Finds a closed orbit of a cyclotron for a given energy. More...

#include <ClosedOrbitFinder.h>

Collaboration diagram for ClosedOrbitFinder< Value_type, Size_type, Stepper >:

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

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

typedef std::vector< value_type >	container_type
	Type of container for storing quantities (path length, orbit, etc.) More...

typedef std::vector< value_type >	state_type
	Type for holding state of ODE values. More...

typedef std::function< void(const state_type &, state_type &, const double)>	function_t

Public Member Functions
	ClosedOrbitFinder (value_type E0, size_type N, Cyclotron *cycl, bool domain=true, int Nsectors=1)
	Sets the initial values for the integration and calls findOrbit(). More...

container_type	getInverseBendingRadius (const value_type &angle=0)
	Returns the inverse bending radius (size of container N+1) More...

container_type	getPathLength (const value_type &angle=0)
	Returns the step lengths of the path (size of container N+1) More...

container_type	getFieldIndex (const value_type &angle=0)
	Returns the field index (size of container N+1) More...

std::pair< value_type, value_type >	getTunes ()
	Returns the radial and vertical tunes (in that order) More...

container_type	getOrbit (value_type angle=0)

container_type	getMomentum (value_type angle=0)

value_type	getAverageRadius ()
	Returns the average orbit radius. More...

value_type	getFrequencyError ()
	Returns the frequency error. More...

bool	isConverged ()
	Returns true if a closed orbit could be found. More...

bool	findOrbit (value_type accuracy, size_type maxit, value_type ekin, value_type dE=1.0, value_type rguess=-1.0, bool isTuneMode=false)
	Computes the closed orbit. More...

void	computeOrbitProperties (const value_type &E)
	Fills in the values of h_m, ds_m, fidx_m. More...

Private Member Functions
value_type	computeTune (const std::array< value_type, 2 > &, value_type, size_type)
	This function is called by the function getTunes(). More...

bool	findOrbitOfEnergy_m (const value_type &, container_type &, value_type &, const value_type &, size_type)

container_type	rotate (value_type angle, container_type &orbitProperty)
	This function computes nzcross_ which is used to compute the tune in z-direction and the frequency error. More...

Private Attributes
std::array< value_type, 2 >	x_m
	Stores current position in horizontal direction for the solutions of the ODE with different initial values. More...

std::array< value_type, 2 >	px_m
	Stores current momenta in horizontal direction for the solutions of the ODE with different initial values. More...

std::array< value_type, 2 >	z_m
	Stores current position in vertical direction for the solutions of the ODE with different initial values. More...

std::array< value_type, 2 >	pz_m
	Stores current momenta in vertical direction for the solutions of the ODE with different initial values. More...

container_type	h_m
	Stores the inverse bending radius. More...

container_type	ds_m
	Stores the step length. More...

container_type	r_m
	Stores the radial orbit (size: N_m+1) More...

container_type	vz_m
	Stores the vertical oribt (size: N_m+1) More...

container_type	pr_m
	Stores the radial momentum. More...

container_type	vpz_m
	Stores the vertical momentum. More...

container_type	fidx_m
	Stores the field index. More...

size_type	nxcross_m
	Counts the number of zero-line crossings in horizontal direction (used for computing horizontal tune) More...

size_type	nzcross_m
	Counts the number of zero-line crossings in vertical direction (used for computing vertical tune) More...

value_type	E0_m
	Is the rest mass [MeV / c**2]. More...

value_type	wo_m
	Is the nominal orbital frequency. More...

size_type	N_m
	Number of integration steps. More...

value_type	dtheta_m
	Is the angle step size. More...

value_type	ravg_m
	Is the average radius. More...

value_type	phase_m
	Is the phase. More...

bool	domain_m

int	nSectors_m

Stepper	stepper_m
	Defines the stepper for integration of the ODE's. More...

std::function< double(double)>	acon_m = [](double wo) { return Physics::c / wo; }

std::function< double(double, double)>	bcon_m
	Cyclotron unit \( \left[T\right] \) (Tesla) More...

Cyclotron *	cycl_m

Detailed Description

template<typename Value_type, typename Size_type, class Stepper>
class ClosedOrbitFinder< Value_type, Size_type, Stepper >

Finds a closed orbit of a cyclotron for a given energy.

Definition at line 42 of file ClosedOrbitFinder.h.

Member Typedef Documentation

template<typename Value_type, typename Size_type, class Stepper>

typedef std::vector<value_type> ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type

Type of container for storing quantities (path length, orbit, etc.)

Definition at line 50 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

typedef std::function<void(const state_type&, state_type&, const double)> ClosedOrbitFinder< Value_type, Size_type, Stepper >::function_t

Definition at line 54 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

typedef Size_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::size_type

Type for specifying sizes.

Definition at line 48 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

typedef std::vector<value_type> ClosedOrbitFinder< Value_type, Size_type, Stepper >::state_type

Type for holding state of ODE values.

Definition at line 52 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

typedef Value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::value_type

Type of variables.

Definition at line 46 of file ClosedOrbitFinder.h.

