pyoculus.toybox.cylindrical_toybox.A_r_squared

pyoculus.toybox.cylindrical_toybox.A_r_squared(rr: array, R: float, Z: float, sf: float, shear: float) → float64

Vector potential \(A_r\) component (giving the poloidal flux \(F\)) for the squared circle equilibrium field. Using it with the psi_squared function makes sense of sf and shear as the \(q\)-factor profile becomes:

\[q(r, z) = sf + shear / 2 * ((r - R)^2 + (z - Z)^2).\]

Parameters:

• rr (array) – Position vector in cylindrical coordinates.

• R (float) – R coordinate of the center of the squared circle.

• Z (float) – Z coordinate of the center of the squared circle.

• sf (float) – Safety factor at \(\rho = 0\).

• shear (float) – Shear of the \(q\)-profile.

Returns:

\(A_r\) component at position rr.

Return type:

float