#include <MultipoleTCurvedVarRadius.h>

Inheritance diagram for MultipoleTCurvedVarRadius:

Collaboration diagram for MultipoleTCurvedVarRadius:

Public Member Functions
	MultipoleTCurvedVarRadius (MultipoleT *element)
void	initialise () override
BGeometryBase &	getGeometry () override
const BGeometryBase &	getGeometry () const override
void	transformCoords (Vector_t &) override
void	transformBField (Vector_t &, const Vector_t &) override
double	getScaleFactor (double x, double s) override
double	getFn (size_t n, double x, double s) override
void	setMaxOrder (size_t orderZ, size_t orderX) override
Vector_t	localCartesianToCurvilinear (const Vector_t &r)
Vector_t	curvilinearToLocalCartesian (const Vector_t &r)
Vector_t	localCartesianToOpalCartesian (const Vector_t &r) override
double	reverseTransformResidual (const Vector_t &r, const Vector_t &target)
double	localCartesianRotation () override
virtual double	getBx (const Vector_t &R)
double	getBz (const Vector_t &R)
virtual double	getBs (const Vector_t &R)

Static Public Attributes
static constexpr size_t	ReverseTransformMaxIterations = 1000
static constexpr double	ReverseTransformTolerance = 1e-6
static constexpr double	TangentStep = 1e-3

Protected Attributes
MultipoleT *	element_m

Private Attributes
std::vector< polynomial::RecursionRelationTwo >	recursion_m
VarRadiusGeometry	varRadiusGeometry_m
Vector_t	localCartesianEntryPoint_
double	localCartesianRotation_ {}

Detailed Description

MultipoleTCurvedVarRadius defines a curved combined function magnet with
variable radius of curvature (up to arbitrary multipole component)
with fringe fields

Class category: AbsBeamline
$Author: Titus Dascalu, Martin Duy Tat, Chris Rogers

The field is obtained from the scalar potential

\[ V = f_0(x,s) z + f_1 (x,s) \frac{z^3}{3!} + f_2 (x,s) \frac{z^5}{5!} + ... \]

(x,z,s) -> Frenet-Serret local coordinates along the magnet
z -> vertical component
assume mid-plane symmetry
set field on mid-plane -> $ B_z = f_0(x,s) = T(x) \cdot S(s) $
T(x) -> transverse profile; this is a polynomial describing the field expansion on the mid-plane inside the magnet (not in the fringe field); 1st term is the dipole strength, 2nd term is the quadrupole gradient * x, etc.
-> when setting the magnet, one gives the multipole coefficients of this polynomial (i.e. dipole strength,
quadrupole gradient, etc.)

----------— example --------------------------------------------—
Setting a combined function magnet with dipole, quadrupole and sextupole components:
$ T(x) = B_0 + B_1 \cdot x + B_2 \cdot x^2 $
user gives $ B_0, B_1, B_2 $
----------— example end ----------------------------------------—

S(s) -> fringe field
recursion -> $ f_n (x,s) = (-1)^n \cdot \sum_{i=0}^{n} C_n^i \cdot T^{(2i)} \cdot S^{(2n-2i)} $
for curved magnets the above recursion is more complicated
$ C_n^i $ -> binomial coeff; $ T^{(n)} $ -> n-th derivative

Definition at line 85 of file MultipoleTCurvedVarRadius.h.

Constructor & Destructor Documentation

◆ MultipoleTCurvedVarRadius()

MultipoleTCurvedVarRadius::MultipoleTCurvedVarRadius ( MultipoleT * element )

explicit

Constructor

Definition at line 34 of file MultipoleTCurvedVarRadius.cpp.

References MultipoleTBase::MultipoleTBase(), and varRadiusGeometry_m.

Here is the call graph for this function:

Member Function Documentation

◆ curvilinearToLocalCartesian()

Vector_t MultipoleTCurvedVarRadius::curvilinearToLocalCartesian ( const Vector_t & r )

Definition at line 164 of file MultipoleTCurvedVarRadius.cpp.

References ReverseTransformMaxIterations, reverseTransformResidual(), and ReverseTransformTolerance.

Referenced by initialise().

Here is the call graph for this function:

◆ getBs()

double MultipoleTBase::getBs ( const Vector_t & R )

virtualinherited

Returns the component of the field along the central axis
Returns zero far outside fringe field $ Bs = sum_n z^(2n+1) / (2n+1)! \partial_s f_n / h_s $

Reimplemented in MultipoleTStraight.

Definition at line 60 of file MultipoleTBase.cpp.

References element_m, and getScaleFactor().

Here is the call graph for this function:

◆ getBx()

double MultipoleTBase::getBx ( const Vector_t & R )

virtualinherited

Returns the radial component of the field
Returns zero far outside fringe field $ Bx = sum_n z^(2n+1) / (2n+1)! * \partial_x f_n $

Reimplemented in MultipoleTStraight.

