Classes
struct	NonlinearLensInvariants

Functions
std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal >	CubicRootsTrig (amrex::ParticleReal a, amrex::ParticleReal b, amrex::ParticleReal c, amrex::ParticleReal d)

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal >	CubicRootsAlg (amrex::ParticleReal a, amrex::ParticleReal b, amrex::ParticleReal c, amrex::ParticleReal d)

void	DiagnosticOutput (ImpactXParticleContainer const &pc, std::string file_name, int step, bool append)

void	DiagnosticOutput (Map6x6 const &cm, RefPart const &ref_part, std::string file_name, int step, bool append)

void	DiagnosticOutput (RefPart const &ref_part, std::string file_name, int step, bool append)

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal >	KineticInvariants (amrex::SmallMatrix< amrex::ParticleReal, 6, 6, amrex::Order::F, 1 > const &Sigma)

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal >	Eigenemittances (amrex::SmallMatrix< amrex::ParticleReal, 6, 6, amrex::Order::F, 1 > const &Sigma)

std::unordered_map< std::string, amrex::ParticleReal >	reduced_beam_characteristics (ImpactXParticleContainer const &pc)

std::unordered_map< std::string, amrex::ParticleReal >	reduced_beam_characteristics (Map6x6 const &cm, RefPart const &ref_part)

Function Documentation

◆ CubicRootsAlg()

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal > impactx::diagnostics::CubicRootsAlg	(	amrex::ParticleReal	a,
		amrex::ParticleReal	b,
		amrex::ParticleReal	c,
		amrex::ParticleReal	d )

Function to return the roots of a cubic polynomial ax^3 + bx^2 + cx + d. The algebraic form of Cardano's formula is used. This implementation expects three real roots, which is verified by checking the sign of the discriminant.

Parameters

[in]	a	coefficient of cubic term
[in]	b	coefficient of quadratic term
[in]	c	coefficient of linear term
[in]	d	coefficient of constant term

Returns: tuple of three real roots

◆ CubicRootsTrig()

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal > impactx::diagnostics::CubicRootsTrig	(	amrex::ParticleReal	a,
		amrex::ParticleReal	b,
		amrex::ParticleReal	c,
		amrex::ParticleReal	d )

Function to return the roots of a cubic polynomial ax^3 + bx^2 + cx + d. The trigonometric form of Cardano's formula is used. This implementation expects three real roots, which is verified by checking the sign of the discriminant.

Parameters

[in]	a	coefficient of cubic term
[in]	b	coefficient of quadratic term
[in]	c	coefficient of linear term
[in]	d	coefficient of constant term

Returns: tuple of three real roots

◆ DiagnosticOutput() [1/3]

void impactx::diagnostics::DiagnosticOutput	(	ImpactXParticleContainer const &	pc,
		std::string	file_name,
		int	step = 0,
		bool	append = false )

ASCII output diagnostics associated with the beam particles.

This prints reduced beam characteristics derived from particles in ASCII.

Parameters

pc	container of the particles use for diagnostics
file_name	the file name to write to
step	the global step
append	open a new file with a fresh header (false) or append data to an existing file (true)

◆ DiagnosticOutput() [2/3]

void impactx::diagnostics::DiagnosticOutput	(	Map6x6 const &	cm,
		RefPart const &	ref_part,
		std::string	file_name,
		int	step = 0,
		bool	append = false )

ASCII output diagnostics associated with the covariance matrix.

This prints reduced beam characteristics derived from the envelope description in ASCII.

Parameters

cm	covariance matrix
ref_part	reference particle
file_name	the file name to write to
step	the global step
append	open a new file with a fresh header (false) or append data to an existing file (true)

◆ DiagnosticOutput() [3/3]

void impactx::diagnostics::DiagnosticOutput	(	RefPart const &	ref_part,
		std::string	file_name,
		int	step = 0,
		bool	append = false )

ASCII output diagnostics associated with the reference particle.

This prints reference particle properties in ASCII.

