This class computes the matched distribution. More...

#include <SigmaGenerator.h>

Collaboration diagram for SigmaGenerator< Value_type, Size_type >:

Public Types
typedef Value_type	value_type
	Type of variables. More...

typedef const value_type	const_value_type
	Type of constant variables. More...

typedef Size_type	size_type
	Type for specifying sizes. More...

typedef boost::numeric::ublas::matrix < value_type >	matrix_type
	Type for storing maps. More...

typedef std::complex< value_type >	complex_t

typedef boost::numeric::ublas::matrix < complex_t >	cmatrix_type
	Type for storing complex matrices. More...

typedef boost::numeric::ublas::compressed_matrix < complex_t, boost::numeric::ublas::row_major >	sparse_matrix_type
	Type for storing the sparse maps. More...

typedef boost::numeric::ublas::vector < value_type >	vector_type
	Type for storing vectors. More...

typedef std::vector< value_type >	container_type
	Container for storing the properties for each angle. More...

typedef FTps< value_type, 2 *3 >	Series
	Type of the truncated powere series. More...

typedef FVps< value_type, 2 *3 >	Map
	Type of a map. More...

typedef std::function< Series(value_type, value_type, value_type)>	Hamiltonian
	Type of the Hamiltonian for the cyclotron. More...

typedef std::function< Series(value_type, value_type, value_type)>	SpaceCharge
	Type of the Hamiltonian for the space charge. More...

Public Member Functions
	SigmaGenerator (value_type I, value_type ex, value_type ey, value_type ez, value_type E, value_type m, const Cyclotron *cycl, size_type N, size_type Nsectors, size_type truncOrder, bool write=true)
	Constructs an object of type SigmaGenerator. More...

bool	match (value_type accuracy, size_type maxit, size_type maxitOrbit, Cyclotron *cycl, value_type denergy, value_type rguess, bool harmonic, bool full)
	Searches for a matched distribution. More...

void	eigsolve_m (const matrix_type &Mturn, sparse_matrix_type &R)

bool	invertMatrix_m (const sparse_matrix_type &R, sparse_matrix_type &invR)

void	decouple (const matrix_type &Mturn, sparse_matrix_type &R, sparse_matrix_type &invR)
	Block diagonalizes the symplex part of the one turn transfer matrix. More...

value_type	isEigenEllipse (const matrix_type &Mturn, const matrix_type &sigma)
	Checks if the sigma-matrix is an eigenellipse and returns the L2 error. More...

matrix_type &	getSigma ()
	Returns the converged stationary distribution. More...

size_type	getIterations () const
	Returns the number of iterations needed for convergence (if not converged, it returns zero) More...

value_type	getError () const
	Returns the error (if the program didn't converged, one can call this function to check the error) More...

std::array< value_type, 3 >	getEmittances () const
	Returns the emittances (ex,ey,ez) in \( \pi\ mm\ mrad \) for which the code converged (since the whole simulation is done on normalized emittances) More...

const double &	getInjectionRadius () const

const double &	getInjectionMomentum () const

Private Member Functions
void	initialize (value_type, value_type)

matrix_type	updateInitialSigma (const matrix_type &, sparse_matrix_type &, sparse_matrix_type &)
	Computes the new initial sigma matrix. More...

void	updateSigma (const std::vector< matrix_type > &, const std::vector< matrix_type > &)
	Computes new sigma matrices (one for each angle) More...

value_type	L2ErrorNorm (const matrix_type &, const matrix_type &)
	Returns the L2-error norm between the old and new sigma-matrix. More...

value_type	L1ErrorNorm (const matrix_type &, const matrix_type &)
	Returns the Lp-error norm between the old and new sigma-matrix. More...

std::string	float2string (value_type val)
	Transforms a floating point value to a string. More...

void	writeOrbitOutput_m (const std::pair< value_type, value_type > &tunes, const value_type &ravg, const value_type &freqError, const container_type &r_turn, const container_type &peo, const container_type &h_turn, const container_type &fidx_turn, const container_type &ds_turn)
	Called within SigmaGenerator::match(). More...

