| Parameter Description | Argument Order | Argument Name | Units | Default Value |
|---|---|---|---|---|
| Bend Field | 1 | B[kG] | kG | 0.0 |
| Pole Face Angle | 2 | Angle[deg] | deg | 0.0 |
| Edge Field Eff Length | 3 | EffLen[cm] | cm | 0.0 |
| Tilt | 4 | T[deg] | degree | 0.0 |
| Tilt Error | 5 | TiltError[deg] | degree | 0.0 |
This element models edge focusing. The first parameter is the bend field "jump" at the magnet edge. Normally this parameter is determined by the bending element that preceeds or follows. The second parameter is the edge face angle. Edge face angles are zero for a pure sector bend. The angles signs are defined so that for a rectangular magnet (parallel edges), the upstream and downstream angles (in degrees) are positive and equal to half the bending angle. The third parameter is the edge field effective length in [cm]. The fourth parameter is the roll angle (tilt) of the entire magnet (in degrees) with respect to the local beam frame. The rotation is performed around the beam trajectory at the magnet entrance. Normally, the edge tilt angle should be equal and identical to that of the corresponding dipole; however, if the dipole tilt angle is not 0 or 90 deg. differs from the bend magnet tilt angle (see B, D-combined function magnet). The inverse focal lengths of the edge field are :
$$ \begin{eqnarray} \frac{1}{f_x} & = & - \frac{1}{\rho}{\tan \,\alpha} \\ \frac{1}{f_y} & = & \frac{1}{\rho}{\tan \,\alpha} - \frac{a}{\rho^2} \end{eqnarray} $$where $\alpha$ is the pole rotation angle, $\rho$ is the bending radius, and $a$ is the effective length of the edge. The effective length of the edge, $a$, may be determined using the following equation:
$$ a = g K \frac{( 1+ \sin^2 \alpha )}{\cos \alpha} $$where $g$ the (full) gap, and $0.5 < K <1$. The numerical parameter $K$ $$ K = \int_{-\infty}^{\infty} \frac {B_y(z) [ B_0 - B_y(z)]}{g B_0^2} \, dz $$ characterizes the magnetic field profile in the edge region which in turn depends on details of the magnet pole face and coil geometries.
Values of $K$ have been determined and tabulated for a few typical profiles.
| Linear drop-off | 1/6 |
| Clamped Rogowski | 0.4 |
| Unclamped Rogowski | 0.7 |
| Square edge | 0.45 |
When the profile is unknown, $K=0.5$ is a good compromise.
Examples:
# Vertically bending rectangular magnet (beam momentum of 445 MeV). # The magnet edges and body have to be listed in the lattice description # as gMAI1R01 bMAI1R01 gMAI1R01 gMAI1R01 B[kG]=-4.84581 Angle[deg]= 9.3943 EffLen[cm]=1.39004 Tilt[deg]=-90 bMAI1R01 L[cm]=100.449 B[kG]=-4.84581 G[kG/cm]=0 Tilt[deg]=-90 #This magnet can also be described in the following way # Next 6 lines have to be in the math header $Pc=445 $Hro=$Pc*1e11/$c; => 1484.36 ; $c is the build-in light velocity ~3e10 cm/c $B=-4.84581; => -4.84581 $L=100.449; => 100.449 $Fi=-180/$PI*$B*$L/$Hro; => 18.7886419 $FiEdge=$Fi/2.; => 9.39432095 $MAI1R01=" gMAI1R01 bMAI1R01 gMAI1R01 " # The magnet is refered in the lattice description as $MAI1R01 for shorteness. #Then in the describtion of elements it looks like this: gMAI1R01 B[kG]=$B Angle[deg]= $FiEdge EffLen[cm]=1.39004 Tilt[deg]=-90 bMAI1R01 L[cm]=$L B[kG]=$B G[kG/cm]=0 Tilt[deg]=-90 # Horizontally bending sector dipole. Lattice description: g b G g B[kG]=-4.84581 Angle[deg]=0 EffLen[cm]=1.39004 Tilt[deg]=0 b L[cm]=100.449 B[kG]=-4.84581 G[kG/cm]=0 Tilt[deg]=0 G B[kG]=4.84581 Angle[deg]=0 EffLen[cm]=1.39004 Tilt[deg]=0