“Small angle” Passmethods#

The “Small angle” passmethods use a linearised approximation of the longitudinal momentum:

\[p_z=1+\delta\]

resulting in:

\[\begin{split}x' &= \frac{p_x}{1+\delta} \\ y' &= \frac{p_y}{1+\delta}\end{split}\]

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,

Field-free space in the small angle approximation.

RF Cavity

Length: Cavity length. If Length is 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. TimeLag and PhaseLag are accumulated as:

\[\mathbf{PhaseLag} - 2 \pi f_{RF} \frac{\mathbf{TimeLag}}{\beta c}\]

4^th 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.

4^th order Forest-Knuth integrator for curved magnets

Length: Length \(L\) of the arc.
PolynomB, PolynomA, MaxOrder, NumIntSteps: see StrMPoleSymplectic4Pass
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.

Thin multipolar kick

Linear passmethods

These passmethods are kept for backward compatibility but their use is discouraged.

Length: Quadrupole Length.
PolynomB, K: Quadrupole strength. If PolynomB[1] exists, it is used for the strength, otherwise K is used

Length: Length \(L\) of the arc.
PolynomB, K: Quadrupole strength. If PolynomB[1] exists, it is used for the strength, otherwise K is 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.