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

Abstract

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%.

Enhancing particle bunch-length measurements based on Radio Frequency Deflector by the use of focusing elements

“…9 ), can be written as: Also in this case, Eq. 11 is a general expression of the formula found in 35 . In the case of conventional layout ( and ), Eqs.…”

“…7 and 8 , the calibration factor can be determined as: The Eq. 9 is a general form of the conventional expression of the calibration factor in 35 .…”

“…In the case of conventional layout ( and ), Eqs. 9 and 11 , provide the and the , respectively 35 , 36 . The terms due to the correlations can be canceled by averaging two measurements in phase opposition: The term is equal to in absence of correlations between the vertical and longitudinal planes.…”

“…including the variation of the centroid on the screen); (ii) the non-conventional layout does not introduce any deterministic error source in the measurement, (iii) the possibility of removing the correlation effects (i.e. ,and ) is preserved, by carrying out two different measurements of in phase opposition (at and ), and then evaluating the average between their squared values 35 , 36 , and (iv) thanks to the dependence of and on the focal length, these quantities can be optimized over a wider range of beam parameters.…”

“…In the case of conventional layout ( M 11 = 1 and M 12 = L ), Eqs. 9 and 11, provide the K CAL and the σ 2 y s,ON , respectively 35,36 . The terms due to the correlations can be canceled by averaging two measurements in phase opposition:…”