Track Methods

Utility functions for creating transfer maps for elements.

track_methods.base_rmatrix(length: Tensor, k1: Tensor, hx: Tensor, species: Species, energy: Tensor | None = None) → Tensor

Create a first order universal transfer map for a beamline element.

Parameters:

  • length – Length of the element in m.

  • k1 – Quadrupole strength in 1/m**2.

  • hx – Curvature (1/radius) of the element in 1/m.

  • species – Particle species of the beam.

  • energy – Beam energy in eV.

Returns:

First order transfer map for the element.

track_methods.base_ttensor(length: Tensor, k1: Tensor, k2: Tensor, hx: Tensor, species: Species, energy: Tensor | None = None) → Tensor

Create a second order universal transfer map for a beamline element. Uses MAD convention.

NOTE: It is possible that gradient components are missing when computing the

over second order T tensors or beams tracked with them in very few highly specific scenarios. Even when it happens, it is unlikely to have a meaningful impact. This comment is left here to make sure this caveat is known.

Parameters:

  • length – Length of the element in m.

  • k1 – Quadrupole strength in 1/m**2.

  • k2 – Sextupole strength in 1/m**3.

  • hx – Curvature (1/radius) of the element in 1/m.

  • species – Particle species of the beam.

  • energy – Beam energy in eV.

Returns:

Second order transfer map for the element.

track_methods.combined_rotation_misalignment_matrix(angle: Tensor, misalignment: Tensor) → Tensor

Apply misalignment and then rotation in the x-y plane.

Parameters:

  • angle – Rotation angle in rad, for example angle = np.pi/2 for vertical = dipole.

  • misalignment – Misalignment vector [dx, dy] in m.

Returns:

Combined rotation and misalignment matrix.

track_methods.drift_matrix(length: Tensor, energy: Tensor, species: Species) → Tensor

Create a first order transfer map for a drift space.

track_methods.misalignment_matrix(misalignment: Tensor) → tuple[Tensor, Tensor]

Shift the beam for tracking beam through misaligned elements.

track_methods.rotation_matrix(angle: Tensor) → Tensor

Rotate the coordinate system in the x-y plane.

Parameters:

angle – Rotation angle in rad, for example angle = np.pi/2 for vertical = dipole.

Returns:

Rotation matrix to be multiplied to the element’s transfer matrix.