Struphy equilibrium

ShearedSlab

Sheared slab MHD equilibrium in a cube with side lengths

L_{x} = a, L_{y} = 2 π a, L_{z} = 2 π R_{0}

. Profiles depend on

x

solely.

Governing formula

\mathbf B(x) &= B_{0} \left( \mathbf e_z + \frac{a}{q(x)R_0}\mathbf e_y\right)\,,\qquad q(x) = q_0 + ( q_1 - q_0 )\frac{x^2}{a^2}\,, p(x) &= \beta\frac{B_{0}^2}{2} \left( 1 + \frac{a^2}{q(x)^2 R_0^2} \right) + B_{0}^2 \frac{a^2}{R_0^2} \left( \frac{1}{q_0^2} - \frac{1}{q(x)^2} \right)\,, n(x) &= n_a + ( 1 - n_a ) \left( 1 - \left(\frac{x}{a}\right)^{n_1} \right)^{n_2} \,.

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

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

Pressurex–y · 5.53e-2 to 1.18e-1

Densityx–y · 2.50e-1 to 9.98e-1

Pressurex–z · 5.53e-2 to 1.18e-1

Densityx–z · 2.50e-1 to 9.98e-1

Pressurey–z · 5.50e-2 to 5.50e-2

Densityy–z · 1.00e+0 to 1.00e+0

X-line · pressure / density

Y-line · pressure / density

Z-line · pressure / density

Parameter	Value	Description
`a`	`1`	"Minor" radius (must be compatible with :math:`L_x=a` and :math:`L_y=2\pi a`, default: 1.).
`R0`	`3`	"Major" radius (must be compatible with :math:`L_z=2\pi R_0`, default: 3.).
`B0`	`1`	z-component of magnetic field (constant) (default: 1.).
`q0`	`1.05`	Safety factor at x=0 (default: 1.05).
`q1`	`1.8`	Safety factor at x=a (default: 1.80).
`n1`	`2`	1st shape factor for ion number density profile (default: 0.).
`n2`	`2`	2nd shape factor for ion number density profile (default: 0.).
`na`	`0.25`	Ion number density at x=a (default: 1.).
`beta`	`0.1`	Plasma beta (ratio of kinematic pressure to B^2/2, default: 0.1).
`q_kind`	`0`	Kind of safety factor profile, (0 or 1, default: 0).