Private Attributes
value_type	I_m
	Stores the value of the current, \( \left[I\right] = A \). More...

std::array< value_type, 3 >	emittance_m
	Stores the desired emittances, \( \left[\varepsilon_{x}\right] = \left[\varepsilon_{y}\right] = \left[\varepsilon_{z}\right] = mm \ mrad \). More...

value_type	wo_m
	Is the orbital frequency, \( \left[\omega_{o}\right] = \frac{1}{s} \). More...

value_type	E_m
	Stores the user-define energy, \( \left[E\right] = MeV \). More...

value_type	gamma_m
	Relativistic factor (which can be computed out ot the kinetic energy and rest mass (potential energy)), \( \left[\gamma\right] = 1 \). More...

value_type	gamma2_m
	Relativistic factor squared. More...

value_type	nh_m
	Harmonic number, \( \left[N_{h}\right] = 1 \). More...

value_type	beta_m
	Velocity (c/v), \( \left[\beta\right] = 1 \). More...

value_type	m_m
	Is the mass of the particles, \( \left[m\right] = \frac{MeV}{c^{2}} \). More...

size_type	niterations_m
	Is the number of iterations needed for convergence. More...

bool	converged_m
	Is true if converged, false otherwise. More...

value_type	Emin_m
	Minimum energy needed in cyclotron, \( \left[E_{min}\right] = MeV \). More...

value_type	Emax_m
	Maximum energy reached in cyclotron, \( \left[E_{max}\right] = MeV \). More...

size_type	N_m
	Number of integration steps for closed orbit computation. More...

size_type	nSectors_m
	Number of (symmetric) sectors the field is averaged over. More...

size_type	nStepsPerSector_m
	Number of integration steps per sector (–> also: number of maps per sector) More...

size_type	nSteps_m
	Number of integration steps in total. More...

value_type	error_m
	Error of computation. More...

size_type	truncOrder_m
	Truncation order of the power series for the Hamiltonian (cyclotron and space charge) More...

bool	write_m
	Decides for writing output (default: true) More...

matrix_type	sigma_m
	Stores the stationary distribution (sigma matrix) More...

std::vector< matrix_type >	sigmas_m
	Vector storing the second moment matrix for each angle. More...

Hamiltonian	H_m
	Stores the Hamiltonian of the cyclotron. More...

SpaceCharge	Hsc_m
	Stores the Hamiltonian for the space charge. More...

Series	x_m
	All variables x, px, y, py, z, delta. More...

Series	px_m

Series	y_m

Series	py_m

Series	z_m

Series	delta_m

double	rinit_m

double	prinit_m

Detailed Description

template<typename Value_type, typename Size_type>
class SigmaGenerator< Value_type, Size_type >

This class computes the matched distribution.

Definition at line 64 of file SigmaGenerator.h.

Member Typedef Documentation

template<typename Value_type, typename Size_type>

typedef boost::numeric::ublas::matrix<complex_t> SigmaGenerator< Value_type, Size_type >::cmatrix_type

Type for storing complex matrices.

Definition at line 79 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef std::complex<value_type> SigmaGenerator< Value_type, Size_type >::complex_t

Definition at line 76 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef const value_type SigmaGenerator< Value_type, Size_type >::const_value_type

Type of constant variables.

Definition at line 70 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef std::vector<value_type> SigmaGenerator< Value_type, Size_type >::container_type

Container for storing the properties for each angle.

Definition at line 88 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef std::function<Series(value_type,value_type,value_type)> SigmaGenerator< Value_type, Size_type >::Hamiltonian

Type of the Hamiltonian for the cyclotron.

Definition at line 94 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef FVps<value_type,2*3> SigmaGenerator< Value_type, Size_type >::Map

Type of a map.

Definition at line 92 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef boost::numeric::ublas::matrix<value_type> SigmaGenerator< Value_type, Size_type >::matrix_type

Type for storing maps.

Definition at line 74 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef FTps<value_type,2*3> SigmaGenerator< Value_type, Size_type >::Series

Type of the truncated powere series.

Definition at line 90 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef Size_type SigmaGenerator< Value_type, Size_type >::size_type

Type for specifying sizes.

Definition at line 72 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef std::function<Series(value_type,value_type,value_type)> SigmaGenerator< Value_type, Size_type >::SpaceCharge

Type of the Hamiltonian for the space charge.

Definition at line 96 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef boost::numeric::ublas::compressed_matrix<complex_t, boost::numeric::ublas::row_major > SigmaGenerator< Value_type, Size_type >::sparse_matrix_type

Type for storing the sparse maps.

Definition at line 84 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef Value_type SigmaGenerator< Value_type, Size_type >::value_type

Type of variables.

Definition at line 68 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

typedef boost::numeric::ublas::vector<value_type> SigmaGenerator< Value_type, Size_type >::vector_type

Type for storing vectors.

Definition at line 86 of file SigmaGenerator.h.

