This browser-side solver uses the up-down symmetric Cerfon/Freidberg Solov’ev basis from the Grad–Shafranov lecture. Adjust the shaping parameters, source-mix parameter, and engineering scales to compare the target boundary against the fitted U = 0 last closed flux surface, the interior flux contours, and a few lecture-style equilibrium figures of merit.
Inverse aspect ratio is ε = a/R0, so smaller values here produce wider plasmas.
Controls the vertical stretching of the target boundary.
Positive δ shifts the top point inward, while negative δ gives negative triangularity through Xtop = 1 - δε.
Interpolates between the two pieces of the particular solution: α = 1 is pure FF’, while α = 0 is pure p’.
Sets the physical size in meters, which combines with R0/a to determine R0.
Used with Ip to form the cylindrical and shaped engineering estimates for the safety factor.
Current is in mega-amperes. The explorer uses it to evaluate the lecture’s qcyl, q*, and βp summaries.
Pressure is in kPa. It feeds the lecture definitions of βt and βp.
Magnetic axis not yet computed.
Awaiting solve.
Awaiting solve.
Awaiting solve.
Awaiting solve.
Awaiting solve.
U(X,Y) = Up(X,Y) + Σj=06 cj Uj(X,Y),
with the coefficients fixed by the outer point, inner point, top point, and local-curvature constraints described in the lecture.
The dashed red curve is the target shaped boundary. The black contour is the fitted U = 0 LCFS. Blue curves are interior flux surfaces generated directly from the same analytic solution.
The curve uses the geometric profile shape from the fit and scales it by the lecture’s shaped engineering estimate q*. This is a useful interpretation aid rather than a full current-profile reconstruction.
The plotted quantity is the normalized flux-surface volume derivative V'(ψ), which is the natural geometric ingredient behind magnetic-well language in the equilibrium and stability lectures.