magnetic_field.h File Reference

#include <map>
#include "fluxfunctions.h"

Go to the source code of this file.

Classes
struct	dg::geo::MagneticFieldParameters
	Meta-data about the magnetic field in particular the flux function. More...
struct	dg::geo::TokamakMagneticField
	A tokamak field as given by R0, Psi and Ipol plus Meta-data like shape and equilibrium. More...
struct	dg::geo::LaplacePsip
	\( \Delta\psi_p = \psi_R/R + \psi_{RR}+\psi_{ZZ} \) More...
struct	dg::geo::Bmodule
	\( |B| = R_0\sqrt{I^2+(\nabla\psi)^2}/R \) More...
struct	dg::geo::InvB
	\( |B|^{-1} = R/R_0\sqrt{I^2+(\nabla\psi)^2} \) More...
struct	dg::geo::LnB
	\( \ln{|B|} \) More...
struct	dg::geo::BR
	\( \frac{\partial |B| }{ \partial R} \) More...
struct	dg::geo::BZ
	\( \frac{\partial |B| }{ \partial Z} \) More...
struct	dg::geo::CurvatureNablaBR
	Approximate \( \mathcal{K}^{R}_{\nabla B} \). More...
struct	dg::geo::CurvatureNablaBZ
	Approximate \( \mathcal{K}^{Z}_{\nabla B} \). More...
struct	dg::geo::CurvatureKappaR
	Approximate \( \mathcal{K}^{R}_{\vec{\kappa}}=0 \). More...
struct	dg::geo::CurvatureKappaZ
	Approximate \( \mathcal{K}^{Z}_{\vec{\kappa}} \). More...
struct	dg::geo::DivCurvatureKappa
	Approximate \( \vec{\nabla}\cdot \mathcal{K}_{\vec{\kappa}} \). More...
struct	dg::geo::DivCurvatureNablaB
	Approximate \( \vec{\nabla}\cdot \mathcal{K}_{\nabla B} \). More...
struct	dg::geo::TrueCurvatureNablaBR
	True \( \mathcal{K}^{R}_{\nabla B} \). More...
struct	dg::geo::TrueCurvatureNablaBZ
	True \( \mathcal{K}^{Z}_{\nabla B} \). More...
struct	dg::geo::TrueCurvatureNablaBP
	True \( \mathcal{K}^{\varphi}_{\nabla B} \). More...
struct	dg::geo::TrueCurvatureKappaR
	True \( \mathcal{K}^R_{\vec{\kappa}} \). More...
struct	dg::geo::TrueCurvatureKappaZ
	True \( \mathcal{K}^Z_{\vec{\kappa}} \). More...
struct	dg::geo::TrueCurvatureKappaP
	True \( \mathcal{K}^\varphi_{\vec{\kappa}} \). More...
struct	dg::geo::TrueDivCurvatureKappa
	True \( \vec{\nabla}\cdot \mathcal{K}_{\vec{\kappa}} \). More...
struct	dg::geo::TrueDivCurvatureNablaB
	True \( \vec{\nabla}\cdot \mathcal{K}_{\nabla B} \). More...
struct	dg::geo::GradLnB
	\( \nabla_\parallel \ln{(B)} \) More...
struct	dg::geo::Divb
	\( \nabla \cdot \vec b \) More...
struct	dg::geo::BFieldP
	\( B^\varphi = R_0I/R^2\) More...
struct	dg::geo::BFieldR
	\( B^R = R_0\psi_Z /R\) More...
struct	dg::geo::BFieldZ
	\( B^Z = -R_0\psi_R /R\) More...
struct	dg::geo::BFieldT
	\( B^{\theta} = B^R\partial_R\theta + B^Z\partial_Z\theta\) More...
struct	dg::geo::BHatR
	\( b^R = B^R/|B|\) More...
struct	dg::geo::BHatZ
	\( b^Z = B^Z/|B|\) More...
struct	dg::geo::BHatP
	\( \hat b^\varphi = B^\varphi/|B|\) More...
struct	dg::geo::BHatRR
	\( \partial_R b^R\) More...
struct	dg::geo::BHatRZ
	\( \partial_Z b^R\) More...
struct	dg::geo::BHatZR
	\( \partial_R b^Z\) More...
struct	dg::geo::BHatZZ
	\( \partial_Z b^Z\) More...
struct	dg::geo::BHatPR
	\( \partial_R \hat b^\varphi\) More...
struct	dg::geo::BHatPZ
	\( \partial_Z \hat b^\varphi\) More...
struct	dg::geo::DivVVP
	\( \nabla\cdot\left( \frac{ \hat b }{\hat b^\varphi}\right)\) More...
struct	dg::geo::RhoP
	\( \sqrt{1. - \psi_p/ \psi_{p,O}} \) More...
struct	dg::geo::Hoo
	Inertia factor \( \mathcal I_0 = B^2/(R_0^2|\nabla\psi_p|^2)\). More...
struct	dg::geo::WallDirection
	Determine if poloidal field points towards or away from the nearest wall. More...

