Struphy equilibrium

CircularTokamak

Tokamak MHD equilibrium with circular concentric flux surfaces.

Governing formula

For a cylindrical coordinate system $(R, ϕ, Z)$ with transformation formulae

x &= R\cos(\phi)\,, &&R = \sqrt{x^2 + y^2}\,, y &= R\sin(\phi)\,, &&\phi = \arctan(y/x)\,, z &= Z\,, &&Z = z\,,

the magnetic field is given by

B = \nabla ψ \times \nabla ϕ + g \nabla ϕ,

where $g = g (R, Z) = B_{0} R_{0} = co n s t .$ is the toroidal field function, $R_{0}$ the major radius of the torus and $B_{0}$ the on-axis magnetic field. The flux $ψ = ψ (R, Z)$ is given by

ψ = - a R_{0} B_{p} \frac{( R - R _{0} ) ^{2} + Z ^{2}}{2 a ^{2}}

for the given constants.

The pressure profile and the number density profile are not specified.

Units are those defined in the parameter file (through `struphy.io.options.BaseUnits`).

Coordinate slices

Pressure and density sampled from the generated equilibrium data. Heatmaps use the perceptually uniform Viridis palette.

XY plane at 0

Pressurex–y · 1.00e+0 to 1.00e+0

Densityx–y · 1.00e+0 to 1.00e+0

XZ plane at 0

Pressurex–z · 1.00e+0 to 1.00e+0

Densityx–z · 1.00e+0 to 1.00e+0

YZ plane at 0

Pressurey–z · 1.00e+0 to 1.00e+0

Densityy–z · 1.00e+0 to 1.00e+0

Coordinate-line profiles

X-line · pressure / density

Y-line · pressure / density

Z-line · pressure / density

Parameters

Parameter	Value	Description
`a`	`1`	Minor radius of torus (default: 1.).
`R0`	`2`	Major radius of torus (default: 2.).
`B0`	`4`	On-axis (r=0) toroidal magnetic field (default: 10.).
`Bp`	`60`	Poloidal magnetic field (default: 12.5).