Fundamentals of Plasma Physics

92 Chapter 3. Motion of a single plasma particle

Suppose there exists a large number or ensemble of particles with densitynσand mean

magnetic momentμ ̄σ.The density of magnetic moments, or magnetization density, of this

ensemble is

M=−

∑

σ

nσμ ̄σBˆ=−

∑

σ

nσ

〈

mσv^2 ⊥

2 B

〉

Bˆ=−P⊥

Bˆ

B

(3.127)

where〈〉denotes averaging over the velocity distribution and Eq.(2.26) has been used.

Inserting Eq.(3.127) into Eq.(3.126) shows that this ensemble of charged particles in a

magnetic field has adiamagnetic current

JM=−∇×

(

P⊥Bˆ

B

)

. (3.128)

Figure 3.11: Gradient of magnetized particles gives apparent current as observed on dashed
line.

Figure 3.11 shows the physical origin ofJM. Here, a collection of ions all rotate clock-

wise in a magnetic field pointing out of the page. The azimuthally directed current on the

dashed curve is the sum of contributions from (i) particles with guiding centers located

one Larmor radiusinsidethe dashed curve and (ii) particles with guiding centers located

one Larmor radiusoutsidethe dashed curve. From the point of view of an observer lo-

cated on the dashed curve, the inside particles [group (i)] constitute a clockwise current,

whereas the outside [group (ii)] particles constitute a counterclockwise current. If there are

unequal numbers of inside and outside particles (indicated here by concentriccircles inside