#include <ChrUniformAcc.H>

Inheritance diagram for impactx::elements::ChrAcc:

Public Types
using	PType = ImpactXParticleContainer::ParticleType

Public Member Functions
	ChrAcc (amrex::ParticleReal ds, amrex::ParticleReal ez, amrex::ParticleReal bz, amrex::ParticleReal dx=DEFAULT_dx, amrex::ParticleReal dy=DEFAULT_dy, amrex::ParticleReal rotation_degree=DEFAULT_rotation_degree, amrex::ParticleReal aperture_x=DEFAULT_aperture_x, amrex::ParticleReal aperture_y=DEFAULT_aperture_y, int nslice=DEFAULT_nslice, std::optional< std::string > name=DEFAULT_name)
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_DEVICE AMREX_FORCE_INLINE void	operator() (RefPart &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< ChrAcc >
void	operator() (ImpactXParticleContainer &pc, int step, int period)
Public Member Functions inherited from impactx::elements::mixin::LinearTransport< ChrAcc >
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::Thick
	Thick (amrex::ParticleReal ds, int nslice)
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE int	nslice () const
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	ds () const
void	reverse ()
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::PipeAperture
	PipeAperture (amrex::ParticleReal aperture_x, amrex::ParticleReal aperture_y)
	PipeAperture ()=default
	PipeAperture (PipeAperture const &)=default
PipeAperture &	operator= (PipeAperture const &)=default
	PipeAperture (PipeAperture &&)=default
PipeAperture &	operator= (PipeAperture &&rhs)=default
	~PipeAperture ()=default
template<typename T_Real = amrex::ParticleReal, typename T_IdCpu = uint64_t>
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void	apply_aperture (T_Real &AMREX_RESTRICT x, T_Real &AMREX_RESTRICT y, T_IdCpu &AMREX_RESTRICT idcpu) const
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	aperture_x () const
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE amrex::ParticleReal	aperture_y () const
Public Member Functions inherited from impactx::elements::mixin::NoFinalize
void	finalize ()

Public Attributes
amrex::ParticleReal	m_ez
amrex::ParticleReal	m_bz
	electric field strength in 1/m
Public Attributes inherited from impactx::elements::mixin::Thick
amrex::ParticleReal	m_ds
int	m_nslice
	segment length in 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]
Public Attributes inherited from impactx::elements::mixin::PipeAperture
amrex::ParticleReal	m_inv_aperture_x = 0
amrex::ParticleReal	m_inv_aperture_y = 0
	inverse of the horizontal aperture size [1/m]

Static Public Attributes
static constexpr auto	type = "ChrAcc"
Static Public Attributes inherited from impactx::elements::mixin::Named
static constexpr std::nullopt_t	DEFAULT_name = std::nullopt
Static Public Attributes inherited from impactx::elements::mixin::LinearTransport< ChrAcc >
static constexpr bool	has_linear_transport
Static Public Attributes inherited from impactx::elements::mixin::Thick
static constexpr int	DEFAULT_nslice = 1
Static Public Attributes inherited from impactx::elements::mixin::Alignment
static constexpr amrex::ParticleReal	degree2rad
static constexpr amrex::ParticleReal	DEFAULT_dx = 0
static constexpr amrex::ParticleReal	DEFAULT_dy = 0
static constexpr amrex::ParticleReal	DEFAULT_rotation_degree = 0
Static Public Attributes inherited from impactx::elements::mixin::PipeAperture
static constexpr amrex::ParticleReal	DEFAULT_aperture_x = 0
static constexpr amrex::ParticleReal	DEFAULT_aperture_y = 0
Static Public Attributes inherited from amrex::simd::Vectorized< amrex::simd::native_simd_size_particlereal >
static constexpr int	simd_width

Private Attributes
amrex::ParticleReal	m_slice_ds
	magnetic field strength in 1/m
amrex::ParticleReal	m_ptf_ref
	m_ds / nslice();
amrex::ParticleReal	m_pti_ref
amrex::ParticleReal	m_bgf
amrex::ParticleReal	m_bgi
amrex::ParticleReal	m_alpha
amrex::ParticleReal	m_alpha_iez

Member Typedef Documentation

◆ PType

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

Constructor & Destructor Documentation

◆ ChrAcc()

impactx::elements::ChrAcc::ChrAcc	(	amrex::ParticleReal	ds,
		amrex::ParticleReal	ez,
		amrex::ParticleReal	bz,
		amrex::ParticleReal	dx = DEFAULT_dx,
		amrex::ParticleReal	dy = DEFAULT_dy,
		amrex::ParticleReal	rotation_degree = DEFAULT_rotation_degree,
		amrex::ParticleReal	aperture_x = DEFAULT_aperture_x,
		amrex::ParticleReal	aperture_y = DEFAULT_aperture_y,
		int	nslice = DEFAULT_nslice,
		std::optional< std::string >	name = DEFAULT_name )

inline

Acceleration in a uniform field Ez, with a uniform solenoidal field Bz.

The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained.

Parameters

ds	Segment length in m.
ez	electric field strength in m^(-1) = (charge * electric field Ez in V/m) / (m*c^2)
bz	magnetic field strength in m^(-1) = (charge * magnetic field Bz in T) / (m*c)
dx	horizontal translation error in m
dy	vertical translation error in m
rotation_degree	rotation error in the transverse plane [degrees]
aperture_x	horizontal half-aperture in m
aperture_y	vertical half-aperture in m
nslice	number of slices used for the application of space charge
name	a user defined and not necessarily unique name of the element

Member Function Documentation

◆ compute_constants()

void impactx::elements::ChrAcc::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()() [1/2]

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::elements::ChrAcc::operator() ( RefPart &AMREX_RESTRICT refpart ) const

inline

This pushes the reference particle.

