field lines passing through the beam: [[spi:math]] (10) When this mass density is equal to the mass per unit area incorporated by the Alfven wave, namely [[spi:math]], the beam is essentially stopped. Here [[spi:math]] is the time it takes the Alfven wave to travel a distance vA [[spi:math]], and n0 mp is the magnetospheric mass density per unit volume. For the argon beam, [[spi:math]], this gives [[spi:math]] few seconds. The beam’s velocity behaves like [[spi:math]] , so the beam can only travel a distance of the order of v0 [[spi:math]] <= 103 km. In this qualitative example, the beam momentum is soaked up by magnetospheric plasma extending at most a few thousand kilometers down the field line on either side of the beam. 18
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