Effects of correlations between particle longitudinal positions and transverse plane on bunch length measurement: A case study on GBS electron LINAC at ELI-NP

In high-brightness LINear ACcelerators (LINACs), electron bunch length can be measured indirectly by a radio frequency deflector (RFD). In this paper, the accuracy loss arising from non-negligible correlations between particle longitudinal positions and the transverse plane (in particular the vertical one) at RFD entrance is analytically assessed. Theoretical predictions are compared with simulation results, obtained by means of ELEctron Generation ANd Tracking (ELEGANT) code, in the case study of the gamma beam system (GBS) at the extreme light infrastructure-nuclear physics (ELI-NP). In particular, the relative error affecting the bunch length measurement, for bunches characterized by both energy chirp and fixed correlation coefficients between longitudinal particle positions and the vertical plane, is reported. Moreover, the relative error versus the correlation coefficients is shown for fixed RFD phase 0 rad and π rad. The relationship between relative error and correlations factors can help the decision of using the bunch length measurement technique with one or two vertical spot size measurements in order to cancel the correlations contribution. In the case of the GBS electron LINAC, the misalignment of one of the quadrupoles before the RFD between -2 mm and 2 mm leads to a relative error less than 5%. The misalignment of the first C-band accelerating section between -2 mm and 2 mm could lead to a relative error up to 10%.