Constructor & Destructor Documentation

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder	(	value_type	E0,
		size_type	N,
		Cyclotron *	cycl,
		bool	domain = `true`,
		int	Nsectors = `1`
	)

Sets the initial values for the integration and calls findOrbit().

Parameters

E0	is the potential energy (particle energy at rest) [MeV].
N	specifies the number of splits (2pi/N), i.e number of integration steps
cycl	is the cyclotron element
domain	is a boolean (default: true). If "true" the closed orbit is computed over a single sector, otherwise over 2*pi.
Nsectors	is an int (default: 1). Number of sectors that the field map is averaged over in order to avoid first harmonic. Only valid if domain is false

Definition at line 246 of file ClosedOrbitFinder.h.

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Member Function Documentation

template<typename Value_type , typename Size_type , class Stepper >

void ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeOrbitProperties ( const value_type & E )

Fills in the values of h_m, ds_m, fidx_m.

Definition at line 818 of file ClosedOrbitFinder.h.

References sqrt(), and value_type().

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template<typename Value_type , typename Size_type , class Stepper >

Value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeTune	(	const std::array< value_type, 2 > &	y,
		value_type	py2,
		size_type	ncross
	)

private

This function is called by the function getTunes().

Transfer matrix Y = [y11, y12; y21, y22] (see Gordon paper for more details).

Parameters

y	are the positions (elements y11 and y12 of Y)
py2	is the momentum of the second solution (element y22 of Y)
ncross	is the number of sign changes (#crossings of zero-line)

Definition at line 760 of file ClosedOrbitFinder.h.

References acos(), cos(), fabs(), Physics::pi, sin(), Physics::two_pi, and Physics::u_two_pi.

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template<typename Value_type , typename Size_type , class Stepper >

bool ClosedOrbitFinder< Value_type, Size_type, Stepper >::findOrbit	(	value_type	accuracy,
		size_type	maxit,
		value_type	ekin,
		value_type	dE = `1.0`,
		value_type	rguess = `-1.0`,
		bool	isTuneMode = `false`
	)

Computes the closed orbit.

Parameters

accuracy	specifies the accuracy of the closed orbit
maxit	is the maximal number of iterations done for finding the closed orbit
ekin	energy for which to find closed orbit (in tune mode: upper limit of range)
dE	step increase [MeV]
rguess	initial radius guess in [mm]
isTuneMode	comptute tunes of all energies in one sweep

Definition at line 396 of file ClosedOrbitFinder.h.

References endl(), Hypervolume::fs, OpalData::getInputBasename(), OpalData::getInstance(), max(), EmissionModelT::NONE, and sqrt().

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template<typename Value_type , typename Size_type , class Stepper >

bool ClosedOrbitFinder< Value_type, Size_type, Stepper >::findOrbitOfEnergy_m	(	const value_type &	E,
		container_type &	init,
		value_type &	error,
		const value_type &	accuracy,
		size_type	maxit
	)

private

Definition at line 573 of file ClosedOrbitFinder.h.

References endl(), sqrt(), Physics::two_pi, Physics::u_two_pi, ClassicException::what(), and ClassicException::where().

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template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getAverageRadius ( )

inline

Returns the average orbit radius.

Definition at line 377 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getFieldIndex ( const value_type & angle = 0 )

inline

Returns the field index (size of container N+1)

Definition at line 315 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getFrequencyError ( )

Returns the frequency error.

Definition at line 384 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getInverseBendingRadius ( const value_type & angle = 0 )

inline

Returns the inverse bending radius (size of container N+1)

Definition at line 295 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getMomentum ( value_type angle = 0 )

inline

Returns the momentum of the orbit (size of container N+1)starting at specific angle (only makes sense when computing the closed orbit for a whole turn) (default value: 0°), \( \left[ p_{r} \right] = \si{m}\). Attention: It computes the starting index of the array. If it's not an integer it just cuts the floating point part, i.e. it takes the next starting index below. There's no interpolation of the momentum.

Parameters

angle is the start angle for the output. Has to be within [0°,360°[ (default: 0°).

Returns: the momentum in \( \beta * \gamma \) units

Definition at line 345 of file ClosedOrbitFinder.h.

References for_each().

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template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getOrbit ( value_type angle = 0 )

inline

Returns the closed orbit (size of container N+1) starting at specific angle (only makes sense when computing the closed orbit for a whole turn) (default value: 0°). Attention: It computes the starting index of the array. If it's not an integer it just cuts the floating point part, i.e. it takes the next starting index below. There's no interpolation of the radius.

Parameters

angle is the start angle for the output. Has to be within [0°,360°[ (default: 0°).

Definition at line 335 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::getPathLength ( const value_type & angle = 0 )

inline

Returns the step lengths of the path (size of container N+1)

Definition at line 305 of file ClosedOrbitFinder.h.

template<typename Value_type , typename Size_type , class Stepper >

std::pair< Value_type, Value_type > ClosedOrbitFinder< Value_type, Size_type, Stepper >::getTunes ( )

Returns the radial and vertical tunes (in that order)

Definition at line 323 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

bool ClosedOrbitFinder< Value_type, Size_type, Stepper >::isConverged ( )

Returns true if a closed orbit could be found.

template<typename Value_type , typename Size_type , class Stepper >

ClosedOrbitFinder< Value_type, Size_type, Stepper >::container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::rotate	(	value_type	angle,
		container_type &	orbitProperty
	)

inlineprivate

This function computes nzcross_ which is used to compute the tune in z-direction and the frequency error.

