I. Grad-B drift
Consider a particle in magnetic field given by:
B = (B0 + αy) · z0
(1)
with initial velocity v0 = 10 · x0 and mass to charge ratio m/q = 103 kg/C.
Determine the Larmor radius, cyclotron frequency and drift velocity for these parameters:
• B0 = 100 T, α = 0.01 m−1T
• B0 = 1 T, α = 1 m−1T
II. Magnetic mirror
A magnetic field given by:
B = B0 [0, 0, 1] −
z
L2
[x, y, −z] (2)
is an example of a magnetic mirror.
• Verify that · B = 0
• Calculate B at the point where the particle is reflected given that the velocity vector at
r(0) = [0, 0, 0] m is v(0) = [0.0, vy, vz] m/s.
Use these parameters:
B0 = 1.0 T, L = 1000 m, vy = 1.0 m/s, vz = 8.0 m/s
Can you calculate the field for L = 1 m using the same method?
1