Question

Plasma question

Question 1. Consider a cylindrically symmetric, time-varying magnetic field that varies parabolically with axial distance z as B &B(t)(1 + Z2/12). Assume that B() increases slowly from the value Bo at time t0 to Bi at t . A charged particle of mass m located at z 0 has perpendicular energy Wio and parallel energy Wzo at t 0. Assume that the guiding center equations of motion are valid and that mag const. a) Give the final perpendicular energy Wii at z 0 (after a time t). b) Write the equation for the motion along z, assuming that the motion is fast compared to the time variation of B(t). Show that the motion is a sinusoidal oscillation along z, and calculate the oscillation frequency Db. This shows that the particle is confined axially in the magnetic field. c) (c) Assume now that Wzo 0 and Rt) I, where R(t) is the radial distance of the guiding center of the particle from the z axis. By using Faraday's law to find the induced electric field EM) and calculating the resulting E x B drift, show that B(r)R。 = const during the slow change from Bo to Bi

Answer 1

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