Normalized coordinate relative to wall along fieldline in phi or s coordinate. More...

Inheritance diagram for dg::geo::WallFieldlineCoordinate:

Public Member Functions
	WallFieldlineCoordinate (const dg::geo::CylindricalVectorLvl0 &vec, const dg::aRealTopology2d< double > &domain, double maxPhi, double eps, std::string type, std::function< bool(double, double)> predicate=mod::everywhere)
	Construct with vector field, domain.

double	do_compute (double R, double Z) const

Public Member Functions inherited from dg::geo::aCylindricalFunctor< WallFieldlineCoordinate >
double	operator() (double R, double Z) const
	`do_compute(R,Z)`

double	operator() (double R, double Z, double phi) const
	`do_compute(R,Z)`

Detailed Description

Normalized coordinate relative to wall along fieldline in phi or s coordinate.

The following differential equation is integrated

\[ \frac{ d R}{d \varphi} = b^R / b^\varphi \\ \frac{ d Z}{d \varphi} = b^Z / b^\varphi \\ \frac{ d s}{s \varphi} = 1 / b^\varphi \]

for initial conditions \( (R,Z,0)\) until either a maximum angle is reached or until \( (R,Z) \) leaves the given domain. In the latter case a bisection algorithm is used to find the exact angle \(\varphi_l\) of leave.

The difference to WallFieldlineDistance is that this class integrates the differential equations in both directions and normalizes the output to \( [-1,1]\). -1 means at the negative sheath (you have to go agains the field to go out of the box), +1 at the postive sheath (you have to go with the field to go out of the box) and anything else is in-between; when the sheath cannot be reached 0 is returned

Attention: The sign of the coordinate (both angle and distance) is defined with respect to the direction of the magnetic field (not the angle coordinate like in Fieldaligned)

Constructor & Destructor Documentation

◆ WallFieldlineCoordinate()

dg::geo::WallFieldlineCoordinate::WallFieldlineCoordinate	(	const dg::geo::CylindricalVectorLvl0 &	vec,
		const dg::aRealTopology2d< double > &	domain,
		double	maxPhi,
		double	eps,
		std::string	type,
		std::function< bool(double, double)>	predicate = mod::everywhere )

inline

Construct with vector field, domain.

Parameters

vec	The vector field to integrate
domain	The box
maxPhi	the maximum angle to integrate to (something like plus or minus 2.*M_PI)
eps	the accuracy of the fieldline integrator
type	either "phi" then the distance is computed in the angle coordinate or "s" then the distance is computed in the s parameter
predicate	only integrate points where predicate is true

Note: The sign of maxPhi does not matter here as both directions are integrated

Member Function Documentation

◆ do_compute()

double dg::geo::WallFieldlineCoordinate::do_compute	(	double	R,
		double	Z ) const