turns. n=1,…,20000 Fig. 5b Normalized Fourier coefficient (blue), (red) for n=1,…,20000 turns for the s4 c4 beam loading factor (). χ=0.06 4. Numerical studies: bunching with linear RF ramp An upper limit can be derived from the simulations for different within the interval “” χ [0, and checking the gap between bunches. We conducted a series of experiments χmax], with 0.06, 0.04 and 0.02, with results shown in Fig. 6. χ=0.1, From now on all phase pictures, demonstrating longitudinal beam dynamics will include the plots of RF generator voltage (red solid), the beam loading voltage (brown solid) and the total resulting voltage (dashed green) with the dimensions shown on the right vertical scales. Fig. 6 after 20000 turns, for different beam loading factors [kV], corresponding to 10%, 6%, 4%, 2% from the design magnitude =425 [kV]. Fig.7 Normalized Fourier coefficients (blue), (red) for n=1,…,20000 and kV, s4 c4 corresponding to 10%, 6%, 4%, 2% from the design magnitude =425 kV. The values of and 0.02 () produce the acceptable quality of bunching. χ=0.04
n=1,…,20000 turns. Fig. 5b Normalized Fourier coefficient s4 (blue), c4 (red) for n=1,…,20000 turns for the beam loading factor χ=0.06 (). 4. Numerical studies: bunching with linear RF ramp An upper “” limit can be derived from the simulations for different χ within the interval [0, χmax], and checking the gap between bunches. We conducted a series of experiments with χ=0.1, 0.06, 0.04 and 0.02, with results shown in Fig. 6. From now on all phase pictures, demonstrating longitudinal beam dynamics will include the plots of RF generator voltage (red solid), the beam loading voltage (brown solid) and the total resulting voltage (dashed green) with the dimensions shown on the right vertical scales. Fig. 6 after 20000 turns, for different beam loading factors [kV], corresponding to 10%, 6%, 4%, 2% from the design magnitude =425 [kV]. Fig.7 Normalized Fourier coefficients s4 (blue), c4 (red) for n=1,…,20000 and kV, corresponding to 10%, 6%, 4%, 2% from the design magnitude =425 kV. The values of χ=0.04 and 0.02 () produce the acceptable quality of bunching.
BL_mu2e_preprint_draft.docx