LocalGeometryMiller#

Author:: B Patel

This is a subclass of the LocalGeometry class. This class is a describes the Miller representation of a local equilibrium as described in:

Miller, R. L., et al. “Noncircular, finite aspect ratio, local equilibrium model.” Physics of Plasmas 5.4 (1998): 973-978.

LocalGeometryMiller inherits from LocalGeometry and is a CleverDict of the major Miller parameters. It can be loaded directly from: - The Miller parameters of an input file - A 2D equilibrium

When loaded from a 2D equilibrium the flux surfaces are contours fits. Parameters like \(\kappa\) and \(\delta\) are calculated from the flux surface. The gradients in these parameters are fitted by matching to the poloidal field

The definition of the different keys are shown in Table 1.

Table 1 Miller Parameter definitions#
Dictionary key	Description
psi_n	Normalised poloidal flux \(\psi_n=\psi_{surface}/\psi_{LCFS}\)
rho	Normalised minor radius \(\rho=r/a\)
Rmaj	Normalised major radius \(R_{maj}/a\)
a_minor	Minor radius (m) \(a\) (if 2D equilibrium exists)
B0	Normalising field \(B_0 = f / R_{maj}\)
Bunit	Effective field (GACODE) \(B_{unit} = \frac{q}{r}\frac{\partial\psi}{\partial r}\)
kappa	Elongation \(\kappa\)
s_kappa	Elongation shear \(\frac{\rho}{\kappa}\frac{\partial\kappa}{\partial\rho}\)
delta	Triangularity \(\delta\)
s_delta	Triangularity shear \(\frac{\rho}{\sqrt{1-\delta^2}}\frac{\partial\delta}{\partial\rho}\)
q	Safety factor \(q\)
shat	Magnetic shear \(\hat{s} = \frac{\rho}{q}\frac{\partial q}{\partial\rho}\)
shift	Shafranov shift \(\Delta = \frac{\partial R_{maj}}{\partial r}\)
beta_prime	Pressure gradient \(\beta'=\frac{8\pi10^{-7}}{B_0^2}\frac{\partial p}{\partial\rho}\)

These will automatically be calculated when loading in GK codes/Numerical equilibria