Choosing Rayleigh Length of Input Radiation to an Undulator

[Brodysseus]

This isn't a homework question but the professor asked us why someone would choose to set the Rayleigh length of input radiation into an undulator to be the length of the undulator, instead of setting it to be half the undulator's length like normal. The best reason I could come up with is that they didn't want the radiation energy spread to be very large, but that seems too simplistic.

This is for a class on synchrotron radiation and free electron lasers, and we were talking about the gain in electromagnetic energy.

 

[Nate810]

Setting the Rayleigh length of input radiation to the same length as the undulator will maximize the gain in electromagnetic energy, since the input radiation will be focused on one spot and not spread out over a large area. This will also provide a more stable output pulse, since the radiation will not have time to diverge due to the short distance between the input radiation and the undulator. Additionally, having the Rayleigh length set to the undulator's length will reduce the amount of time required to reach the maximum gain since the input radiation will not have to travel any further than necessary.