“Small angle” Passmethods#
The “Small angle” passmethods use a linearised approximation of the longitudinal momentum:
resulting in:
These methods are fast and are assigned by default when creating AT elements.
Default passmethods
IdentityPass#
Thin element with no effect. However, the element may define transverse apertures limiting the physical aperture,
DriftPass#
Field-free space in the small angle approximation.
- Length
Drift length.
RFCavityPass#
RF Cavity
- Length
Cavity length. If
Lengthis non-zero, a drift of half-length is added on each side of a thin cavity.- Voltage
Cavity voltage
- Frequency
Cavity frequency
- TimeLag
Time lag expressed as path lengthening: \(\beta c \tau\).
- PhaseLag
Phase lag in radians.
TimeLagandPhaseLagare accumulated as:\[\mathbf{PhaseLag} - 2 \pi f_{RF} \frac{\mathbf{TimeLag}}{\beta c}\]
StrMPoleSymplectic4Pass#
4th order Forest-Knuth integrator for straight magnets
- Length
Magnet Length.
- PolynomB, PolynomA
Polynomial field expansion.
- MaxOrder
Maximum order of the polynomial expansion: only indices from 0 to
MaxOrder(included) are used.- NumIntSteps
Number of integration steps (magnet slices). Optional, default 10.
BndMPoleSymplectic4Pass#
4th order Forest-Knuth integrator for curved magnets
- Length
Length \(L\) of the arc.
- PolynomB, PolynomA, MaxOrder, NumIntSteps
- BendingAngle
Dipole bending angle \(\theta\)
- EntranceAngle
Angle of the entrance pole face \(\varepsilon_1\) with respect to the plane perpendicular to the input trajectory. Use 0 for a sector magnet, \(\theta/2\) for a rectangular magnet.
- EntranceAngle
Angle of the exit pole face \(\varepsilon_2\) with respect to the plane perpendicular to the output trajectory. Use 0 for a sector magnet, \(\theta/2\) for a rectangular magnet.
ThinMPolePass#
Thin multipolar kick
- PolynomB, PolynomA, MaxOrder
Linear passmethods
These passmethods are kept for backward compatibility but their use is discouraged.
QuadLinearPass#
- Length
Quadrupole Length.
- PolynomB, K
Quadrupole strength. If
PolynomB[1]exists, it is used for the strength, otherwiseKis used
BendLinearPass#
- Length
Length \(L\) of the arc.
- PolynomB, K
Quadrupole strength. If
PolynomB[1]exists, it is used for the strength, otherwiseKis used- BendingAngle
Dipole bending angle \(\theta\)
- EntranceAngle
Angle of the entrance pole face \(\varepsilon_1\) with respect to the plane perpendicular to the input trajectory. Use 0 for a sector magnet, \(\theta/2\) for a rectangular magnet.
- ExitAngle
Angle of the exit pole face \(\varepsilon_2\) with respect to the plane perpendicular to the output trajectory. Use 0 for a sector magnet, \(\theta/2\) for a rectangular magnet.
GWigSymplecticPass#
2 nd and 4th order Forest-Wu-Robin integrator for wigglers without radiation.
- Length
Length \(L\) of the element.
- MaxOrder, NumIntSteps
- Period
Wiggler period \(L_w\).
- Peak magnetic field, B_0
Maximum magnetic field \(B_0\) of the wiggler.
- Nmeth
Indicates the integration method: 2nd or 4th order integrator.
- NHharm
Number of horizontal harmonics of the wiggler.
- NVharm
Number of vertical harmonics of the wiggler.
- By
6 x NHharm array containing the following quantities. row 1: Horizontal harmonic counter; row 2: relative amplitudes of wiggler harmonics; row 3: \(k_x*L_w/2\pi\); row 4: \(k_y*L_w/2\pi\); row 5: \(k_z*L_w/2\pi\); row 6: \(\theta_n\), the relative phase of the nth wiggler harmonic. \(k_x\), \(k_y\) and \(k_z\) are defined in [1].
- Bx
6 x NVharm array containing the following quantities. row 1: Vertical harmonic counter; row 2: relative amplitudes of wiggler harmonics; row 3: \(k_x*L_w/2\pi\); row 4: \(k_y*L_w/2\pi\); row 5: \(k_z*L_w/2\pi\); row 6: \(\theta_n\), the relative phase of the nth wiggler harmonic. \(k_x\), \(k_y\) and \(k_z\) are defined in [1].