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Drift Class

The public Drift class is an OpticElement wrapper around DriftAtom, which inherits from Magnet. It represents free-space transport without external fields.

In this page we focus on the first-order matrix and on how it is implemented in OCELOT.

Drift in the Element Architecture​

Drift follows the standard no-edge wrapper/atom structure:

  • public wrapper: Drift
  • atom: DriftAtom
  • default active transformation: TransferMap
  • additionally supported active transformations: SecondTM, KickTM, RungeKuttaTM, RungeKuttaTrTM
  • has_edge = False, so the element is represented by a single MAIN map without entrance or exit maps

The first-order matrix is built by the atom layer and then applied by TransferMap.

Class Definition Snippet​

from ocelot.cpbd.elements import Drift

d = Drift(l=1.0)

# full parameter list:
# Drift(l=0.0, eid=None, tm=None)

Parameters​

  • l (float): drift length [m]
  • eid (str, optional): element identifier

First-Order Transfer Matrix​

For a drift, both the curvature and the quadrupole strength are zero. In the notation used by uni_matrix(...), this means:

hx=0,k1=0h_x = 0, \qquad k_1 = 0

and the first-order matrix becomes:

R(z)=[1z0000010000001z0000010000001r56000001]R(z)= \begin{bmatrix} 1 & z & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & z & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & r_{56} \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}

with

r56=−zβ2γ2r_{56} = -\frac{z}{\beta^2 \gamma^2}

At relativistic beam energies this term is usually very small, so in many numerical printouts it appears as 0 or -0.

How OCELOT Implements It​

The implementation path is:

Drift
    -> DriftAtom
    -> Magnet.create_first_order_main_params(...)
    -> uni_matrix(...)
    -> FirstOrderParams(R, B, tilt)
    -> TransferMap

Wrapper and atom​

Drift constructs a DriftAtom.

DriftAtom stores only the element length and does not override create_first_order_main_params(...).

Inherited first-order hook​

Because DriftAtom inherits from Magnet, it uses:

create_first_order_main_params(energy, delta_length=None)

from Magnet.

That method calls:

R = uni_matrix(length, k1=0.0, hx=0.0, sum_tilts=0, energy=energy)

which is exactly the linear drift map.

Zero-field Runge-Kutta path​

DriftAtom also implements a Runge-Kutta hook:

create_runge_kutta_main_params(...)

which returns a zero magnetic field. This is why Drift can also be used with RungeKuttaTM and RungeKuttaTrTM.

Example of Use​

import numpy as np
from ocelot.cpbd.elements import Drift

d = Drift(l=1.0)

np.set_printoptions(precision=4, suppress=True)
print(d.R(energy=1.0))  # [GeV]
[array([[ 1.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  1., -0.],
       [ 0.,  0.,  0.,  0.,  0.,  1.]])]