Definition at line 48 of file MultipoleTBase.cpp.

References element_m.

◆ getBz()

double MultipoleTBase::getBz ( const Vector_t & R )

inherited

Returns the vertical field component
Returns zero far outside fringe field $ Bz = sum_n f_n * z^(2n) / (2n)! $

Definition at line 37 of file MultipoleTBase.cpp.

References element_m, and getFn().

Here is the call graph for this function:

◆ getFn()

double MultipoleTCurvedVarRadius::getFn	(	size_t	n,
		double	x,
		double	s )

overridevirtual

Calculate fn(x, s) by expanding the differential operator (from Laplacian and scalar potential) in terms of polynomials

Parameters

n	-> nth derivative
x	-> Coordinate x
s	-> Coordinate s

Implements MultipoleTBase.

Definition at line 128 of file MultipoleTCurvedVarRadius.cpp.

References MultipoleTBase::element_m, and recursion_m.

◆ getGeometry() [1/2]

const BGeometryBase & MultipoleTCurvedVarRadius::getGeometry ( ) const

inlineoverridevirtual

Return the cell geometry

Implements MultipoleTBase.

Definition at line 94 of file MultipoleTCurvedVarRadius.h.

References varRadiusGeometry_m.

◆ getGeometry() [2/2]

BGeometryBase & MultipoleTCurvedVarRadius::getGeometry ( )

inlineoverridevirtual

Return the cell geometry

Implements MultipoleTBase.

Definition at line 92 of file MultipoleTCurvedVarRadius.h.

References varRadiusGeometry_m.

◆ getScaleFactor()

double MultipoleTCurvedVarRadius::getScaleFactor	(	double	x,
		double	s )

overridevirtual

Returns the scale factor $ h_s = 1$

Parameters

x	-> Coordinate x
s	-> Coordinate s

Implements MultipoleTBase.

Definition at line 118 of file MultipoleTCurvedVarRadius.cpp.

References MultipoleTBase::element_m.

◆ initialise()

void MultipoleTCurvedVarRadius::initialise ( )

overridevirtual

Initialise the element

Implements MultipoleTBase.

Definition at line 39 of file MultipoleTCurvedVarRadius.cpp.

References atan2(), curvilinearToLocalCartesian(), MultipoleTBase::element_m, localCartesianEntryPoint_, localCartesianRotation_, setMaxOrder(), TangentStep, and varRadiusGeometry_m.

Here is the call graph for this function:

◆ localCartesianRotation()

double MultipoleTCurvedVarRadius::localCartesianRotation ( )

inlineoverridevirtual

Reimplemented from MultipoleTBase.

Definition at line 124 of file MultipoleTCurvedVarRadius.h.

References localCartesianRotation_.

◆ localCartesianToCurvilinear()

Vector_t MultipoleTCurvedVarRadius::localCartesianToCurvilinear ( const Vector_t & r )

Definition at line 87 of file MultipoleTCurvedVarRadius.cpp.

References MultipoleTBase::element_m, and coordinatetransform::CoordinateTransform::getTransformation().

Referenced by reverseTransformResidual(), and transformCoords().

Here is the call graph for this function:

◆ localCartesianToOpalCartesian()

Vector_t MultipoleTCurvedVarRadius::localCartesianToOpalCartesian ( const Vector_t & r )

overridevirtual

Implements MultipoleTBase.

Definition at line 75 of file MultipoleTCurvedVarRadius.cpp.

References cos(), localCartesianEntryPoint_, localCartesianRotation_, and sin().

Here is the call graph for this function:

◆ reverseTransformResidual()

double MultipoleTCurvedVarRadius::reverseTransformResidual	(	const Vector_t &	r,
		const Vector_t &	target )

Definition at line 153 of file MultipoleTCurvedVarRadius.cpp.

References c, localCartesianToCurvilinear(), and sqrt().

Referenced by curvilinearToLocalCartesian().

Here is the call graph for this function:

◆ setMaxOrder()

void MultipoleTCurvedVarRadius::setMaxOrder	(	size_t	orderZ,
		size_t	orderX )

overridevirtual

Set the number of terms used in calculation of field components
Maximum power of z in Bz is 2 * maxOrder_m

Parameters

order -> Number of terms in expansion in z

Reimplemented from MultipoleTBase.

Definition at line 107 of file MultipoleTCurvedVarRadius.cpp.

References MultipoleTBase::element_m, recursion_m, polynomial::RecursionRelationTwo::resizeX(), and polynomial::RecursionRelationTwo::truncate().

Referenced by initialise().

Here is the call graph for this function:

◆ transformBField()

void MultipoleTCurvedVarRadius::transformBField	(	Vector_t &	B,
		const Vector_t &	R )

overridevirtual

Transform B-field from Frenet-Serret coordinates to lab coordinates

Implements MultipoleTBase.

