10.9 BRAT—Bending magnet RAy Tracing using (Bx, By, Bz) vs (x, y, z).

Bending magnet RAy Tracing using (Bx, By, Bz) vs (x, y, z).
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no

Bending magnet RAy Tracing using (Bx, By, Bz) vs (x, y, z).

Bending magnet RAy Tracing using (Bx, By, Bz) vs (x, y, z).

Bending magnet RAy Tracing using (Bx, By, Bz) vs (x, y, z). This element is a companion to the commandline program abrat. It integrates through a 3-D field map for a bending magnet, including coordinate transformations. No synchrotron radiation calculations are included at this time.

Coordinates

The coordinates of the field map are right-handed system (x, y, z), where z is along the length of the magnet, x is to the right as viewed along the direction of beam propagation, and y is up. The user must specify the (x, z) coordinates of three points:

• Nominal entrance point: XENTRY and ZENTRY. These give the coordinates of reference trajectory at the exit of the previous element. In the limit of a hard-edge model, this would be at the entrance to the magnetic field region.
• Vertex point: XVERTEX and ZVERTEX. These give the coordinates of vertex point, which is the intersection of the reference lines from the entrance and exit.
• Nominal exit point: XEXIT and ZEXIT. These give the coordinates of reference trajectory at the exit of the previous element. In the limit of a hard-edge model, this would be at the exit from the magnetic field region.

The bending angle is equal to the angle between two lines: the line from ENTRY to VERTEX and the line from VERTEX to EXIT. The L and ANGLE parameters supplied by the user are used for geometry calculations (e.g., floor coordinates) only.

The DXMAP, DZMAP, YAWMAP, and FSE values can be used to optimize the field map to ensure that the horizontal reference trajectory is not displaced at the exit of the element. The optimization feature of the abrat program can be used to determine these values.

Matrix generation

elegant will use tracking to determine the transport matrix for BRAT elements, which is needed for computation of twiss parameters and other operations. This can require some time, so elegant will cache the matrices and re-use them for identical elements.

If matrices are not of particular interest, significant time savings can be realized by setting USE_SBEND_MATRIX=1. Of course, any matrix-based results (e.g., twiss parameters) are then dubious at best.

Symmetry

By default, the BRAT element should be supplied with the full 3D field map of the magnet. To allow saving memory and reducing the time to load data, partial magnetic field maps can be loaded as well, but the user must specify the symmetry of the magnet to ensure that the fields are modeled correctly in the full volume. This is done using the ySymmetry and zSymmetry parameters in the input file, which may have one of three values: none (default), even, and odd. A normal (upright) multipole magnet would have ySymmetry=odd, while a skew multipole would have ySymmetry=even.

Note that when using these symmetries, the user is not required to limit the field map to y ≥ 0, though doing so saves the most memory. If possible, it is recommended to provide the fields over y ≥-2Δy, so that the transverse interpolation as a few points on both sides of y = 0. This will ensure better results near the origin.

Integration methods

The original (and default) integration method is Bulirsch-Stoer integration of the Lorentz force equation. As an alternative, one can use the faster, rotation-based method of the FTABLE element. For repeated use, the two methods should be compared and a choice made based on the user’s needs.