PHYS 515: Plasma Physics & MHD Grade Assigments for 9/19/00 1. Birdsall's problem: solve problem 2.3 in the Sturrock handout 2. Magnetic mirrors. Assume a magnetic field with only a z-component, that only varies in the z-direction, and has a minimum at z=0. a) Write down the lowest order expansion for this field. (Note: such a field is not divergenceless, but we ignore that for the moment, since we will only be using the momentum equation for a particle) b) Write down the equation of motion for a test particle of mass m and charge q in that field, in cylindrical coordinates. c) Derive two conserved quantities for the particle motion, and write down the differential equation for the remaining velocity components d) Show that when the field is no longer allowed to be divergenceless, and cylindrical symmetry is preserved, there will now be a magnetic mirror.