For the magnetic mirror system of problem 3.3 suppose that the axial magnetic field changes in time, that is B_axial = B(z, t)ẑ. Considering that the magnetic moment

is an adiabatic invariant (note that its value is the same at z = 0 and at

show that the longitudinal adiabatic invariant can be written in the form

Data from Problem 3.3

Consider a system of two coaxial magnetic mirrors whose axis coincides with the z axis, being symmetrical about the plane z = 0, as shown schematically in Fig. 20. Describe semiquantitatively the motion of a charged particle in this magnetic mirror system considering that at z = 0 the particle has v_∥ = v⁰_∥ and v_⊥ = v_⊥⁰. What relation must exist between

(particle pitch angle at z = 0) for the particle to be reflected at z_m?

Figure 20

Transcribed Image Text:

m = mv (z, t) B(z,t)