Constructor & Destructor Documentation

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::SigmaGenerator	(	value_type	I,
		value_type	ex,
		value_type	ey,
		value_type	ez,
		value_type	E,
		value_type	m,
		const Cyclotron *	cycl,
		size_type	N,
		size_type	Nsectors,
		size_type	truncOrder,
		bool	write = `true`
	)

Constructs an object of type SigmaGenerator.

Parameters

I	specifies the current for which a matched distribution should be found, \( [I] = A \)
ex	is the emittance in x-direction (horizontal), \( \left[\varepsilon_{x}\right] = \pi\ mm\ mrad \)
ey	is the emittance in y-direction (longitudinal), \( \left[\varepsilon_{y}\right] = \pi\ mm\ mrad \)
ez	is the emittance in z-direction (vertical), \( \left[\varepsilon_{z}\right] = \pi\ mm\ mrad \)
E	is the energy, \( \left[E\right] = MeV \)
m	is the mass of the particles \( \left[m\right] = \frac{MeV}{c^{2}} \)
cycl	is the cyclotron element
N	is the number of integration steps (closed orbit computation). That's why its also the number of maps (for each integration step a map)
Nsectors	is the number of sectors that the field map is averaged over (closed orbit computation)
truncOrder	is the truncation order for power series of the Hamiltonian
write	is a boolean (default: true). If true all maps of all iterations are stored, otherwise not.

Definition at line 323 of file SigmaGenerator.h.

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Member Function Documentation

template<typename Value_type , typename Size_type >

void SigmaGenerator< Value_type, Size_type >::decouple	(	const matrix_type &	Mturn,
		sparse_matrix_type &	R,
		sparse_matrix_type &	invR
	)

Block diagonalizes the symplex part of the one turn transfer matrix.

It computes the transformation matrix R and its inverse invR.

Parameters

Mturn	is a 6x6 dimensional one turn transfer matrix
R	is the 6x6 dimensional transformation matrix (gets computed)
invR	is the 6x6 dimensional inverse transformation (gets computed)

Definition at line 816 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

void SigmaGenerator< Value_type, Size_type >::eigsolve_m	(	const matrix_type &	Mturn,
		sparse_matrix_type &	R
	)

Eigenvalue / eigenvector solver

Parameters

Mturn	is a 6x6 dimensional one turn transfer matrix
R	is the 6x6 dimensional transformation matrix (gets computed)

Definition at line 681 of file SigmaGenerator.h.

References abs(), Physics::e, Attrib::Distribution::R, and sqrt().

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template<typename Value_type , typename Size_type >

std::string SigmaGenerator< Value_type, Size_type >::float2string ( value_type val )

private

Transforms a floating point value to a string.

Parameters

val	is the floating point value which is transformed to a string

Definition at line 1175 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

std::array< Value_type, 3 > SigmaGenerator< Value_type, Size_type >::getEmittances ( ) const

inline

Returns the emittances (ex,ey,ez) in \( \pi\ mm\ mrad \) for which the code converged (since the whole simulation is done on normalized emittances)

Definition at line 864 of file SigmaGenerator.h.

References Physics::pi.

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::value_type SigmaGenerator< Value_type, Size_type >::getError ( ) const

inline

Returns the error (if the program didn't converged, one can call this function to check the error)

Definition at line 857 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

const double& SigmaGenerator< Value_type, Size_type >::getInjectionMomentum ( ) const

inline

Definition at line 182 of file SigmaGenerator.h.

References SigmaGenerator< Value_type, Size_type >::prinit_m.

template<typename Value_type, typename Size_type>

const double& SigmaGenerator< Value_type, Size_type >::getInjectionRadius ( ) const

inline

Definition at line 178 of file SigmaGenerator.h.

References SigmaGenerator< Value_type, Size_type >::rinit_m.

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::size_type SigmaGenerator< Value_type, Size_type >::getIterations ( ) const

inline

Returns the number of iterations needed for convergence (if not converged, it returns zero)

Definition at line 850 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::matrix_type & SigmaGenerator< Value_type, Size_type >::getSigma ( )

inline

Returns the converged stationary distribution.

Definition at line 843 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

void SigmaGenerator< Value_type, Size_type >::initialize	(	value_type	nuz,
		value_type	ravg
	)

private

Initializes a first guess of the sigma matrix with the assumption of a spherical symmetric beam (ex = ey = ez). For each angle split the same initial guess is taken.

Parameters

nuz	is the vertical tune
ravg	is the average radius of the closed orbit

Definition at line 879 of file SigmaGenerator.h.

