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A.12 Radial coordinate to be deleted

We know that the toroidal flux ψt, safety factor q, and the Ψ in the GS equation are related by the following equations:

dψt = 2πqdΨ
(563)

∫ Ψ =⇒ ψt = 2π qdΨ 0
(564)

Define:

∘ --- ρ ≡ ψt π
(565)

(In the Toray_ga code, the radial coordinate ρ is defined as

∘ -ψt-- ρ ≡ πB--, t0
(566)

where Bt0 is a constant factor.ρ defined this way is of length dimension, which is an effective geometry radius obtained by approximating the flux surface as circular.)

 

I use Eq. (565) to define ρ. Then we have

ψt = πρ2
(567)

dψt =⇒ -dρ = 2πρ
(568)

=⇒ dψtdψ-= 2πρ dψ dρ
(569)

dψ =⇒ 2πqdρ-= 2πρ
(570)

dψ ρ = ⇒ ---= - dρ q
(571)

Eq. (571) is used to transform between ψ and ρ.

dρ = ∘---1----- Φ∕πR20B01 2--1--- πB0R20dΦ = 1 ρ1 2---1-- πB0R202πqdψ = 1 ρ--1-- B0R20qdψ

⇒ dψ = ρB0R20- qdρ(πa2)

 

pict

Fig. 39: to be delted, Isosurface of α = 2π∕8. The surface is made of a family of contours of α = 2π∕8, which are all magnetic field lines. These field lines are traced by starting from a series of points on the low-field-side midplane (𝜃 = 0) at different radial locations and the field lines are followed by a complete poloidal loop. Magnetic field from EAST discharge #59954@3.03s.

 

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