Question

please solve me this plasma question asap. thank you so much

Question 1 Consider a cylindrically symmetric, time-varying magnetic field that varies parabolically with axial distance z as B- 2B(t)(1 z2/l2). Assume that B(t) increases slowly from the value Bo at timet0 to Bi at t. A charged particle of mass m located at z-0 has perpendicular energy Wio and parallel energy Wo at. Assume that the guiding center equations of motion are valid and that mag const a) Give the final perpendicular energy WL1 at z 0 (after a time ty). 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 s, and calculate the oscillation frequency o. This shows that the particle is confined axially in the magnetic field. c) (c) Assume now that Wzo 0 and R(t) < 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 E (t) and calculating the resulting E x B drift, show that BOR') const during the slow change from Bo to Bi

Answer 1

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