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5.8 Radial drift –check!!

dΨ- dt = Vd ⋅∇Ψ = -1 Ωb ×( ) μ-∇B + v2κ m ∥⋅∇Ψ

dΨ- dt = -1- BΩB ×(-μ 2 ) m ∇B + v∥κ⋅∇Ψ

dΨ- dt = −-1- B ΩB ×∇Ψ ⋅( μ∇B + v2κ) m ∥

using

B = ∇Ψ ×∇ϕ + g∇ϕ

( ) dΨ- = −-1-(∇ Ψ × ∇ϕ × ∇Ψ + g∇ ϕ× ∇ Ψ)⋅ μ-∇B + v2∥κ dt B Ω m
(103)

Noting that both ∇B and κ are approximatedly along −Rˆ direction, which is perpendicular to ∇ϕ, Eq. (103) is written as

dΨ- dt = −-1- BΩ(g∇ϕ ×∇Ψ) ⋅(-μ∇B + v2κ) m ∥

dΨ- dt = -1- B ΩgBp ⋅(μ- 2 ) m ∇B + v∥κ

if

dΨ --- dt(Ψlcfs − Ψaxis) > 0,

then the drift from the local magnetic surface is outward, otherwise, the drift is inward.

dΨ --- dt(Ψlcfs − Ψaxis) = 1 --- BΩgBp ⋅ (−ˆR)(Ψlcfs − Ψaxis)

Examining the right-hand side of Eq. (5.8), we find that Bp and (Ψlcfs − Ψaxis) change signs simutaneouslly when the toroidal plasma current Iϕ change sign, thus the direction of Bp(Ψlcfs − Ψaxis) is independent of the sign of Iϕ. Therefore the sign of the radial drift is independent of the sign of Iϕ.

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