Collaboration diagram for 3.2 Magnetic field, curvatures and associated functors:

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

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...

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 }
	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
static 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. More...

CylindricalVectorLvl1	dg::geo::createEPhi (int sign)
	Contravariant components of the unit vector field (0, 0, +/- 1/R) and its Divergence and derivative (0,0) in cylindrical coordinates. More...

CylindricalVectorLvl0	dg::geo::createCurvatureNablaB (const TokamakMagneticField &mag, int sign)
	Approximate curvature vector field (CurvatureNablaBR, CurvatureNablaBZ, Constant(0)) More...

CylindricalVectorLvl0	dg::geo::createCurvatureKappa (const TokamakMagneticField &mag, int sign)
	Approximate curvature vector field (CurvatureKappaR, CurvatureKappaZ, Constant(0)) More...

CylindricalVectorLvl0	dg::geo::createTrueCurvatureKappa (const TokamakMagneticField &mag)
	True curvature vector field (TrueCurvatureKappaR, TrueCurvatureKappaZ, TrueCurvatureKappaP) More...

CylindricalVectorLvl0	dg::geo::createTrueCurvatureNablaB (const TokamakMagneticField &mag)
	True curvature vector field (TrueCurvatureNablaBR, TrueCurvatureNablaBZ, TrueCurvatureNablaBP) More...

CylindricalVectorLvl0	dg::geo::createGradPsip (const TokamakMagneticField &mag)
	Gradient Psip vector field (PsipR, PsipZ, 0) More...

CylindricalVectorLvl1	dg::geo::createBHat (const TokamakMagneticField &mag)
	Contravariant components of the magnetic unit vector field and its Divergence and derivative in cylindrical coordinates. More...

Detailed Description

Enumeration Type Documentation

◆ description

enum class dg::geo::description

strong

How flux function looks like. Decider on whether and what flux aligned grid to construct.

The reason for this enum is that it is very hard to automatically detect if the construction of a flux aligned X-grid is possible, but for a human it is very easy to see.

Enumerator
standardO	closed flux surfaces centered around an O-point located near (R_0, 0); flux-aligned grids can be constructed
standardX	closed flux surfaces centered around an O-point located near (R_0, 0) and bordered by a separatrix with a single X-point; flux-aligned X-grids can be constructed
doubleX	closed flux surfaces centered around an O-point located near (R_0, 0) and bordered by a separatrix with two X-points; flux-aligned X-grids cannnot be constructed
none	no shaping: Purely toroidal magnetic field
square	closed flux surfaces centered around an O-point and bordered by a square with four X-points in the corners (mainly the Guenter field)
centeredX	one X-point in the middle, no O-point, only open flux surfaces, X-grids cannot be constructed

◆ equilibrium

enum class dg::geo::equilibrium

strong

How flux-function is computed. Decides how to construct magnetic field.

Enumerator
solovev	dg::geo::solovev::Psip
taylor	dg::geo::taylor::Psip
polynomial	dg::geo::polynomial::Psip
guenter	dg::geo::guenter::Psip
toroidal	dg::geo::createToroidalField
circular	dg::geo::circular::Psip

◆ modifier

enum class dg::geo::modifier

strong

How flux-function is modified.

Enumerator
none	no modification
heaviside	Psip is dampened to a constant outside a critical value.
sol_pfr	Psip is dampened in the SOL and PFR regions but not in the closed field line region.

Function Documentation

◆ createBHat()

CylindricalVectorLvl1 dg::geo::createBHat ( const TokamakMagneticField & mag )

inline

Contravariant components of the magnetic unit vector field and its Divergence and derivative in cylindrical coordinates.

