Verify FWHM values for numerically generated distributions

[elenafuengar]

Currently, BIHC generates the different bunch profiles using the bunch length input by the user. However in practice, the bunch length is computed (i.e. in the BQM) as the FWHM value for the measured distribution.

One can analytically compute the equivalent sigma (as done by C. Zannini in the past) to use for different bunch profiles so that the distribution shape match the FWHM value. This would be, in principle, closer to reality.

Same bunch length	Modified bunch length to match FWHM

The bunch length factors found analytically for the cos2 and parabolic distributions are available on the slide. We can reproduce this in BIHC:

Same bunch length	Modified bunch length to match FWHM

However, the bunch length factors for the Binomial and the q-Gaussian are dependent on the exponent and q-value, respectively. One needs to analytically calculate them in order to follow this equivalent bunch length approach for all distributions.

Here is the link to Carlo Zannini's presentation:
https://www.slideserve.com/matteo/mke-heating-with-and-without-serigraphy-powerpoint-ppt-presentation

[elenafuengar]

Furthermore, comparison of impact in the power loss:

• Narrow band resonator impedance:

Same bunch length	Modified bunch length to match FWHM

• Broadband resonator impedance:

Same bunch length	Modified bunch length to match FWHM