MultipoleTStraight Class Reference

#include <MultipoleTStraight.h>

Inheritance diagram for MultipoleTStraight:

Collaboration diagram for MultipoleTStraight:

Public Member Functions
	MultipoleTStraight (MultipoleT *element)
void	initialise () override
BGeometryBase &	getGeometry () override
const BGeometryBase &	getGeometry () const override
void	transformCoords (Vector_t &R) override
void	transformBField (Vector_t &, const Vector_t &) override
double	getScaleFactor (double, double) override
double	getBx (const Vector_t &R) override
double	getBs (const Vector_t &R) override
double	getFn (size_t n, double x, double s) override
Vector_t	localCartesianToOpalCartesian (const Vector_t &r) override
Public Member Functions inherited from MultipoleTBase
	MultipoleTBase (MultipoleT *element)
virtual	~MultipoleTBase ()=default
double	getBz (const Vector_t &R)
virtual void	setMaxOrder (size_t, size_t)
virtual double	localCartesianRotation ()

Private Attributes
StraightGeometry	straightGeometry_m

Additional Inherited Members
Protected Attributes inherited from MultipoleTBase
MultipoleT *	element_m

Detailed Description

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MultipoleTiStraight defines a straight combined function magnet (up to arbitrary multipole component) with fringe fields

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

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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

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Definition at line 82 of file MultipoleTStraight.h.

Constructor & Destructor Documentation

MultipoleTStraight()

MultipoleTStraight::MultipoleTStraight ( MultipoleT *  element )

explicit

Constructor

Definition at line 33 of file MultipoleTStraight.cpp.

Member Function Documentation

getBs()

double MultipoleTStraight::getBs ( const Vector_t &  R )

overridevirtual

Get s-component of the B-field
This function has been overloaded because calculating
the B-field directly is quicker and more accurate

Reimplemented from MultipoleTBase.

Definition at line 55 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, MultipoleT::getFringeDeriv(), MultipoleT::getMaxFOrder(), and MultipoleT::getTransDeriv().

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getBx()

double MultipoleTStraight::getBx ( const Vector_t &  R )

overridevirtual

Get x-component of the B-field
This function has been overloaded because calculating
the B-field directly is quicker and more accurate

Reimplemented from MultipoleTBase.

Definition at line 41 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, MultipoleT::getFringeDeriv(), MultipoleT::getMaxFOrder(), and MultipoleT::getTransDeriv().

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getFn()

double MultipoleTStraight::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 69 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, MultipoleT::getFringeDeriv(), and MultipoleT::getTransDeriv().

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getGeometry() [1/2]

const BGeometryBase & MultipoleTStraight::getGeometry ( ) const

inlineoverridevirtual

Return the cell geometry

Implements MultipoleTBase.

Definition at line 91 of file MultipoleTStraight.h.

References straightGeometry_m.

getGeometry() [2/2]

BGeometryBase & MultipoleTStraight::getGeometry ( )

inlineoverridevirtual

Return the cell geometry

Implements MultipoleTBase.

Definition at line 89 of file MultipoleTStraight.h.

References straightGeometry_m.

getScaleFactor()

double MultipoleTStraight::getScaleFactor ( double  , double    )

inlineoverridevirtual

Returns the scale factor \( h_s = 1\)

Parameters

x	-> Coordinate x
s	-> Coordinate s

Implements MultipoleTBase.

Definition at line 100 of file MultipoleTStraight.h.

initialise()

void MultipoleTStraight::initialise ( )

overridevirtual

Initialise the element

Implements MultipoleTBase.

Definition at line 37 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, MultipoleT::getLength(), StraightGeometry::setElementLength(), and straightGeometry_m.

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localCartesianToOpalCartesian()

Vector_t MultipoleTStraight::localCartesianToOpalCartesian ( const Vector_t &  r )

overridevirtual

Implements MultipoleTBase.

Definition at line 82 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, and MultipoleT::getLength().

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transformBField()

void MultipoleTStraight::transformBField ( Vector_t &  , const Vector_t &    )

inlineoverridevirtual

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

Implements MultipoleTBase.

Definition at line 95 of file MultipoleTStraight.h.

transformCoords()

void MultipoleTStraight::transformCoords ( Vector_t &  R )

overridevirtual

Transform to Frenet-Serret coordinates for sector magnets

Implements MultipoleTBase.

Definition at line 86 of file MultipoleTStraight.cpp.

References MultipoleTBase::element_m, and MultipoleT::getLength().

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Member Data Documentation

straightGeometry_m

StraightGeometry MultipoleTStraight::straightGeometry_m

private

Geometry

Definition at line 122 of file MultipoleTStraight.h.

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

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

• src/Classic/AbsBeamline/MultipoleTStraight.h
• src/Classic/AbsBeamline/MultipoleTStraight.cpp