Parameters

ref_part	reference particle
file_name	the file name to write to
step	the global step
append	open a new file with a fresh header (false) or append data to an existing file (true)

◆ Eigenemittances()

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal > impactx::diagnostics::Eigenemittances ( amrex::SmallMatrix< amrex::ParticleReal, 6, 6, amrex::Order::F, 1 > const & Sigma )

This function returns the three eigenemittances denoted e1, e2, and e3 as constructed from the 6x6 beam covariance matrix. These three quantities are invariant under any linear symplectic transport map, and reduce to the projected normalized rms emittances in the limit of uncoupled transport.

input - Sigma symmetric 6x6 covariance matrix returns - tuple containing eigenemittances e1, e2, and e3

Returns the three eigenemittances denoted e1, e2, and e3 as constructed from the 6x6 beam covariance matrix. These three quantities are invariant under any linear symplectic transport map, and reduce to the projected normalized rms emittances in the limit of uncoupled transport. These quantities are described in:

G. Rangarajan, F. Neri, and A. Dragt, "Generalized Emittance Invariants," in Proc. 1989 IEEE Part. Accel. Conf., Chicago, IL, 1989, doi:10.1109/PAC.1989.73422. A. Dragt, F. Neri, and G. Rangarajan, "General Moment Invariants for Linear Hamiltonian Systems," Phys. Rev. A 45, 2572-2585 (1992), doi:10.1103/PhysRevA.45.2572.

Parameters

[in] Sigma symmetric 6x6 covariance matrix

Returns: tuple containing eigenemittances e1, e2, and e3

◆ KineticInvariants()

std::tuple< amrex::ParticleReal, amrex::ParticleReal, amrex::ParticleReal > impactx::diagnostics::KineticInvariants ( amrex::SmallMatrix< amrex::ParticleReal, 6, 6, amrex::Order::F, 1 > const & Sigma )

This function returns the three independent kinetic invariants denoted I2, I4, and I6 as constructed from the 6x6 beam covariance matrix. These three quantities are invariant under any linear symplectic transport map, and are used in the calculation of the three eigenemittances.

input - Sigma symmetric 6x6 covariance matrix returns - tuple containing invariants I2, I4, and I6

Returns the three independent kinematic moment invariants denoted I2, I4, and I6 as constructed from the 6x6 beam covariance matrix. These three quantities are invariant under any linear symplectic transport map, and are used in the calculation of the three eigenemittances, as described in:

G. Rangarajan, F. Neri, and A. Dragt, "Generalized Emittance Invariants," in Proc. 1989 IEEE Part. Accel. Conf., Chicago, IL, 1989, doi:10.1109/PAC.1989.73422. A. Dragt, F. Neri, and G. Rangarajan, "General Moment Invariants for Linear Hamiltonian Systems," Phys. Rev. A 45, 2572-2585 (1992), doi:10.1103/PhysRevA.45.2572.

Parameters

[in] Sigma symmetric 6x6 covariance matrix

Returns: tuple containing invariants I2, I4, and I6

◆ reduced_beam_characteristics() [1/2]

std::unordered_map< std::string, amrex::ParticleReal > impactx::diagnostics::reduced_beam_characteristics ( ImpactXParticleContainer const & pc )

Compute moments of the beam distribution from particle data

This uses an MPI Allreduce and returns a result on all ranks.

◆ reduced_beam_characteristics() [2/2]

std::unordered_map< std::string, amrex::ParticleReal > impactx::diagnostics::reduced_beam_characteristics	(	Map6x6 const &	cm,
		RefPart const &	ref_part )

Compute moments of the beam distribution from covariance matrix

Classes

Functions

Function Documentation

◆ CubicRootsAlg()

◆ CubicRootsTrig()

◆ DiagnosticOutput() [1/3]

◆ DiagnosticOutput() [2/3]

◆ DiagnosticOutput() [3/3]

◆ Eigenemittances()

◆ KineticInvariants()

◆ reduced_beam_characteristics() [1/2]

◆ reduced_beam_characteristics() [2/2]