This function rotates the calculated closed orbit finder properties to the initial angle

Definition at line 873 of file ClosedOrbitFinder.h.

Member Data Documentation

template<typename Value_type, typename Size_type, class Stepper>

std::function<double(double)> ClosedOrbitFinder< Value_type, Size_type, Stepper >::acon_m = [](double wo) { return Physics::c / wo; }

private

This quantity is defined in the paper "Transverse-Longitudinal Coupling by Space Charge in Cyclotrons" of Dr. Christian Baumgarten (2012) The lambda function takes the orbital frequency \( \omega_{o} \) (also defined in paper) as input argument.

Definition at line 226 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

std::function<double(double, double)> ClosedOrbitFinder< Value_type, Size_type, Stepper >::bcon_m

private

Initial value:

= [](double e0, double wo) {
            return e0 * 1.0e7 / ( 1.0 * Physics::c * Physics::c / wo);
        }

Cyclotron unit \( \left[T\right] \) (Tesla)

The lambda function takes the orbital frequency \( \omega_{o} \) as input argument.

Definition at line 232 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

Cyclotron* ClosedOrbitFinder< Value_type, Size_type, Stepper >::cycl_m

private

Definition at line 236 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

bool ClosedOrbitFinder< Value_type, Size_type, Stepper >::domain_m

private

Stores the last orbit value (since we have to return to the beginning to check the convergence in the findOrbit() function. This last value is then deleted from the array but is stored in lastOrbitVal_m to compute the vertical oscillations) Stores the last momentum value (since we have to return to the beginning to check the convergence in the findOrbit() function. This last value is then deleted from the array but is stored in lastMomentumVal_m to compute the vertical oscillations) Boolean which is true by default. "true": orbit integration over one sector only, "false": integration over 2*pi

Definition at line 211 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::ds_m

private

Stores the step length.

Definition at line 157 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::dtheta_m

private

Is the angle step size.

Definition at line 185 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::E0_m

private

Is the rest mass [MeV / c**2].

Definition at line 175 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::fidx_m

private

Stores the field index.

Definition at line 167 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::h_m

private

Stores the inverse bending radius.

Definition at line 155 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

size_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::N_m

private

Number of integration steps.

Definition at line 183 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

int ClosedOrbitFinder< Value_type, Size_type, Stepper >::nSectors_m

private

Number of sectors to average the field map over in order to avoid first harmonic. Only valid if domain is false

Definition at line 216 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

size_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::nxcross_m

private

Counts the number of zero-line crossings in horizontal direction (used for computing horizontal tune)

Definition at line 170 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

size_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::nzcross_m

private

Counts the number of zero-line crossings in vertical direction (used for computing vertical tune)

Definition at line 172 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::phase_m

private

Is the phase.

Definition at line 191 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::pr_m

private

Stores the radial momentum.

Definition at line 163 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

std::array<value_type,2> ClosedOrbitFinder< Value_type, Size_type, Stepper >::px_m

private

Stores current momenta in horizontal direction for the solutions of the ODE with different initial values.

Definition at line 148 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

std::array<value_type,2> ClosedOrbitFinder< Value_type, Size_type, Stepper >::pz_m

private

Stores current momenta in vertical direction for the solutions of the ODE with different initial values.

Definition at line 152 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::r_m

private

Stores the radial orbit (size: N_m+1)

Definition at line 159 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::ravg_m

private

Is the average radius.

Definition at line 188 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

Stepper ClosedOrbitFinder< Value_type, Size_type, Stepper >::stepper_m

private

Defines the stepper for integration of the ODE's.

Definition at line 219 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::vpz_m

private

Stores the vertical momentum.

Definition at line 165 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

container_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::vz_m

private

Stores the vertical oribt (size: N_m+1)

Definition at line 161 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder().

template<typename Value_type, typename Size_type, class Stepper>

value_type ClosedOrbitFinder< Value_type, Size_type, Stepper >::wo_m

private

Is the nominal orbital frequency.

Definition at line 181 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

std::array<value_type,2> ClosedOrbitFinder< Value_type, Size_type, Stepper >::x_m

private

Stores current position in horizontal direction for the solutions of the ODE with different initial values.

Definition at line 146 of file ClosedOrbitFinder.h.

template<typename Value_type, typename Size_type, class Stepper>

std::array<value_type,2> ClosedOrbitFinder< Value_type, Size_type, Stepper >::z_m

private

Stores current position in vertical direction for the solutions of the ODE with different initial values.

Definition at line 150 of file ClosedOrbitFinder.h.

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

src/Distribution/ClosedOrbitFinder.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename Value_type, typename Size_type, class Stepper> class ClosedOrbitFinder< Value_type, Size_type, Stepper >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename Value_type, typename Size_type, class Stepper>
class ClosedOrbitFinder< Value_type, Size_type, Stepper >