#include <ChrUniformAcc.H>
Public Types | |
| using | PType = ImpactXParticleContainer::ParticleType |
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::LinearTransport< ChrAcc > | |
| 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_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
Constructor & Destructor Documentation
◆ ChrAcc()
|
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()
|
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]
|
inline |
This pushes the reference particle.
- Parameters
-
[in,out] refpart reference particle
◆ operator()() [2/2]
|
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()
|
inline |
Reverse the element (negate ds)
◆ transport_map()
|
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().
- Parameters
-
[in] refpart reference particle after this slice's reference advance (pt = ptf_ref)
- Returns
- 6x6 transport matrix
Member Data Documentation
◆ m_alpha
|
private |
◆ m_alpha_iez
|
private |
◆ m_bgf
|
private |
◆ 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
|
private |
m_ds / nslice();
◆ m_pti_ref
|
private |
◆ m_slice_ds
|
private |
magnetic field strength in 1/m
◆ type
|
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/ChrUniformAcc.H
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