10.10 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.

This element provides a symplectic straight-pole, bending magnet with the exact Hamiltonian in Cartesian coordinates. The quadrupole, sextupole, and other multipole terms are defined in Cartesian coordinates. The magnet at present is restricted to having rectangular ends with symmetric entry and exit. 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, and ETILT) set to zero.

Edge angles and edge effects

The 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). The user may also specify edge multipoles using the EDGE_MULTIPOLE parameter.

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

Incoherent synchrotron radiation, when requested with ISR=1, normally uses gaussian distributions for the excitation of the electrons. 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.

Adding errors

When adding errors, care should be taken to choose the right parameters. The FSE and ETILT 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. The most common thing is to assign errors to FSE and ETILT. Note that when adding errors to FSE, the error is assumed to come from the power supply, which means that multipole strengths also change.

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.