#include <NonlinearLens.H>

Inheritance diagram for impactx::elements::NonlinearLens:

Public Types
using	PType = ImpactXParticleContainer::ParticleType

Public Member Functions
	NonlinearLens (amrex::ParticleReal knll, amrex::ParticleReal cnll, amrex::ParticleReal dx=0, amrex::ParticleReal dy=0, amrex::ParticleReal rotation_degree=0, std::optional< std::string > name=std::nullopt)

void	reverse ()

void	compute_constants (RefPart const &refpart)

template<typename T_Real = amrex::ParticleReal, typename T_IdCpu = uint64_t>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	operator() (T_Real &AMREX_RESTRICT x, T_Real &AMREX_RESTRICT y, T_Real &AMREX_RESTRICT t, T_Real &AMREX_RESTRICT px, T_Real &AMREX_RESTRICT py, T_Real &AMREX_RESTRICT pt, T_IdCpu &AMREX_RESTRICT idcpu, RefPart const &AMREX_RESTRICT refpart) const

AMREX_GPU_HOST AMREX_FORCE_INLINE Map6x6	transport_map (RefPart const &AMREX_RESTRICT refpart) const

Public Member Functions inherited from impactx::elements::mixin::Named
AMREX_GPU_HOST void	set_name (std::string const &new_name)

AMREX_GPU_HOST	Named (std::optional< std::string > name)

AMREX_GPU_HOST_DEVICE	~Named ()

AMREX_GPU_HOST	Named (Named const &other)

AMREX_GPU_HOST Named &	operator= (Named const &other)

AMREX_GPU_HOST_DEVICE	Named (Named &&other) noexcept

AMREX_GPU_HOST_DEVICE Named &	operator= (Named &&other) noexcept

AMREX_FORCE_INLINE std::string	name () const

AMREX_FORCE_INLINE bool	has_name () const

Public Member Functions inherited from impactx::elements::mixin::BeamOptic< NonlinearLens >
void	operator() (ImpactXParticleContainer &pc, int step, int period)

void	operator() (ImpactXParticleContainer::iterator &pti, RefPart &AMREX_RESTRICT ref_part, bool spin)

Public Member Functions inherited from impactx::elements::mixin::LinearTransport< NonlinearLens >
AMREX_GPU_HOST AMREX_FORCE_INLINE void	operator() (Map6x6 &AMREX_RESTRICT cm, RefPart const &AMREX_RESTRICT ref) const

Public Member Functions inherited from impactx::elements::mixin::Thin
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	operator() (RefPart &AMREX_RESTRICT refpart) const

void	reverse ()

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE int	nslice () const

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	ds () const

Public Member Functions inherited from impactx::elements::mixin::Alignment
	Alignment (amrex::ParticleReal dx, amrex::ParticleReal dy, amrex::ParticleReal rotation_degree)

	Alignment ()=default

	Alignment (Alignment const &)=default

Alignment &	operator= (Alignment const &)=default

	Alignment (Alignment &&)=default

Alignment &	operator= (Alignment &&rhs)=default

	~Alignment ()=default

void	compute_constants (RefPart const &refpart)

template<typename T_Real>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	shift_in (T_Real &AMREX_RESTRICT x, T_Real &AMREX_RESTRICT y, T_Real &AMREX_RESTRICT px, T_Real &AMREX_RESTRICT py) const

template<typename T_Real>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	shift_out (T_Real &AMREX_RESTRICT x, T_Real &AMREX_RESTRICT y, T_Real &AMREX_RESTRICT px, T_Real &AMREX_RESTRICT py) const

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	dx () const

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	dy () const

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	rotation () const

Public Member Functions inherited from impactx::elements::mixin::NoFinalize
void	finalize ()

Public Attributes
amrex::ParticleReal	m_knll

amrex::ParticleReal	m_cnll
	integrated strength of the nonlinear lens (m)

Public Attributes inherited from impactx::elements::mixin::Alignment
amrex::ParticleReal	m_dx = 0

amrex::ParticleReal	m_dy = 0
	horizontal translation error [m]

amrex::ParticleReal	m_rotation = 0
	vertical translation error [m]

Static Public Attributes
static constexpr auto	type = "NonlinearLens"

Static Public Attributes inherited from impactx::elements::mixin::LinearTransport< NonlinearLens >
static constexpr bool	has_linear_transport

Static Public Attributes inherited from impactx::elements::mixin::Alignment
static constexpr amrex::ParticleReal	degree2rad = ablastr::constant::math::pi / 180.0

Private Attributes
amrex::ParticleReal	m_inv_cnll
	distance of singularities from the origin (m)

amrex::ParticleReal	m_kick
	1 / m_cnll

Member Typedef Documentation

◆ PType

using impactx::elements::NonlinearLens::PType = ImpactXParticleContainer::ParticleType

Constructor & Destructor Documentation

◆ NonlinearLens()

impactx::elements::NonlinearLens::NonlinearLens	(	amrex::ParticleReal	knll,
		amrex::ParticleReal	cnll,
		amrex::ParticleReal	dx = 0,
		amrex::ParticleReal	dy = 0,
		amrex::ParticleReal	rotation_degree = 0,
		std::optional< std::string >	name = std::nullopt )

inline

Single short segment of the nonlinear magnetic insert element

A thin lens associated with a single short segment of the nonlinear magnetic insert described by V. Danilov and S. Nagaitsev, PRSTAB 13, 084002 (2010), Sect. V.A. This element appears in MAD-X as type NLLENS.

