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14.6 Miller’s formula for shaped flux surfaces

According to Refs. [8, 20], Miller’s formula for a series of shaped flux surfaces is given by

R = R0(r)+ rcos{𝜃+ arcsin[δ(r)sin𝜃]},
(493)

Z = κ(r)rsin 𝜃,
(494)

where κ(r) and δ(r) are elongation and triangularity profile, R0(r) is the Shafranov shift profile, which is given by

aR′[ (r)2] R0(r) = R0 (a)− --0-1 − -- , 2 a
(495)

where R0′ is a constant, R0(a) is the major radius of the center of the boundary flux surface. The triangularity profile is

(r)2 δ(r) = δ0-- , a
(496)

and the elongation profile is

(r)4 κ(r) = κ0 − 0.3+ 0.3 a .
(497)

The nominal ITER parameters are κ0 = 1.8, δ0 = 0.5 and R0′ = −0.16. I wrote a code to plot the shapes of the flux surface (/home/yj/project/miller_flux_surface). An example of the results is given in Fig. 35.


Fig. 35: Flux-surfaces given by Eqs. (493) and (494) with r∕a varying from 0.1 to 1.0 (corresponding boundary surface). Other parameters are R0(a)∕a = 3, κ0 = 1.8, δ0 = 0.5, R0′ = −0.16.

 

 

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