Drift¶

A drift is field-free propagation: the beam coasts in a straight line with no transverse force. The simplest element in the catalog and the one that makes up the majority of any real lattice.

TL;DR (TraceWin users)¶

	TraceWin	HELIX
Keyword	`DRIFT L aperture [aperture_y x_shift y_shift]`	`Drift(name, length, aperture, ...)`
Length	mm	mm
Aperture	mm (radius for round; `aperture_y` makes it rectangular)	same
`x_shift`, `y_shift`	beam-frame static offset (mm)	folded into the misalignment `dx`, `dy`

Conventions:

HELIX length is in mm (matches TraceWin).
The longitudinal M[4,5] slip term is included (Δφ[deg] = -360·L·ΔW / (β³·γ³·m·λ_RF)) — this is what causes the bunch to drift in φ when there's an energy spread.
Drift apertures are enforced: the tracker checks apertures after every element and inside every drift sub-step bundle. With only aperture set the pipe is circular (x² + y² > aperture² loses the particle); setting aperture_y > 0 switches to a rectangular check with half-widths (aperture, aperture_y). Use a dedicated Aperture element for shaped point collimators.

Tutorial (newcomers)¶

A drift just propagates the beam. The full 6×6 transfer matrix is

\[ M_{\text{drift}} = \begin{pmatrix} 1 & L & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & L & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & M_{56} \\ 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix} \]

with L in metres and the longitudinal phase-slip element

\[ M_{56} \;=\; -\,\frac{360\,L\,[\text{mm}]}{\beta^{3}\,\gamma^{3}\,m\,\lambda_{\text{RF}}} \quad [\text{deg}/\text{MeV}] \]

This term causes off-energy particles to slip in phase relative to the synchronous reference — the longitudinal counterpart of transverse drift expansion. HELIX stores lengths in mm and converts to metres internally before applying the matrix.

A pencil beam with non-zero divergence drifts outward linearly: position grows like x = x₀ + L·x'₀. This is why a long beamline without focusing always blows up — the beam keeps spreading.

Block	Effect
(x, x') 2×2	identity-with-L: standard transverse drift
(y, y') 2×2	identity-with-L: same in the other plane
(Δφ, ΔW) 2×2	drift-like phase slip via M₅₆
Cross blocks	all zero (drift has no coupling)

Example¶

A 5×100 mm drift chain propagating a low-current 3 MeV proton beam:

from linac_gen.core.particle import PROTON
from linac_gen.core.reference import ReferenceParticle
from linac_gen.core.lattice import Lattice
from linac_gen.core.simulation import Simulation
from linac_gen.core.config import BeamConfig
from linac_gen.distributions.factory import create_beam
from linac_gen.elements.drift import Drift

ref = ReferenceParticle(species=PROTON, w_kin=3.0, frequency=352.21)
beam_cfg = BeamConfig(
    species="proton", energy=3.0, frequency=352.21,
    current=0.0, n_particles=2000,
    distribution="gaussian", cutoff=4.0,
    emit_nx=0.10, emit_ny=0.10, emit_z=0.20,
    alpha_x=0.0, beta_x=1.0,
    alpha_y=0.0, beta_y=1.0,
    alpha_z=0.0, beta_z=1.0,
)
beam = create_beam(beam_cfg, seed=0)

lat = Lattice()
for i in range(5):
    lat.add(Drift(name=f"D{i}", length=100.0))

sim = Simulation(lat, beam)
res = sim.run()
print(f"σ_x: start = {res.sigma_x[0]:.3f} mm, end = {res.sigma_x[-1]:.3f} mm")

The σ_x grows because the matched beta function is short relative to the drift length — exactly what physics predicts.

API reference (developers)¶

linac_gen.elements.drift.Drift(
    name: str,
    length: float,                # mm
    aperture: float = 0.0,        # mm (round radius; informational)
    aperture_y: float | None = None,  # mm; >0 makes the check rectangular
    x_shift: float = 0.0,         # mm; folded into dx
    y_shift: float = 0.0,         # mm; folded into dy
    dx: float = 0.0,              # mm; transverse misalignment
    dy: float = 0.0,
    dz: float = 0.0,              # mm; longitudinal offset
    tilt_deg: float = 0.0,        # rotation about z
    pitch_deg: float = 0.0,       # rotation about x (reserved)
    yaw_deg: float = 0.0,         # rotation about y (reserved)
    n_steps: int = 1,
)

Parameter	Default	Units	Notes
`name`	(required)	—	element identifier
`length`	(required)	mm	drift length
`aperture`	0.0	mm	circular pipe radius, enforced by the tracker; 0 = no check
`aperture_y`	None	mm	when > 0, the check becomes rectangular with half-widths (`aperture`, `aperture_y`)
`x_shift`	0.0	mm	TraceWin DRIFT slot 4; static offset
`y_shift`	0.0	mm	TraceWin DRIFT slot 5
`dx`, `dy`, `dz`	0.0	mm	misalignment offsets (Misalignment mixin); only `dx`/`dy` honoured by the tracker
`tilt_deg`	0.0	deg	rotation about longitudinal axis
`pitch_deg`, `yaw_deg`	0.0	deg	stored — not honoured by the tracker
`n_steps`	1	—	unused for transfer-map elements: drift integration density comes from `lattice.step_config` (PARTRAN_STEP); quads/bends/solenoids always track in exactly 2 substeps

Methods¶

transfer_matrix(ref, ds=None) → np.ndarray — 6×6 linear matrix. ds lets you query a partial drift.
track(beam, ds=None) → None — applies the matrix to live particles in-place. Reference particle s and phi_s advance.

Source¶

linac_gen/elements/drift.py:1 (54 lines).