References Physics::alpha, Physics::c, Physics::e, endl(), Physics::epsilon_0, K, Physics::mu_0, Physics::pi, and sqrt().

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template<typename Value_type , typename Size_type >

bool SigmaGenerator< Value_type, Size_type >::invertMatrix_m	(	const sparse_matrix_type &	R,
		sparse_matrix_type &	invR
	)

Parameters

R	is the 6x6 dimensional transformation matrix
invR	is the 6x6 dimensional inverse transformation (gets computed)

Returns: true if success

Definition at line 788 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::value_type SigmaGenerator< Value_type, Size_type >::isEigenEllipse	(	const matrix_type &	Mturn,
		const matrix_type &	sigma
	)

Checks if the sigma-matrix is an eigenellipse and returns the L2 error.

The idea of this function is taken from Dr. Christian Baumgarten's program.

Parameters

Mturn	is the one turn transfer matrix
sigma	is the sigma matrix to be tested

Definition at line 829 of file SigmaGenerator.h.

template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::value_type SigmaGenerator< Value_type, Size_type >::L1ErrorNorm	(	const matrix_type &	oldS,
		const matrix_type &	newS
	)

private

Returns the Lp-error norm between the old and new sigma-matrix.

Parameters

oldS	is the old sigma matrix
newS	is the new sigma matrix

Definition at line 1158 of file SigmaGenerator.h.

References abs(), and for_each().

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template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::value_type SigmaGenerator< Value_type, Size_type >::L2ErrorNorm	(	const matrix_type &	oldS,
		const matrix_type &	newS
	)

private

Returns the L2-error norm between the old and new sigma-matrix.

Parameters

oldS	is the old sigma matrix
newS	is the new sigma matrix

Definition at line 1143 of file SigmaGenerator.h.

References sqrt().

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template<typename Value_type , typename Size_type >

bool SigmaGenerator< Value_type, Size_type >::match	(	value_type	accuracy,
		size_type	maxit,
		size_type	maxitOrbit,
		Cyclotron *	cycl,
		value_type	denergy,
		value_type	rguess,
		bool	harmonic,
		bool	full
	)

Searches for a matched distribution.

Returns "true" if a matched distribution within the accuracy could be found, returns "false" otherwise.

Parameters

accuracy	is used for computing the equilibrium orbit (to a certain accuracy)
maxit	is the maximum number of iterations (the program stops if within this value no stationary distribution was found)
maxitOrbit	is the maximum number of iterations for finding closed orbit
angle	defines the start of the sector (one can choose any angle between 0° and 360°)
denergy	energy step size for closed orbit finder [MeV]
rguess	value of radius for closed orbit finder
type	specifies the magnetic field format (e.g. CARBONCYCL)
harmonic	is a boolean. If "true" the harmonics are used instead of the closed orbit finder.
full	match over full turn not just single sector

Definition at line 424 of file SigmaGenerator.h.

References Physics::e, endl(), Cyclotron::getPHIinit(), Attrib::Distribution::R, and value_type().

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template<typename Value_type , typename Size_type >

SigmaGenerator< Value_type, Size_type >::matrix_type SigmaGenerator< Value_type, Size_type >::updateInitialSigma	(	const matrix_type &	M,
		sparse_matrix_type &	R,
		sparse_matrix_type &	invR
	)

private

Computes the new initial sigma matrix.

Parameters

M	is the 6x6 one turn transfer matrix
R	is the transformation matrix
invR	is the inverse transformation matrix

Definition at line 1041 of file SigmaGenerator.h.

References endl(), interpolation::im(), and prod().

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template<typename Value_type , typename Size_type >

void SigmaGenerator< Value_type, Size_type >::updateSigma	(	const std::vector< matrix_type > &	Mscs,
		const std::vector< matrix_type > &	Mcycs
	)

private

Computes new sigma matrices (one for each angle)

Mscs is a vector of all space charge maps Mcycs is a vector of all cyclotron maps

Definition at line 1111 of file SigmaGenerator.h.

References endl(), and prod().

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template<typename Value_type , typename Size_type >

void SigmaGenerator< Value_type, Size_type >::writeOrbitOutput_m	(	const std::pair< value_type, value_type > &	tunes,
		const value_type &	ravg,
		const value_type &	freqError,
		const container_type &	r_turn,
		const container_type &	peo,
		const container_type &	h_turn,
		const container_type &	fidx_turn,
		const container_type &	ds_turn
	)

private

Called within SigmaGenerator::match().

