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Course: ENGR 525, Fall 2009
School: Wisconsin
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OF UNIVERSITY WISCONSIN ECE/NEEP/Physics 525 Introduction to Plasmas Spring Semester 2007 Problem Set #2 Due: Thursday, February 15, 2007 1. a) Charged particle drifts - nonuniform magnetic field. The magnetic field strength in the equatorial plane of a dipole (e.g., the earth's magnetic field outside the earth's surface) is given by B = B0 (r0 /r)3 . Show that the azimuthal drift speed of the guiding center...

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OF UNIVERSITY WISCONSIN ECE/NEEP/Physics 525 Introduction to Plasmas Spring Semester 2007 Problem Set #2 Due: Thursday, February 15, 2007 1. a) Charged particle drifts - nonuniform magnetic field. The magnetic field strength in the equatorial plane of a dipole (e.g., the earth's magnetic field outside the earth's surface) is given by B = B0 (r0 /r)3 . Show that the azimuthal drift speed of the guiding center caused by the cyclotron motion of a charge particle in such a field is given by vgc = 3v rL 2r provided the motion is adiabatic and v = 0. b) Is a proton with kinetic energy E = E = 2 MeV moving adiabatically if it is placed in the equatorial plane at 6000 km (i.e., about one earth radius) above sea level? Assume B = 0.5 gauss at sea level. Explain your answer. If it is, use the result of part a) to calculate the time taken by the particle to drift once around the earth. 2. Charged particle drifts: E B. In a "smooth-bore" magnetron, a uniform axial magnetic field Bz is crossed by a radial electric field Er that exists in the evacuated space between two coaxial straight metallic cylinders. a) Find the drift velocities terms in of E, B, c and the radial position r for both positive and negative inner electrodes. b) Find the minimum values for r at which stable orbits exist if E is a vacuum field, i.e., if Er = E0 a/r. 3. Charged particle drifts: gravitational drift. A collisionless neutral plasma of mass density = n(mi + me ) is bounded by two parallel conducting plates separated by a distance L. The gravitational acceleration g is at right angles to a uniform magnetic field B and both of these are parallel to the plates as indicated in the figure. a) If switch S is closed and if the ammeter I has negligible impedance, what is the durrent density J in the plasma? (Note that the plates have to b...

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Wisconsin - ENGR - 525
Wisconsin - ENGR - 525
Wisconsin - ENGR - 525
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