Implementation object of a Multipole magnetic field. More...

#include <FieldTypes.h>

Inheritance diagram for dd4hep::MultipoleField:

Public Member Functions
	MultipoleField ()
	Initializing constructor. More...

virtual void	fieldComponents (const double pos, double field)
	Call to access the field components at a given location. More...

Public Member Functions inherited from dd4hep::CartesianField::Object
	Object ()
	Default constructor. More...

virtual	~Object ()
	Default destructor. More...

Public Member Functions inherited from dd4hep::CartesianField::TypedObject
	NamedObject (const char nam, const char typ="")
	Default constructor. More...

	NamedObject (const std::string &nam)
	Default constructor. More...

	NamedObject (const std::string &nam, const std::string &typ)
	Default constructor. More...

	NamedObject ()=default
	Default constructor. More...

	NamedObject (const NamedObject &c)=default
	Default constructor. More...

	NamedObject (NamedObject &&c)=default
	Default constructor. More...

Public Member Functions inherited from dd4hep::NamedObject
	NamedObject (const char nam, const char typ="")
	Initializing constructor. More...

	NamedObject (const std::string &nam)
	Initializing constructor. More...

	NamedObject (const std::string &nam, const std::string &typ)
	Initializing constructor. More...

	NamedObject ()=default
	Standard constructor. More...

	NamedObject (const NamedObject &c)=default
	Copy constructor. More...

	NamedObject (NamedObject &&c)=default
	Move constructor. More...

virtual	~NamedObject ()=default
	Default destructor. More...

NamedObject &	operator= (const NamedObject &c)=default
	Assignment operator. More...

NamedObject &	operator= (NamedObject &&c)=default
	Move assignment operator. More...

const char *	GetName () const
	Access name. More...

void	SetName (const char *nam)
	Set name (used by Handle) More...

void	SetTitle (const char *tit)
	Set Title (used by Handle) More...

const char *	GetTitle () const
	Get name (used by Handle) More...

Public Attributes
Coefficents	coefficents { }
	Multi-pole coefficients. More...

Coefficents	skews { }
	Multi-pole skews. More...

Solid	volume { }
	Boundary volume (optional) More...

Transform3D	transform { }
	Position transformation of the field. Only stored here for reference. More...

Transform3D	inverse { }
	Inverse position transformation of the field. More...

Rotation3D	rotation { }
	The rotation part of the transformation. Need to rotate the field. More...

double	B_z { 0e0 }
	Constant Z field overlay. More...

Public Attributes inherited from dd4hep::CartesianField::Object
Properties	properties
	Field extensions. More...

Public Attributes inherited from dd4hep::CartesianField::TypedObject
int	field_type { UNKNOWN }
	Field type. More...

Public Attributes inherited from dd4hep::NamedObject
std::string	name
	The object name. More...

std::string	type
	The object type. More...

Private Attributes
unsigned char	flag { 0 }
	The access to the field will be optimized. Remember properties. More...

Transform3D::Point	translation { }
	Translation of the transformation. More...

Additional Inherited Members
Public Types inherited from dd4hep::CartesianField::Object
typedef std::vector< double >	Coefficents
	Utility definition for concrete implementations. More...

Detailed Description

Implementation object of a Multipole magnetic field.

Generic multipole magnetic field using the Multipole approach. The dipole is assumed to be horizontal as it is used for bending beams in large colliders ie. the dipole field lines are vertical.

The different momenta are given by:

$\begin{eqnarray*} B_y + i*B_x &=& ( 1/(n-1)! )* C_n * (x + iy)^{n-1} \\ B_sum = B_y + i B_x &=& Sum_{n=1..4} ( 1/(n-1)! )*(b_n + ia_n) (x + iy)^{n-1} \\ \end{eqnarray*}$

With C_n being the complex multipole coefficients and b_n the "normal multipole coefficients" and a_n the "skew multipole coefficients".

The maximal momentum used is the octopole momentum.

