| Parameter Description | Argument Order | Argument Name | Units | Default Value |
|---|---|---|---|---|
| Length | 1 | L | cm | 0.0 |
| Gradient | 2 | G[kG/cm] | kG/cm | 0.0 |
| Tilt | 3 | T | degrees | 0.0 |
| Horizontal Offset | 4 | OfsX[cm] | cm | 0.0 |
| Vertical Offset | 5 | OfsY[cm] | cm | 0.0 |
Rotations (e.g Tilt) are performed in the beam frame about an axis tangent to the beam trajectory.
Examples: Qfs L[cm]=45 G[kG/cm]=0.277565 Tilt[deg]=45 Qd L[cm]=45 G[kG/cm]=-0.445846
A quadrupole can have offsets in the horizontal and vertical planes. Such offsets, when present, cause beam kicks proportional to quad displacements in the corresponding planes (for tilt=0). Similarly to correctors, quadrupole displacements cause excitation of the beam trajectory. They are accounted for in all trajectory related calculations, including optics calculations on a reference orbit.
Example: QQf L[cm]=45 G[kG/cm]=0.277 Tilt[deg]=0 OfsX[cm]=0.1 OfsY[cm]=0.01
In tracking mode, the quadrupole map includes edge aberrations due to the fringe field. The transfer map is computed in the hard-edge approximation. For the upstream edge, the edge map in the horizontal and vertical planes are respectively $$ \Delta x = \frac{k_1}{12(1+\delta)} \left[ x^3 + 3xy^2 \right] $$ $$ \Delta x' = \frac{k_1}{4(1+\delta)} \left[ 2 xyy' - (x^2 + y^2) x' \right] $$ $$ \Delta y = -\frac{k_1}{12(1+\delta)} \left[ y^3 + 3x^2y \right] $$ $$ \Delta y' = -\frac{k_1}{4(1+\delta)} \left[ 2 yxx' - (x^2 + y^2) y' \right] $$
Here, $k_1 = eG/p = G/B\rho$ is the optical quadrupole strength and $\delta = \Delta p/p$ is the relative momentum deviation. The signs of the edge aberrations are reversed at the downstream end. A switch is provided under the preferences menu to optionally turn the edge effects off. References: