#include <MultipoleTCurvedConstRadius.h>

Inheritance diagram for MultipoleTCurvedConstRadius:

Collaboration diagram for MultipoleTCurvedConstRadius:

Public Member Functions
	MultipoleTCurvedConstRadius (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	localCartesianToOpalCartesian (const Vector_t &r) override
virtual double	getBx (const Vector_t &R)
double	getBz (const Vector_t &R)
virtual double	getBs (const Vector_t &R)
virtual double	localCartesianRotation ()

Protected Attributes
MultipoleT *	element_m

Private Attributes
std::vector< polynomial::RecursionRelation >	recursion_m
PlanarArcGeometry	planarArcGeometry_m

Detailed Description

MultipoleT defines a curved combined function magnet with constant 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 83 of file MultipoleTCurvedConstRadius.h.

Constructor & Destructor Documentation

◆ MultipoleTCurvedConstRadius()

MultipoleTCurvedConstRadius::MultipoleTCurvedConstRadius ( MultipoleT * element )

explicit

Constructor

Definition at line 32 of file MultipoleTCurvedConstRadius.cpp.

References MultipoleTBase::MultipoleTBase(), and planarArcGeometry_m.

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Member Function Documentation

◆ 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().

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