Fundamentals of Plasma Physics

80 Chapter 3. Motion of a single plasma particle

̂

R̂

R

B

center of curvature

Figure 3.5: Local cylindrical coordinate system defined by curved magnetic field,ˆφ=B.ˆ

The drifts can be summarized as

v⊥gc=vE+v∇B+vc+vP (3.87)

where

1. the ‘EcrossB’ drift is
   vE=

E×B

B^2

(3.88)

2. the ‘gradB’ drift is
   v∇B=−
   mv^2 L 0
   2 qB^3

∇B×B (3.89)

3. the ‘curvature’ drift is

vc=−

mv‖^2 gc

qB^2

B̂·∇B̂×B=^1

qB^2

(

mv‖^2 gcRˆ

R

)

×B (3.90)

4. the ‘polarization’ drift is

vP=−

m

qB^2

[

d

dt

(vE+v∇B+vc)

]

×B. (3.91)