The lower momenta are:

Dipole (n=1):
$\begin{eqnarray*} B_y &=& b_1 \\ B_x &=& a_1 \\ B_z &=& constant \\ \end{eqnarray*}$

Quadrupole (n=2):

$\begin{eqnarray*} B_y &=& b_2 x - a_2 y \\ B_x &=& b_2 y + a_2 x \\ \end{eqnarray*}$

Sextupole (n=3):

$\begin{eqnarray*} B_y + i B_x &=& (1/2) * (b_3 +ia_3) (x^2 + 2ixy - y^2) \\ B_y &=& (1/2) * ( b_3 x^2 - b_3 y^2 - 2 a_3 xy) \\ B_x &=& (1/2) * (a_3 x^2 - a_3 y^2 + 2 b_3 xy) \\ \end{eqnarray*}$

Octopole (n=4):

$\begin{eqnarray*} B_y + i B_x &=& (1/6) * (b_4 +ia_4) (x^3 + 3ix^2y - 3xy^2 -iy^3) \\ B_y &=& (1/6) * (b_4 x^3 - 3 b_4 x y^2 - 3 a_4 x^2 y + a_4 y^3) \\ B_x &=& (1/6) * (3 b_4 x^2 y - b_4 y^3 + a_4 x^3 - 3 a_4 x y^2) \ \ \end{eqnarray*}$

The defined field components only apply within the shape 'volume'. If 'volume' is an invalid shape (ie. not defined), then the field components are valied throughout the 'universe'.

See also: http://cas.web.cern.ch/sites/cas.web.cern.ch/files/lectures/bruges-2009/wolski-1.pdf; http://cas.web.cern.ch/sites/cas.web.cern.ch/files/lectures/varna-2010/brandt-1-web.pdf; https://en.wikipedia.org/wiki/Multipole_magnet

Author: M.Frank

Version: 1.0

Definition at line 152 of file FieldTypes.h.

Constructor & Destructor Documentation

◆ MultipoleField()

MultipoleField::MultipoleField ( )

Initializing constructor.

Definition at line 101 of file FieldTypes.cpp.

Member Function Documentation

◆ fieldComponents()

void MultipoleField::fieldComponents	(	const double *	pos,
		double *	field
	)

virtual

Call to access the field components at a given location.

Compute the field components at a given location and add to given field.

Implements dd4hep::CartesianField::Object.

Definition at line 106 of file FieldTypes.cpp.

Member Data Documentation

◆ B_z

double dd4hep::MultipoleField::B_z { 0e0 }

Constant Z field overlay.

Definition at line 167 of file FieldTypes.h.

◆ coefficents

Coefficents dd4hep::MultipoleField::coefficents { }

Multi-pole coefficients.

Definition at line 155 of file FieldTypes.h.

◆ flag

unsigned char dd4hep::MultipoleField::flag { 0 }

private

The access to the field will be optimized. Remember properties.

Definition at line 171 of file FieldTypes.h.

◆ inverse

Transform3D dd4hep::MultipoleField::inverse { }

Inverse position transformation of the field.

Definition at line 163 of file FieldTypes.h.

◆ rotation

Rotation3D dd4hep::MultipoleField::rotation { }

The rotation part of the transformation. Need to rotate the field.

Definition at line 165 of file FieldTypes.h.

◆ skews

Coefficents dd4hep::MultipoleField::skews { }

Multi-pole skews.

Definition at line 157 of file FieldTypes.h.

◆ transform

Transform3D dd4hep::MultipoleField::transform { }

Position transformation of the field. Only stored here for reference.

Definition at line 161 of file FieldTypes.h.

◆ translation

Transform3D::Point dd4hep::MultipoleField::translation { }

private

Translation of the transformation.

Definition at line 173 of file FieldTypes.h.

◆ volume

Solid dd4hep::MultipoleField::volume { }

Boundary volume (optional)

Definition at line 159 of file FieldTypes.h.

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

DDCore/include/DD4hep/FieldTypes.h
DDCore/src/FieldTypes.cpp

Public Member Functions

Public Attributes

Private Attributes

Additional Inherited Members