#include <ClosedOrbitFinder.h>

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

Public Types
typedef Value_type	value_type
	Type of variables.
typedef Size_type	size_type
	Type for specifying sizes.
typedef std::vector< value_type >	container_type
	Type of container for storing quantities (path length, orbit, etc.).
typedef std::vector< value_type >	state_type
	Type for holding state of ODE values.
typedef std::function< void(const state_type &, state_type &, const double)>	function_t

Public Member Functions
	ClosedOrbitFinder (value_type E0, value_type q, size_type N, Cyclotron *cycl, bool domain=true, int Nsectors=1)
	Sets the initial values for the integration and calls findOrbit().
container_type	getInverseBendingRadius (const value_type &angle=0)
	Returns the inverse bending radius (size of container N+1).
container_type	getPathLength (const value_type &angle=0)
	Returns the step lengths of the path (size of container N+1).
container_type	getFieldIndex (const value_type &angle=0)
	Returns the field index (size of container N+1).
std::pair< value_type, value_type >	getTunes ()
	Returns the radial and vertical tunes (in that order).
container_type	getOrbit (value_type angle=0)
container_type	getMomentum (value_type angle=0)
value_type	getAverageRadius ()
	Returns the average orbit radius.
value_type	getFrequencyError ()
	Returns the frequency error.
bool	isConverged ()
	Returns true if a closed orbit could be found.
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.
void	computeOrbitProperties (const value_type &E)
	Fills in the values of h_m, ds_m, fidx_m.

Private Member Functions
value_type	computeTune (const std::array< value_type, 2 > &, value_type, size_type)
	This function is called by the function getTunes().
bool	findOrbitOfEnergy_m (const value_type &, container_type &, value_type &, const value_type &, size_type)
container_type	rotate (value_type angle, const container_type &orbitProperty)
	This function computes nzcross_ which is used to compute the tune in z-direction and the frequency error.

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.
std::array< value_type, 2 >	px_m
	Stores current momenta in horizontal direction for the solutions of the ODE with different initial values.
std::array< value_type, 2 >	z_m
	Stores current position in vertical direction for the solutions of the ODE with different initial values.
std::array< value_type, 2 >	pz_m
	Stores current momenta in vertical direction for the solutions of the ODE with different initial values.
container_type	h_m
	Stores the inverse bending radius.
container_type	ds_m
	Stores the step length.
container_type	r_m
	Stores the radial orbit (size: N_m+1).
container_type	vz_m
	Stores the vertical oribt (size: N_m+1).
container_type	pr_m
	Stores the radial momentum.
container_type	vpz_m
	Stores the vertical momentum.
container_type	fidx_m
	Stores the field index.
size_type	nxcross_m
	Counts the number of zero-line crossings in horizontal direction (used for computing horizontal tune).
size_type	nzcross_m
	Counts the number of zero-line crossings in vertical direction (used for computing vertical tune).
value_type	E0_m
	Is the rest mass [MeV / c**2].
value_type	q_m
value_type	wo_m
	Is the nominal orbital frequency.
size_type	N_m
	Number of integration steps.
value_type	dtheta_m
	Is the angle step size.
value_type	ravg_m
	Is the average radius.
value_type	phase_m
	Is the phase.
bool	domain_m
int	nSectors_m
Stepper	stepper_m
	Defines the stepper for integration of the ODE's.
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).
Cyclotron *	cycl_m

Detailed Description

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

Definition at line 54 of file ClosedOrbitFinder.h.

Member Typedef Documentation

◆ container_type

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 62 of file ClosedOrbitFinder.h.

◆ function_t

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 66 of file ClosedOrbitFinder.h.

◆ size_type

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 60 of file ClosedOrbitFinder.h.

◆ state_type

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 64 of file ClosedOrbitFinder.h.

◆ value_type

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 58 of file ClosedOrbitFinder.h.

Constructor & Destructor Documentation

◆ ClosedOrbitFinder()

template<typename Value_type, typename Size_type, class Stepper>

ClosedOrbitFinder< Value_type, Size_type, Stepper >::ClosedOrbitFinder	(	value_type	E0,
		value_type	q,
		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].
q	is the particle charge [e]
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 262 of file ClosedOrbitFinder.h.

