Skip to main content

SecondTM Class

Description​

The SecondTM class extends the Transformation base class to implement a second-order transformation. It handles both main and edge transformations for elements, assuming the element has implemented the corresponding methods to generate second-order parameters. This transformation can apply second-order terms to the particle coordinates, beyond the linear behavior modeled by a first-order transformation.

Inheritance​

  • Inherits: Transformation

Constructor​

__init__(self, create_tm_param_func, delta_e_func, tm_type: TMTypes, length: float, delta_length: float = 0.0)​

Parameters​

  • create_tm_param_func: A callback function that generates the second-order transformation parameters (including rotation matrix R, second-order tensor T, translation vector B, etc.).
  • delta_e_func: A callback function for calculating the energy change (ΔE\Delta E), if applicable.
  • tm_type (TMTypes): The type of transformation (MAIN, ENTRANCE, EXIT, etc.).
  • length (float): The full length of the element (for main transformations).
  • delta_length (float, optional): Defines a subset length of the element if only a portion is considered. Defaults to 0.0.

Behavior:

  • Initializes a second-order multiplication method (SecondOrderMult().tmat_multip) for matrix operations.
  • Calls the parent constructor (Transformation) to set up the transformation.

Class Methods​

from_element(cls, element: Element, tm_type: TMTypes = TMTypes.MAIN, delta_l=None, **params)​

Creates a SecondTM transformation from a MagneticLattice element. This method calls cls.create with:

  • Functions for entrance, main, and exit second-order parameter generation (if the element supports edges).
  • A function for calculating ΔE\Delta E.
  • The element's length (element.l) and an optional partial length delta_l.

Parameters:

  • element (Element): The beamline element for which to create the second-order transformation.
  • tm_type (TMTypes): The transformation type (ENTRANCE, MAIN, or EXIT).
  • delta_l (float, optional): A partial length of the element, if needed.
  • params: Additional keyword arguments.

Returns:

  • A SecondTM instance configured with the element's parameter-generating functions.

Instance Methods​

t_apply(self, energy, X, U5666=0.0) -> np.ndarray​

Applies the second-order transformation to the phase-space coordinates in X.

Parameters:

  • energy (float): The beam energy in GeV.
  • X (np.ndarray): A 6×N6 \times N array representing the particle coordinates (x, px, y, py, tau, p).
  • U5666 (float, optional): An additional parameter (if needed) for higher-order corrections; defaults to 0.0.

Returns:

  • Updated coordinates in X.

Process:

  1. Retrieves the transformation parameters (R, T, B, optional tilt).
  2. Applies the second-order multiplication function self.multiplication(X, R, T).
  3. Adds the translation vector B.
  4. Returns the updated X.

map_function(self, X, energy: float) -> np.ndarray​

Implements the transformation by calling t_apply on the given coordinates X at the specified energy.

Parameters:

  • X (np.ndarray): The particle coordinates.
  • energy (float): The beam energy.

Returns:

  • The transformed particle coordinates.

calculate_Tb(self, energy) -> np.ndarray​

A placeholder method indicating the calculation of a “Tb” matrix, which could be necessary for certain advanced second-order calculations.

Returns:

  • A NumPy array representing the Tb matrix.

Note:

  • Raises NotImplementedError by default, indicating this function is not yet fully implemented.