Consider the magnetic mirror system shown in Fig. 20. Suppose that the axial magnetic field is given by

where B₀ and a₀ are positive constants, and that the mirroring planes are given by z = –z_m and z = z_m·

(a) For a charged particle trapped in this mirror system, show that the z component of the particle velocity is given by

(b) The average force acting on the particle guiding center, along the z axis, is given by

Show that the particle performs a simple harmonic motion between the mirroring planes, with a period given by

(c) If the motion of the particle is to be limited to the region | z | m, what restriction must be imposed on the total energy and on the magnetic moment?

Figure 20.

Transcribed Image Text:

B(z)= Bo[1 + (z/ao)²]