Distance to wall along fieldline in phi or s coordinate More...

Inheritance diagram for dg::geo::WallFieldlineDistance:

Public Member Functions
	WallFieldlineDistance (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
	Integrate fieldline until wall is reached.

Public Member Functions inherited from dg::geo::aCylindricalFunctor< WallFieldlineDistance >
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

Distance 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. Either the angle \( \varphi_l\) or the corresponding \( s_l\) is returned by the function.

Attention: The sign of the angle coordinate in this class (unlike in Fieldaligned) is defined with respect to the direction of the magnetic field. Thus, for a positive maxPhi, the distance (both "phi" and "s") will be positive and for negative maxPhi the distance is negative.

Constructor & Destructor Documentation

◆ WallFieldlineDistance()

dg::geo::WallFieldlineDistance::WallFieldlineDistance	(	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

Member Function Documentation

◆ do_compute()

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

inline

Integrate fieldline until wall is reached.

If wall is not reached integration stops at maxPhi given in the constructor