10.12 CCBEND—A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.

A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : yes

A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.

A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.

A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.

A canonically-integrated straight dipole magnet, assumed to have multipoles defined in Cartesian coordinates.

This element provides a symplectic straight-pole, bending magnet with the exact Hamiltonian in Cartesian coordinates [61]. The quadrupole, sextupole, and other multipole terms are defined in Cartesian coordinates. The magnet at present is restricted to having rectangular ends. This is quite different from CSBEND, where the edge angles are user-defined and where the field expansion is in curvilinear coordinates. Strictly speaking, CSBEND is only valid when the dipole is built with curved, beam-following poles.

Integration of particles in CCBEND is very similar to what’s done for KQUAD, KSEXT, and KOCT. The only real difference is that coordinate transformations are performed at the entrance and exit to orient the incoming central trajectory to the straight magnet axis. In addition, the fractional strength error is adjusted to ensure that the outgoing central trajectory is correct.

By default, two adjustments are made at start-up and whenever the length, angle, gradient, or sextupole term change:

1. The fractional strength error is altered to ensure the correct deflecting angle. This is required because the bending field varies along the trajectory. By default, this affects all field components together, per the usual convention in elegant. To restrict the strength change to the dipole term, set COMPENSATE_KN=1. To turn off this optimization, set OPTIMIZE_FSE=0.
2. The transverse position is adjusted to center the trajectory in the magnet. If the sagitta is σ and ANGLE is positive, the initial and final x coordinates are x = -σ∕2, while the center coordinate is x = σ∕2. To turn off this optimization, set OPTIMIZE_DX=0.

One can block the re-optimization of these parameters by setting OPTIMIZE_FSE_ONCE and OPTIMIZE_DX_ONCE to 1. Note also that the optimization is performed with all error-defining parameters (DX, DY, DZ, FSE, ETILT, etc.) set to zero. However, errors that are assigned to, say, the K1 value directly would not be recognized as such. For this reason, assigning errors to K1 is not recommended; instead, use the FSE_QUADRUPOLE parameter.

Having computed the ideal trajectory through a CCBEND element, elegant can suppress any errors in the trajectory. Such errors may occur due to limited accuracy in numerical integration. It is recommended to set REFERENCE_CORRECTION=1 to ensure that the path length is corrected. Optionally, setting REFERENCE_CORRECTION=2 would instead correct residual transverse trajectory errors. Using REFERENCE_CORRECTION=3 corrects both types of error.

Edge angles and edge effects

The user may specify edge multipoles using the EDGE_MULTIPOLE parameter. In addition, the CCBEND element supports two fringe models, selected via the FRINGEMODEL parameter, which may have a value of 0 (default) or 1.

• — The default edge angle treatment in CCBEND is relatively simple, consisting of a vertical focusing effect with momentum dependence to all orders. Also included are edge pseudo-sextupoles (due to the body K₁ term) and pseudo-octupoles (due to the body K₂ term).
• — This model is based on theoretical work and code by R. Lindberg, and includes soft-fringe effects via a series of fringe integrals. The integrals can be computed with the companion program straightDipoleFringeCalc from a generalized gradient expansion (GGE). The GGE can be created using either computeCBGGE (for cylindrical-boundary data) or computeRBGGE for (rectangular-boundary data). There is an example in the elegant examples collection.

Multipole errors

Multipole errors are specified for the body and edge in the same fashion as for the KQUAD element. The reference is the dipole field by default, but this may be changed using the REFERENCE_ORDER parameter.

Radiation effects

If SYNCH_RAD is non-zero, classical synchrotron radiation is included in tracking. Incoherent synchrotron radiation, when requested with ISR=1, normally uses gaussian distributions for the excitation of the electrons. (To exclude ISR for single-particle tracking, set ISR1PART=0.) Setting USE_RAD_DIST=1 invokes a more sophisticated algorithm that uses correct statistics for the photon energy and number distributions. In addition, if USE_RAD_DIST=1 one may also set ADD_OPENING_ANGLE=1, which includes the photon angular distribution when computing the effect on the emitting electron.

If SYNCH_RAD and SR_IN_ORDINARY_MATRIX are non-zero, classical synchrotron radiation will be included in the ordinary matrix (e.g., for twiss_output and matrix_output). Symplecticity is not assured, but the results may be interesting nonetheless. A more rigorous approach is to use moments_output. SR_IN_ORDINARY_MATRIX does not affect tracking.

Adding errors

When adding errors, care should be taken to choose the right parameters. The FSE, FSE_DIPOLE, FSE_QUADRUPOLE, ETILT, EPITCH, and YAW, DX, DY, and DZ parameters are used for assigning errors to the strength and alignment relative to the ideal values given by ANGLE and TILT. One can also assign errors to ANGLE and TILT, but this has a different meaning: in this case, one is assigning errors to the survey itself. The reference beam path changes, so there is no orbit/trajectory error. Note that when adding errors to FSE, the error is assumed to come from the power supply, which means that multipole strengths also change.

Assigning errors to K1 is also possible, but is not the best approach, since it changes the internal reference trajectory calculation for the element.

Splitting dipoles

The CCBEND element does not support splitting. Important: Users should not attempt to split CCBEND elements by hand, since this will not result in the correct geometry entering and exiting the various parts.

Matrix generation

elegant will use tracking to determine the transport matrix for CCBEND 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.