Parameters

[in,out] refpart reference particle

◆ operator()() [2/2]

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

AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void impactx::elements::ChrAcc::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 chracc functor, so that a variable of this type can be used like a chracc 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
refpart	reference particle (unused)

◆ reverse()

void impactx::elements::ChrAcc::reverse ( )

inline

Reverse the element (negate ds)

◆ transport_map()

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

inline

This function returns the linear transport map.

Jacobian at the reference trajectory of the ChrAcc push (see

See also: operator()). The nonlinear push composes, in order: (1) static->dynamic unit conversion: diag(1, bgi, 1, bgi, 1, bgi) acting on (x, px, y, py, t, pt); (2) solenoid-like focusing by phase advance theta (cf. Sol); (3) rotation by the same theta in the (x, y) plane; (4) dynamic->static unit conversion: diag(1, 1/bgf, 1, 1/bgf, 1, 1/bgf) on the output; plus a symplectic correction to t. Here theta = (alpha/ez) * log((pzf_ref - ptf_ref)/(pzi_ref - pti_ref)) with alpha = Bz/2, ez the normalized longitudinal electric field, pzi_ref = sqrt(pti_ref^2 - 1), pzf_ref = sqrt(ptf_ref^2 - 1), and (pti_ref, ptf_ref) = (initial, final) reference pt on this slice.

This routine is called after the reference particle has been advanced by one slice (see diagnostics/LinearMap.cpp), so refpart.pt holds ptf_ref and pti_ref = ptf_ref + ez * slice_ds.

The closed-form linear map was derived with SymPy by Jacobian of the exact push at (x, px, y, py, t, pt) = 0. Writing c = cos(theta0), s = sin(theta0) with theta0 the reference phase advance above, the nonzero entries are R(1,1) = c^2, R(1,2) = bgi * c*s / alpha, R(1,3) = c*s, R(1,4) = bgi * s^2 / alpha, R(2,1) = -alpha * c*s / bgf, R(2,2) = (bgi/bgf) * c^2, R(2,3) = -alpha * s^2 / bgf, R(2,4) = (bgi/bgf) * c*s, R(3,1) = -c*s, R(3,2) = -bgi * s^2 / alpha, R(3,3) = c^2, R(3,4) = bgi * c*s / alpha, R(4,1) = alpha * s^2 / bgf, R(4,2) = -(bgi/bgf) * c*s, R(4,3) = -alpha * c*s / bgf, R(4,4) = (bgi/bgf) * c^2, R(5,5) = 1, R(5,6) = (bgi/ez) * (ptf_ref/pzf_ref - pti_ref/pzi_ref), R(6,6) = bgi/bgf. All other entries are zero. The quadratic-in-(px, py, x, y) part of the t correction vanishes at linear order.

References:

A. J. Dragt, Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics, Univ. of Maryland, 2020 (MaryLie documentation), chapter on uniform-Ez acceleration with solenoidal focusing;
H. Wiedemann, Particle Accelerator Physics, 4th ed., Springer 2015, chapters on electrostatic acceleration and solenoid focusing;
The Hamiltonian and nonlinear push follow Chad Mitchell's formulation already implemented in
See also
operator().
Ideal behavior only: alignment and rotation errors and feed-down from an off-axis reference orbit are ignored.

Parameters

[in] refpart reference particle after this slice's reference advance (pt = ptf_ref)

Returns: 6x6 transport matrix

Member Data Documentation

◆ m_alpha

amrex::ParticleReal impactx::elements::ChrAcc::m_alpha

private

◆ m_alpha_iez

amrex::ParticleReal impactx::elements::ChrAcc::m_alpha_iez

private

◆ m_bgf

amrex::ParticleReal impactx::elements::ChrAcc::m_bgf

private

◆ m_bgi

amrex::ParticleReal impactx::elements::ChrAcc::m_bgi

private

◆ m_bz

amrex::ParticleReal impactx::elements::ChrAcc::m_bz

electric field strength in 1/m

◆ m_ez

amrex::ParticleReal impactx::elements::ChrAcc::m_ez

◆ m_ptf_ref

amrex::ParticleReal impactx::elements::ChrAcc::m_ptf_ref

private

m_ds / nslice();

◆ m_pti_ref

amrex::ParticleReal impactx::elements::ChrAcc::m_pti_ref

private

◆ m_slice_ds

amrex::ParticleReal impactx::elements::ChrAcc::m_slice_ds

private

magnetic field strength in 1/m

◆ type

auto impactx::elements::ChrAcc::type = "ChrAcc"

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/impactx/checkouts/latest/src/elements/ChrUniformAcc.H

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Attributes

Member Typedef Documentation

◆ PType

Constructor & Destructor Documentation

◆ ChrAcc()

Member Function Documentation

◆ compute_constants()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ reverse()

◆ transport_map()

Member Data Documentation

◆ m_alpha

◆ m_alpha_iez

◆ m_bgf

◆ m_bgi

◆ m_bz

◆ m_ez

◆ m_ptf_ref

◆ m_pti_ref

◆ m_slice_ds

◆ type