#include <TaperedPL.H>

Inheritance diagram for impactx::elements::TaperedPL:

Public Types
using	PType = ImpactXParticleContainer::ParticleType

Public Member Functions
	TaperedPL (amrex::ParticleReal k, amrex::ParticleReal taper, int unit, 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 const &AMREX_RESTRICT x, T_Real const &AMREX_RESTRICT y, T_Real const &AMREX_RESTRICT t, T_Real &AMREX_RESTRICT px, T_Real &AMREX_RESTRICT py, T_Real const &AMREX_RESTRICT pt, T_IdCpu const &AMREX_RESTRICT idcpu, RefPart const &AMREX_RESTRICT refpart) const

template<typename T_Real = amrex::ParticleReal, typename T_IdCpu = uint64_t>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	spin_and_phasespace_push (T_Real const &AMREX_RESTRICT x, T_Real const &AMREX_RESTRICT y, T_Real const &AMREX_RESTRICT t, T_Real &AMREX_RESTRICT px, T_Real &AMREX_RESTRICT py, T_Real const &AMREX_RESTRICT pt, T_Real &AMREX_RESTRICT sx, T_Real &AMREX_RESTRICT sy, T_Real &AMREX_RESTRICT sz, T_IdCpu const &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< TaperedPL >
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< TaperedPL >
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	rotate_in (T_Real &AMREX_RESTRICT sx, T_Real &AMREX_RESTRICT sy) 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

template<typename T_Real>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	rotate_out (T_Real &AMREX_RESTRICT sx, T_Real &AMREX_RESTRICT sy) 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

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE bool	misaligned () const

AMREX_GPU_HOST AMREX_FORCE_INLINE Map6x6	rotation_map () const

AMREX_GPU_HOST AMREX_FORCE_INLINE Map6x6	rotate_aligned_map (Map6x6 const &R) const

Public Member Functions inherited from impactx::elements::mixin::SpinTransport
template<typename T_Real = amrex::ParticleReal>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	rotate_spin (T_Real const &AMREX_RESTRICT lambdax, T_Real const &AMREX_RESTRICT lambday, T_Real const &AMREX_RESTRICT lambdaz, T_Real &AMREX_RESTRICT sx, T_Real &AMREX_RESTRICT sy, T_Real &AMREX_RESTRICT sz) const

template<typename T_Real = amrex::ParticleReal>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	tbmt_precession_vector (T_Real const &AMREX_RESTRICT x, T_Real const &AMREX_RESTRICT ux, T_Real const &AMREX_RESTRICT uy, T_Real const &AMREX_RESTRICT uz, T_Real const &AMREX_RESTRICT gamma, amrex::ParticleReal const &AMREX_RESTRICT h, amrex::ParticleReal const &AMREX_RESTRICT gyro_anomaly, T_Real const &AMREX_RESTRICT Bx, T_Real const &AMREX_RESTRICT By, T_Real const &AMREX_RESTRICT Bz, T_Real const &AMREX_RESTRICT Ex, T_Real const &AMREX_RESTRICT Ey, T_Real const &AMREX_RESTRICT Ez, T_Real &AMREX_RESTRICT Omegax, T_Real &AMREX_RESTRICT Omegay, T_Real &AMREX_RESTRICT Omegaz) const

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

Public Attributes
amrex::ParticleReal	m_k

amrex::ParticleReal	m_taper
	linear focusing strength (field gradient)

int	m_unit
	horizontal taper parameter

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 = "TaperedPL"

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

Static Public Attributes inherited from impactx::elements::mixin::Alignment
static constexpr amrex::ParticleReal	degree2rad

Static Public Attributes inherited from amrex::simd::Vectorized< amrex::simd::native_simd_size_particlereal >
static constexpr int	simd_width

Private Attributes
amrex::ParticleReal	m_beta
	units for linear focusing strength (field gradient)

amrex::ParticleReal	m_ibeta
	relativistic beta

amrex::ParticleReal	m_g
	inverse of beta

Member Typedef Documentation

◆ PType

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

Constructor & Destructor Documentation

◆ TaperedPL()

impactx::elements::TaperedPL::TaperedPL	(	amrex::ParticleReal	k,
		amrex::ParticleReal	taper,
		int	unit,
		amrex::ParticleReal	dx = 0,
		amrex::ParticleReal	dy = 0,
		amrex::ParticleReal	rotation_degree = 0,
		std::optional< std::string >	name = std::nullopt )

inline

A short segment of a nonlinear plasma lens with a transverse taper.

