10.108 SREFFECTS—Lumped simulation of synchrotron radiation effects (damping and quantum excitation) for rings.

Lumped simulation of synchrotron radiation effects (damping and quantum excitation) for rings.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no

This element is intended for storage ring modeling only and provides a fast alternative to element-by-element modeling of synchrotron radiation. It should be used with care because the results will not necessarily be self-consistent. This is particularly an issue when there is dispersion at the location of the SREFFECTS element.

There are several types of storage ring simulation in which one may want to use this element:

• Simulation of instabilities or other dynamics where radiation damping or quantum excitation is important.
• Simulation of dynamics with an rf cavity when the synchronous phase is significantly different from 180 degrees, so that average radiation losses must be included.
• Computation of dynamic and momentum aperture in the presence of radiation damping.

The major parameters (JX, JY, EXREF, SDELTAREF, DDELTAREF, and PREF) can be supplied explicitly by the user, or filled in by elegant if the twiss_output command is given with radiation_integrals=1.

In explicit initialization, the user supplies the quantities EXREF, EYREF, SDELTAREF, DDELTAREF, and PREF. These are, respectively, the reference values for the x-plane emittance, y-plane emittance, fractional momentum spread, energy loss per turn, and momentum. The first four values pertain to the reference momentum. JX, JY, and JDELTA may also be given, although the defaults work for typical lattices.

In automatic initialization, the user turns on the radiation integral feature in twiss_output, causing elegant to automatically compute the above quantities. This will occur only if PREF=0. The COUPLING parameter can be used to change the partitioning of quantum excitation between the horizontal and vertical planes. Because the radiation integrals computation in twiss_output pertains to the horizontal plane only, the user must supply either EYREF or COUPLING if non-zero vertical emittance is desired.

The user may elect to turn off some aspects of the synchrotron radiation model. These should be changed from the default values with care!

• DAMPING — Default is 1. If set to 0, then no radiation damping effects will be included. More precisely, it is equivalent to setting JX=JY=JDELTA=1. Damping still occurs at any rf cavities (since elegant works in trace space).
• QEXCITATION — Default is 1. If set to 0, then no quantum excitation effects are included, which is to say that all particles will experience the same perturbation.
• LOSSES — Default is 1. If set to 0, no average energy losses are included.

There are a number of caveats that must be observed when using this element.

1. If there is dispersion at the location of the SREFFECTS element, the closed orbit will change because of the average momentum change, but it will disagree with tracking results. The reason is that in tracking SREFFECTS must displace the beam to the new equilibrium orbit, because otherwise there will be additional betatron motion excited and the wrong equilibrium emittance will be obtained. (Since the SREFFECTS element is already adding the betatron motion excitation for the entire ring, elegant is forced to offset each particle by Δδ to suppress any additional excitation.)

   This issue can be resolved by placing the SREFFECTS element next to the rf cavity and setting INCLUDE_OFFSETS=0. Since the average momentum change is zero from the two elements, no additional betatron motion will be generated. Optionally, one can also use many SREFFECTS elements at equivalent locations in the lattice, which will decrease the magnitude of the effect.

2. When used for dynamic aperture and momentum aperture determination, one should set QEXCITATION=0. Putting the rf cavity (if any) right next to the SREFFECTS element is a good idea to avoid spurious excitation of betatron motion.
3. Nothing prevents including this element in a lattice when doing frequency map analysis, although it probably doesn’t make any sense. Only the average energy loss per turn will be included. Again, putting an rf cavity right after SREFFECTS is a good idea.
4. In versions 19.0 and later, elegant includes the effect of SREFFECTS on the closed orbit. This presents a dilemna when automatic initialization is used, because in order to perform automatic initialization, elegant has to compute the optics functions. However, it must determine the closed orbit to compute the optics functions. The solution to this is for the user to pre-compute the twiss parameters and radiation integrals using twiss_output with output_at_each_step=0. The user is free to subsequently give twiss_output with output_at_each_step=1 to obtain the results on the closed orbit.
5. Computation of Twiss parameters does not fully include the effects of synchrotron radiation losses when these are imposed using SREFFECTS elements. If PREF=0 (automatic initialization), these effects are completely missing. If PREF is non-zero, then elegant will use the DDELTAREF parameter to compute the energy offset from the element, and thus its effect on the beam trajectory.