Parameters

tunes
ravg	is the average radius [m]
r_turn	is the radius [m]
peo	is the momentum
h_turn	is the inverse bending radius
fidx_turn	is the field index
ds_turn	is the path length element

Definition at line 1183 of file SigmaGenerator.h.

References endl().

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Member Data Documentation

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::beta_m

private

Velocity (c/v), \( \left[\beta\right] = 1 \).

Definition at line 202 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

bool SigmaGenerator< Value_type, Size_type >::converged_m

private

Is true if converged, false otherwise.

Definition at line 208 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::delta_m

private

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::E_m

private

Stores the user-define energy, \( \left[E\right] = MeV \).

Definition at line 194 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::Emax_m

private

Maximum energy reached in cyclotron, \( \left[E_{max}\right] = MeV \).

Definition at line 212 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::Emin_m

private

Minimum energy needed in cyclotron, \( \left[E_{min}\right] = MeV \).

Definition at line 210 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

std::array<value_type,3> SigmaGenerator< Value_type, Size_type >::emittance_m

private

Stores the desired emittances, \( \left[\varepsilon_{x}\right] = \left[\varepsilon_{y}\right] = \left[\varepsilon_{z}\right] = mm \ mrad \).

Definition at line 190 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::error_m

private

Error of computation.

Definition at line 224 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::gamma2_m

private

Relativistic factor squared.

Definition at line 198 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::gamma_m

private

Relativistic factor (which can be computed out ot the kinetic energy and rest mass (potential energy)), \( \left[\gamma\right] = 1 \).

Definition at line 196 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

Hamiltonian SigmaGenerator< Value_type, Size_type >::H_m

private

Stores the Hamiltonian of the cyclotron.

Definition at line 239 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

SpaceCharge SigmaGenerator< Value_type, Size_type >::Hsc_m

private

Stores the Hamiltonian for the space charge.

Definition at line 242 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::I_m

private

Stores the value of the current, \( \left[I\right] = A \).

Definition at line 188 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::m_m

private

Is the mass of the particles, \( \left[m\right] = \frac{MeV}{c^{2}} \).

Definition at line 204 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::N_m

private

Number of integration steps for closed orbit computation.

Definition at line 214 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::nh_m

private

Harmonic number, \( \left[N_{h}\right] = 1 \).

Definition at line 200 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::niterations_m

private

Is the number of iterations needed for convergence.

Definition at line 206 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::nSectors_m

private

Number of (symmetric) sectors the field is averaged over.

Definition at line 216 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::nSteps_m

private

Number of integration steps in total.

Definition at line 221 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::nStepsPerSector_m

private

Number of integration steps per sector (–> also: number of maps per sector)

Definition at line 218 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

double SigmaGenerator< Value_type, Size_type >::prinit_m

private

Definition at line 248 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::getInjectionMomentum().

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::px_m

private

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::py_m

private

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

double SigmaGenerator< Value_type, Size_type >::rinit_m

private

Definition at line 247 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::getInjectionRadius().

template<typename Value_type, typename Size_type>

matrix_type SigmaGenerator< Value_type, Size_type >::sigma_m

private

Stores the stationary distribution (sigma matrix)

Definition at line 233 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

std::vector<matrix_type> SigmaGenerator< Value_type, Size_type >::sigmas_m

private

Vector storing the second moment matrix for each angle.

Definition at line 236 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

size_type SigmaGenerator< Value_type, Size_type >::truncOrder_m

private

Truncation order of the power series for the Hamiltonian (cyclotron and space charge)

Definition at line 227 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

value_type SigmaGenerator< Value_type, Size_type >::wo_m

private

Is the orbital frequency, \( \left[\omega_{o}\right] = \frac{1}{s} \).

Definition at line 192 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

bool SigmaGenerator< Value_type, Size_type >::write_m

private

Decides for writing output (default: true)

Definition at line 230 of file SigmaGenerator.h.

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::x_m

private

All variables x, px, y, py, z, delta.

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::y_m

private

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

template<typename Value_type, typename Size_type>

Series SigmaGenerator< Value_type, Size_type >::z_m

private

Definition at line 245 of file SigmaGenerator.h.

Referenced by SigmaGenerator< Value_type, Size_type >::SigmaGenerator().

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

src/Distribution/SigmaGenerator.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename Value_type, typename Size_type> class SigmaGenerator< Value_type, Size_type >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename Value_type, typename Size_type>
class SigmaGenerator< Value_type, Size_type >