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Edge

A dipole edge models the fringe-field kick at the entrance or exit of a real dipole magnet. Two edges flank a Dipole to give a complete sector- or rectangular-bend model.

TL;DR (TraceWin users)

TraceWin HELIX
Keyword EDGE pole_rotation rho gap k1 k2 [aperture hv] Edge(name, pole_rotation, rho, gap, ...)
pole_rotation edge angle in degrees same
rho bending radius (mm) same
gap full gap height (mm) same
k1, k2 fringe coefficients same

Conventions:

  • pole_rotation is the angle between the magnet face and the local reference trajectory. 0° = sector face (perpendicular to trajectory). Non-zero ⇒ rectangular or wedge magnet.
  • k1, k2 are TraceWin's fringe-field coefficients (defaults 0.45 and 2.80). Only k1 enters the matrix — k2 is parsed and stored for round-trip fidelity but not applied.
  • The edge applies a thin angular kick: x' ↛ x' + (tan β / ρ)·x in the bending plane.

Tutorial (newcomers)

A real dipole has an extended fringe field beyond its geometric length. Two effects matter:

  1. Geometric edge focusing — the slanted face of a rectangular bend acts like a thin lens with focal length f = ρ / tan(β) where β is the pole rotation angle. This is the dominant fringe contribution for a wedge magnet.
  2. Quadrupole-component fringe — the field rolloff at the edge isn't sharp; it falls off over a length proportional to the gap. HELIX captures this with the first-order k1 fringe correction (the second-order k2 is stored but not applied).

The edge element implements both as a thin matrix kick.

Full 6×6 transfer matrix

For an edge with pole rotation β and fringe correction ψ, the thin-edge transfer matrix in (x, x', y, y', Δφ, ΔW) is:

\[ M_{\text{edge}} = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ \tan\beta/\rho & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & -\tan(\beta-\psi)/\rho & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{pmatrix} \]

with the fringe correction (dimensionless)

\[ \psi = \frac{k_1\,g}{\rho} \, \frac{1+\sin^2\beta}{\cos\beta} \]

where g is the full magnetic gap. ψ is zero when gap = 0 or k1 = 0. Note that k2 does not appear — the implemented matrix uses the first-order ψ only; k2 is stored for .dat round-tripping but never applied.

Block Effect
(x, x') 2×2 thin-lens focusing in bending plane: f_x = ρ / tan(β)
(y, y') 2×2 thin-lens defocusing in non-bending plane: f_y = -ρ / tan(β − ψ)
(Δφ, ΔW) 2×2 identity (zero-length element does no longitudinal work)
Cross blocks all zero

For a vertical bend (hv = 1), x and y swap throughout.

A sector bend has β = 0 → tan(β) = 0 → no edge focusing → the Edge element collapses to the identity and can be omitted.

Example

from linac_gen.elements.edge import Edge
from linac_gen.elements.dipole import Dipole

# A horizontal 30° rectangular bend with 15° symmetric edges
edge_in  = Edge(name="E1_in",  pole_rotation=15.0, rho=1500.0,
                gap=20.0, k1=0.45, hv=0)
bend     = Dipole(name="B1", angle=30.0, rho=1500.0, hv=0)
edge_out = Edge(name="E1_out", pole_rotation=15.0, rho=1500.0,
                gap=20.0, k1=0.45, hv=0)

A sector bend (no edge focusing) skips the Edge elements entirely.

API reference (developers)

Parameter Default Units Notes
name (required) — identifier
pole_rotation (required) deg edge angle β between face and trajectory
rho (required) mm bending radius (matches the partner Dipole)
gap 0.0 mm full magnet gap height; 0 disables the fringe correction
k1 0.45 — first-order fringe coefficient (TraceWin default)
k2 2.80 — second-order fringe coefficient — parsed/stored, not applied by the matrix
aperture 0.0 mm stored but not used at this stage
hv 0 int 0 = horizontal bend, 1 = vertical

Edge is a PassiveElement — it has no misalignment or field-error mixin parameters.

Source

linac_gen/elements/edge.py:1

See also

← Dipole · Continue to RFGap →