Namespaces
namespace	dg
namespace	dg::geo

Enumerations
enum class	dg::geo::equilibrium {   dg::geo::equilibrium::solovev , dg::geo::equilibrium::taylor , dg::geo::equilibrium::polynomial , dg::geo::equilibrium::guenter ,   dg::geo::equilibrium::toroidal , dg::geo::equilibrium::circular }
	How flux-function is computed. Decides how to construct magnetic field. More...
enum class	dg::geo::modifier { dg::geo::modifier::none , dg::geo::modifier::heaviside , dg::geo::modifier::sol_pfr , dg::geo::modifier::sol_pfr_2X }
	How flux-function is modified. More...
enum class	dg::geo::description {   dg::geo::description::standardO , dg::geo::description::standardX , dg::geo::description::doubleX , dg::geo::description::none ,   dg::geo::description::square , dg::geo::description::centeredX }
	How flux function looks like. Decider on whether and what flux aligned grid to construct. More...

Functions
TokamakMagneticField	dg::geo::periodify (const TokamakMagneticField &mag, double R0, double R1, double Z0, double Z1, dg::bc bcx, dg::bc bcy)
	Use dg::geo::Periodify to periodify every function in the magnetic field.
CylindricalVectorLvl1	dg::geo::createEPhi (int sign)
	Contravariant components of the unit vector field (0, 0, \(\pm 1/R \)) and its Divergence and derivative (0,0) in cylindrical coordinates.
CylindricalVectorLvl0	dg::geo::createCurvatureNablaB (const TokamakMagneticField &mag, int sign)
	Approximate curvature vector field (CurvatureNablaBR, CurvatureNablaBZ, Constant(0))
CylindricalVectorLvl0	dg::geo::createCurvatureKappa (const TokamakMagneticField &mag, int sign)
	Approximate curvature vector field (CurvatureKappaR, CurvatureKappaZ, Constant(0))
CylindricalVectorLvl0	dg::geo::createTrueCurvatureKappa (const TokamakMagneticField &mag)
	True curvature vector field (TrueCurvatureKappaR, TrueCurvatureKappaZ, TrueCurvatureKappaP)
CylindricalVectorLvl0	dg::geo::createTrueCurvatureNablaB (const TokamakMagneticField &mag)
	True curvature vector field (TrueCurvatureNablaBR, TrueCurvatureNablaBZ, TrueCurvatureNablaBP)
CylindricalVectorLvl0	dg::geo::createGradPsip (const TokamakMagneticField &mag)
	Gradient Psip vector field (PsipR, PsipZ, 0)
CylindricalVectorLvl1	dg::geo::createBHat (const TokamakMagneticField &mag)
	Contravariant components of the magnetic unit vector field and its Divergence and derivative in cylindrical coordinates.

Detailed Description

MagneticField objects