Parameters

knll	integrated strength of the nonlinear lens (m)
cnll	distance of singularities from the origin (m)
dx	horizontal translation error in m
dy	vertical translation error in m
rotation_degree	rotation error in the transverse plane [degrees]
name	a user defined and not necessarily unique name of the element

Member Function Documentation

◆ compute_constants()

void impactx::elements::NonlinearLens::compute_constants ( RefPart const & refpart )

inline

Compute and cache the constants for the push.

In particular, used to pre-compute and cache variables that are independent of the individually tracked particle.

Parameters

refpart reference particle

◆ operator()()

template<typename T_Real = amrex::ParticleReal, typename T_IdCpu = uint64_t>

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::elements::NonlinearLens::operator()	(	T_Real &AMREX_RESTRICT	x,
		T_Real &AMREX_RESTRICT	y,
		T_Real &AMREX_RESTRICT	t,
		T_Real &AMREX_RESTRICT	px,
		T_Real &AMREX_RESTRICT	py,
		T_Real &AMREX_RESTRICT	pt,
		T_IdCpu &AMREX_RESTRICT	idcpu,
		RefPart const &AMREX_RESTRICT	refpart ) const

inline

This is a nonlinear lens functor, so that a variable of this type can be used like a nonlinear lens function.

The

See also: compute_constants method must be called before pushing particles through this operator.

Parameters

x	particle position in x
y	particle position in y
t	particle position in t
px	particle momentum in x
py	particle momentum in y
pt	particle momentum in t
idcpu	particle global index (unused)
refpart	reference particle (unused)

◆ reverse()

void impactx::elements::NonlinearLens::reverse ( )

inline

Reverse the element (negate strength)

◆ transport_map()

AMREX_GPU_HOST AMREX_FORCE_INLINE Map6x6 impactx::elements::NonlinearLens::transport_map ( RefPart const &AMREX_RESTRICT refpart ) const

inline

This function returns the linear transport map.

The Danilov-Nagaitsev kick implemented by

See also: operator() is dpx - i*dpy = -(knll / cnll) * F'(zeta), with zeta = (x + i*y) / cnll and F'(zeta) = zeta / (1 - zeta^2) + arcsin(zeta) / (1 - zeta^2)^(3/2). The Taylor series around zeta = 0 starts at F'(zeta) = 2*zeta + (8/3)*zeta^3 + O(zeta^5), so the linearized map at the reference trajectory is a thin quadrupole with equal and opposite focusing strengths in the two transverse planes: R(2,1) = -2 * knll / cnll^2, R(4,3) = +2 * knll / cnll^2.

Ideal behavior only: alignment and rotation errors, as well as feed-down from an off-axis reference orbit, are ignored; the map is evaluated at (x, y) = (0, 0).

This element appears in MAD-X as type NLLENS. The linear limit above is the MAD-X linear quadrupole equivalent of the NLLENS thin kick (cf. MAD-X Physical Methods Manual, nonlinear lens).

Reference: V. Danilov and S. Nagaitsev, Phys. Rev. ST Accel. Beams 13, 084002 (2010), Sect. V.A

Parameters

[in] refpart reference particle (unused)

Returns: 6x6 transport matrix

Member Data Documentation

◆ m_cnll

amrex::ParticleReal impactx::elements::NonlinearLens::m_cnll

integrated strength of the nonlinear lens (m)

◆ m_inv_cnll

amrex::ParticleReal impactx::elements::NonlinearLens::m_inv_cnll

private

distance of singularities from the origin (m)

◆ m_kick

amrex::ParticleReal impactx::elements::NonlinearLens::m_kick

private

1 / m_cnll

◆ m_knll

amrex::ParticleReal impactx::elements::NonlinearLens::m_knll

◆ type

auto impactx::elements::NonlinearLens::type = "NonlinearLens"

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/impactx/checkouts/1402/src/elements/NonlinearLens.H

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Attributes

Member Typedef Documentation

◆ PType

Constructor & Destructor Documentation

◆ NonlinearLens()

Member Function Documentation

◆ compute_constants()

◆ operator()()

◆ reverse()

◆ transport_map()

Member Data Documentation

◆ m_cnll

◆ m_inv_cnll

◆ m_kick

◆ m_knll

◆ type