Parameters

k	integrated plasma lens (linear) focusing strength in m^(-1) = (length in m) * (azimuthal field gradient in T/m) / (rigidity in T-m) OR integrated azimuthal magnetic field gradient in T (k > 0)
unit	Unit specification unit = 0 integrated linear focusing strength in m^(-1) unit = 1 integrated linear focusing strength in T
taper	horizontal taper parameter in m^(-1) = 1 / (horizontal dispersion in 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::TaperedPL::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::TaperedPL::operator()	(	T_Real const &AMREX_RESTRICT	x,
		T_Real const &AMREX_RESTRICT	y,
		T_Real const &AMREX_RESTRICT	t,
		T_Real &AMREX_RESTRICT	px,
		T_Real &AMREX_RESTRICT	py,
		T_Real const &AMREX_RESTRICT	pt,
		T_IdCpu const &AMREX_RESTRICT	idcpu,
		RefPart const &AMREX_RESTRICT	refpart ) const

inline

This is a tapered PL functor, so that a variable of this type can be used like a shortrf function.

Parameters

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

◆ reverse()

void impactx::elements::TaperedPL::reverse ( )

inline

Reverse the element (negate strength)

◆ spin_and_phasespace_push()

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

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::elements::TaperedPL::spin_and_phasespace_push	(	T_Real const &AMREX_RESTRICT	x,
		T_Real const &AMREX_RESTRICT	y,
		T_Real const &AMREX_RESTRICT	t,
		T_Real &AMREX_RESTRICT	px,
		T_Real &AMREX_RESTRICT	py,
		T_Real const &AMREX_RESTRICT	pt,
		T_Real &AMREX_RESTRICT	sx,
		T_Real &AMREX_RESTRICT	sy,
		T_Real &AMREX_RESTRICT	sz,
		T_IdCpu const &AMREX_RESTRICT	idcpu,
		RefPart const &AMREX_RESTRICT	refpart ) const

inline

This operator pushes the particle spin.

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
sx	particle spin x-component
sy	particle spin y-component
sz	particle spin z-component
idcpu	particle global index
refpart	reference particle

◆ transport_map()

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

inline

This function returns the linear transport map.

The tapered plasma-lens kick implemented by

See also: operator() is dpx = -g * ( x + taper/2 * (x^2 + y^2) ) dpy = -g * ( y + taper * x * y ) where g is the integrated focusing strength (in units that match m_unit: either m^-1 directly, or rigidity-normalized from T via refpart.rigidity_Tm()).

Linearized at the reference trajectory (x = y = 0), the taper contributes only quadratic terms and drops out. The element therefore reduces to a thin axisymmetric focusing kick: R(2,1) = -g, R(4,3) = -g.

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

MAD-X convention: no direct analogue. Its linear limit coincides with a thin axisymmetric focusing quadrupole-like kick (equivalent to a MAD-X MULTIPOLE with normal KNL of equal strength in both transverse planes), but MAD-X has no element that carries the quadratic taper term.

Physics references:

C. Lindstrøm et al., "Achromatic optics using nonlinear plasma lenses for beam-quality preservation between plasma-accelerator stages", submitted (2026), https://arxiv.org/abs/2604.17605

Parameters

[in] refpart reference particle (used only for the unit conversion when m_unit == 1)

Returns: 6x6 transport matrix

Member Data Documentation

◆ m_beta

amrex::ParticleReal impactx::elements::TaperedPL::m_beta

private

units for linear focusing strength (field gradient)

◆ m_g

amrex::ParticleReal impactx::elements::TaperedPL::m_g

private

inverse of beta

◆ m_ibeta

amrex::ParticleReal impactx::elements::TaperedPL::m_ibeta

private

relativistic beta

◆ m_k

amrex::ParticleReal impactx::elements::TaperedPL::m_k

◆ m_taper

amrex::ParticleReal impactx::elements::TaperedPL::m_taper

linear focusing strength (field gradient)

◆ m_unit

int impactx::elements::TaperedPL::m_unit

horizontal taper parameter

◆ type

auto impactx::elements::TaperedPL::type = "TaperedPL"

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/impactx/checkouts/26.06/src/elements/TaperedPL.H

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Attributes

Member Typedef Documentation

◆ PType

Constructor & Destructor Documentation

◆ TaperedPL()

Member Function Documentation

◆ compute_constants()

◆ operator()()

◆ reverse()

◆ spin_and_phasespace_push()

◆ transport_map()

Member Data Documentation

◆ m_beta

◆ m_g

◆ m_ibeta

◆ m_k

◆ m_taper

◆ m_unit

◆ type