Definition at line 95 of file MultipoleTCurvedVarRadius.cpp.

References cos(), cosh(), MultipoleTBase::element_m, log(), sin(), and tanh().

Here is the call graph for this function:

◆ transformCoords()

void MultipoleTCurvedVarRadius::transformCoords ( Vector_t & R )

overridevirtual

Transform to Frenet-Serret coordinates for sector magnets

Implements MultipoleTBase.

Definition at line 62 of file MultipoleTCurvedVarRadius.cpp.

References cos(), localCartesianEntryPoint_, localCartesianRotation_, localCartesianToCurvilinear(), and sin().

Here is the call graph for this function:

Member Data Documentation

◆ element_m

MultipoleT* MultipoleTBase::element_m

protectedinherited

Definition at line 91 of file MultipoleTBase.h.

Referenced by getBs(), MultipoleTStraight::getBs(), getBx(), MultipoleTStraight::getBx(), getBz(), MultipoleTCurvedConstRadius::getFn(), MultipoleTCurvedVarRadius::getFn(), MultipoleTStraight::getFn(), MultipoleTCurvedConstRadius::getScaleFactor(), MultipoleTCurvedVarRadius::getScaleFactor(), MultipoleTCurvedConstRadius::initialise(), MultipoleTCurvedVarRadius::initialise(), MultipoleTStraight::initialise(), MultipoleTCurvedVarRadius::localCartesianToCurvilinear(), MultipoleTCurvedConstRadius::localCartesianToOpalCartesian(), MultipoleTStraight::localCartesianToOpalCartesian(), MultipoleTBase(), MultipoleTCurvedConstRadius::setMaxOrder(), MultipoleTCurvedVarRadius::setMaxOrder(), MultipoleTCurvedConstRadius::transformBField(), MultipoleTCurvedVarRadius::transformBField(), MultipoleTCurvedConstRadius::transformCoords(), and MultipoleTStraight::transformCoords().

◆ localCartesianEntryPoint_

Vector_t MultipoleTCurvedVarRadius::localCartesianEntryPoint_

private

Definition at line 131 of file MultipoleTCurvedVarRadius.h.

Referenced by initialise(), localCartesianToOpalCartesian(), and transformCoords().

◆ localCartesianRotation_

double MultipoleTCurvedVarRadius::localCartesianRotation_ {}

private

Definition at line 132 of file MultipoleTCurvedVarRadius.h.

Referenced by initialise(), localCartesianRotation(), localCartesianToOpalCartesian(), and transformCoords().

◆ recursion_m

std::vector<polynomial::RecursionRelationTwo> MultipoleTCurvedVarRadius::recursion_m

private

Objects for storing differential operator acting on Fn

Definition at line 128 of file MultipoleTCurvedVarRadius.h.

Referenced by getFn(), and setMaxOrder().

◆ ReverseTransformMaxIterations

size_t MultipoleTCurvedVarRadius::ReverseTransformMaxIterations = 1000

staticconstexpr

Definition at line 121 of file MultipoleTCurvedVarRadius.h.

Referenced by curvilinearToLocalCartesian().

◆ ReverseTransformTolerance

double MultipoleTCurvedVarRadius::ReverseTransformTolerance = 1e-6

staticconstexpr

Definition at line 122 of file MultipoleTCurvedVarRadius.h.

Referenced by curvilinearToLocalCartesian().

◆ TangentStep

double MultipoleTCurvedVarRadius::TangentStep = 1e-3

staticconstexpr

Definition at line 123 of file MultipoleTCurvedVarRadius.h.

Referenced by initialise().

◆ varRadiusGeometry_m

VarRadiusGeometry MultipoleTCurvedVarRadius::varRadiusGeometry_m

private

Geometry

Definition at line 130 of file MultipoleTCurvedVarRadius.h.

Referenced by getGeometry(), getGeometry(), initialise(), and MultipoleTCurvedVarRadius().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Attributes

Protected Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MultipoleTCurvedVarRadius()

Member Function Documentation

◆ curvilinearToLocalCartesian()

◆ getBs()

◆ getBx()

◆ getBz()

◆ getFn()

◆ getGeometry() [1/2]

◆ getGeometry() [2/2]

◆ getScaleFactor()

◆ initialise()

◆ localCartesianRotation()

◆ localCartesianToCurvilinear()

◆ localCartesianToOpalCartesian()

◆ reverseTransformResidual()

◆ setMaxOrder()

◆ transformBField()

◆ transformCoords()

Member Data Documentation

◆ element_m

◆ localCartesianEntryPoint_

◆ localCartesianRotation_

◆ recursion_m

◆ ReverseTransformMaxIterations

◆ ReverseTransformTolerance

◆ TangentStep

◆ varRadiusGeometry_m