References ClosedOrbitFinder(), cycl_m, domain_m, ds_m, dtheta_m, E0_m, fidx_m, h_m, N_m, nSectors_m, nxcross_m, nzcross_m, phase_m, pi, pr_m, q_m, r_m, ravg_m, stepper_m, vpz_m, vz_m, and wo_m.

Referenced by ClosedOrbitFinder().

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Member Function Documentation

◆ computeOrbitProperties()

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 851 of file ClosedOrbitFinder.h.

References acon_m, bcon_m, cycl_m, ds_m, dtheta_m, E0_m, fidx_m, h_m, N_m, pr_m, r_m, ravg_m, value_type(), vz_m, and wo_m.

Referenced by findOrbit().

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◆ computeTune()

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 793 of file ClosedOrbitFinder.h.

References cos(), cycl_m, domain_m, Physics::pi, Physics::two_pi, and Physics::u_two_pi.

Referenced by getTunes().

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◆ findOrbit()

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 [m]
isTuneMode	comptute tunes of all energies in one sweep

Definition at line 415 of file ClosedOrbitFinder.h.

References acon_m, computeOrbitProperties(), cycl_m, domain_m, E0_m, endl(), findOrbitOfEnergy_m(), OpalData::getAuxiliaryOutputDirectory(), OpalData::getInputBasename(), OpalData::getInstance(), getMomentum(), getOrbit(), getTunes(), gmsg, level3(), N_m, NONE, phase_m, pr_m, r_m, ravg_m, vpz_m, vz_m, and wo_m.

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◆ findOrbitOfEnergy_m()

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 605 of file ClosedOrbitFinder.h.

References acon_m, bcon_m, cycl_m, dtheta_m, E0_m, endl(), gmsg, N_m, nSectors_m, nxcross_m, nzcross_m, phase_m, pr_m, px_m, pz_m, r_m, stepper_m, Physics::two_pi, Physics::u_two_pi, vpz_m, vz_m, OpalException::what(), OpalException::where(), wo_m, x_m, and z_m.

Referenced by findOrbit().

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◆ getAverageRadius()

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 398 of file ClosedOrbitFinder.h.

References ravg_m.

◆ getFieldIndex()

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 334 of file ClosedOrbitFinder.h.

References fidx_m, and rotate().

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◆ getFrequencyError()

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 405 of file ClosedOrbitFinder.h.

References phase_m.

◆ getInverseBendingRadius()

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 312 of file ClosedOrbitFinder.h.

References h_m, and rotate().

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◆ getMomentum()

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 366 of file ClosedOrbitFinder.h.

References acon_m, pr_m, rotate(), and wo_m.

Referenced by findOrbit().

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◆ getOrbit()

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 355 of file ClosedOrbitFinder.h.

References r_m, and rotate().

Referenced by findOrbit().

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◆ getPathLength()

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 323 of file ClosedOrbitFinder.h.

References ds_m, and rotate().

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◆ getTunes()

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 343 of file ClosedOrbitFinder.h.

References computeTune(), nxcross_m, nzcross_m, px_m, pz_m, x_m, and z_m.

Referenced by findOrbit().

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◆ isConverged()

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.

◆ rotate()

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,
		const 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 906 of file ClosedOrbitFinder.h.

References dtheta_m, and Physics::two_pi.

Referenced by getFieldIndex(), getInverseBendingRadius(), getMomentum(), getOrbit(), and getPathLength().

Member Data Documentation

◆ acon_m

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 242 of file ClosedOrbitFinder.h.

Referenced by computeOrbitProperties(), findOrbit(), findOrbitOfEnergy_m(), and getMomentum().

◆ bcon_m

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:

= [this](double e0, double wo) {
        return e0 * 1.0e7 / (q_m * 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 248 of file ClosedOrbitFinder.h.

Referenced by computeOrbitProperties(), and findOrbitOfEnergy_m().

◆ cycl_m

template<typename Value_type, typename Size_type, class Stepper>

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

private

Definition at line 252 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder(), computeOrbitProperties(), computeTune(), findOrbit(), and findOrbitOfEnergy_m().

◆ domain_m

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 227 of file ClosedOrbitFinder.h.

Referenced by ClosedOrbitFinder(), computeTune(), and findOrbit().