Parameters

mag	the tokamak magnetic field

Returns: the tuple BHatR, BHatZ, BHatP, Divb, DivVVP constructed from mag

◆ createCurvatureKappa()

CylindricalVectorLvl0 dg::geo::createCurvatureKappa	(	const TokamakMagneticField &	mag,
		int	sign
	)

inline

Approximate curvature vector field (CurvatureKappaR, CurvatureKappaZ, Constant(0))

Parameters

mag	the tokamak magnetic field
sign	indicate positive or negative unit vector in approximation

Returns: the tuple CurvatureKappaR, CurvatureKappaZ, dg::geo::Constant(0) constructed from mag

Note: The contravariant components in cylindrical coordinates

◆ createCurvatureNablaB()

CylindricalVectorLvl0 dg::geo::createCurvatureNablaB	(	const TokamakMagneticField &	mag,
		int	sign
	)

inline

Approximate curvature vector field (CurvatureNablaBR, CurvatureNablaBZ, Constant(0))

Parameters

mag	the tokamak magnetic field
sign	indicate positive or negative unit vector in approximation

Returns: the tuple CurvatureNablaBR, CurvatureNablaBZ, dg::geo::Constant(0) constructed from mag

Note: The contravariant components in cylindrical coordinates

◆ createEPhi()

CylindricalVectorLvl1 dg::geo::createEPhi ( int sign )

inline

Contravariant components of the unit vector field (0, 0, +/- 1/R) and its Divergence and derivative (0,0) in cylindrical coordinates.

Parameters

sign	indicate positive or negative unit vector

Returns: the tuple dg::geo::Constant(0), dg::geo::Constant(0), \( 1/R \), Constant(0), Constant(0)

Note: This is equivalent to inserting a toroidal magnetic field into the dg::geo::createBHat function.

◆ createGradPsip()

CylindricalVectorLvl0 dg::geo::createGradPsip ( const TokamakMagneticField & mag )

inline

Gradient Psip vector field (PsipR, PsipZ, 0)

Parameters

mag	the tokamak magnetic field

Returns: the tuple PsipR, PsipZ, 0 constructed from mag

Note: The contravariant components in cylindrical coordinates

◆ createTrueCurvatureKappa()

CylindricalVectorLvl0 dg::geo::createTrueCurvatureKappa ( const TokamakMagneticField & mag )

inline

True curvature vector field (TrueCurvatureKappaR, TrueCurvatureKappaZ, TrueCurvatureKappaP)

Parameters

mag	the tokamak magnetic field

Returns: the tuple TrueCurvatureKappaR, TrueCurvatureKappaZ, TrueCurvatureKappaP constructed from mag

Note: The contravariant components in cylindrical coordinates

◆ createTrueCurvatureNablaB()

CylindricalVectorLvl0 dg::geo::createTrueCurvatureNablaB ( const TokamakMagneticField & mag )

inline

True curvature vector field (TrueCurvatureNablaBR, TrueCurvatureNablaBZ, TrueCurvatureNablaBP)

Parameters

mag	the tokamak magnetic field

Returns: the tuple TrueCurvatureNablaBR, TrueCurvatureNablaBZ, TrueCurvatureNablaBP constructed from mag

Note: The contravariant components in cylindrical coordinates

◆ periodify()

static TokamakMagneticField dg::geo::periodify	(	const TokamakMagneticField &	mag,
		double	R0,
		double	R1,
		double	Z0,
		double	Z1,
		dg::bc	bcx,
		dg::bc	bcy
	)

inlinestatic

Use dg::geo::Periodify to periodify every function in the magnetic field.

Note that derivatives are periodified with dg::inverse boundary conditions

Parameters

mag	The magnetic field to periodify
R0	left boundary in R
R1	right boundary in R
Z0	lower boundary in Z
Z1	upper boundary in Z
bcx	boundary condition in x (determines how function is periodified)
bcy	boundary condition in y (determines how function is periodified)

Attention: So far this was only tested for Neumann boundary conditions. It is uncertain if Dirichlet boundary conditions work

Returns: new periodified magnetic field

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ description

◆ equilibrium

◆ modifier

Function Documentation

◆ createBHat()

◆ createCurvatureKappa()

◆ createCurvatureNablaB()

◆ createEPhi()

◆ createGradPsip()

◆ createTrueCurvatureKappa()

◆ createTrueCurvatureNablaB()

◆ periodify()