1. I. Syratchev, structure team meeting, 19.09.2007 Re-circulation Re-visited I. Syratchev

2. I. Syratchev, structure team meeting, 19.09.2007 I. Syratchev April 1999 beam Load Ohmic Losses PETS Load Ohmic Losses Power divider beam  From PETS, A1 Structure Output, A2 Structure Input, A3 To RF Load, A4 Variable polarized power divider basics Traveling wave with re-circulation Circular waveguide with H11 mode beam RF

3. I. Syratchev, structure team meeting, 19.09.2007 Traveling wave (constant impedance) Q-factor 5000 at 12 GHz Traveling wave with re-circulation beam loading PETS (Structure input) PETS Structure input Structure output (Load) Structure output beam loading No beam Tf=31 ns α = 32.92 Loss=0.627 BL=0.234 Pg = 1.35 η norm =1.29 Tf=62 ns α = 28.25 Loss=0.393 BL=0.141 Pg = 1.224 η norm =0.955 # Example 1. Fixed input parameters: - Input power - Input cell - Beam pulse length - Back loop RF power losses – 0.95 We do change: -Structure length (losses and filling time) We do adjust for the max. efficiency for the case with recirculation: - Optimal divider angle - beam current Benchmarked with the similar TW case.

4. I. Syratchev, structure team meeting, 19.09.2007 Power gain = 1.35 Power gain = 1.76 # Example 2. T beam injection = 2x T filling T beam injection = 3x T filling # Example 3. Q= 2Q 0 Power gain = 1.43 # Example 4. The beam loading is not optimal. Divider angle is kept constant Power gain = 1.42 BL=BL OPT 0.85 To provide beam loading compensation, the ramp duration and beam injection time were adjusted: T ramp = 1.14 x T filling T injection = 2xT filling + 0.24xTfilling Power into the load  0 BL=BL OPT 1.15 Power gain = 1.265 T ramp = 0.87 x T filling T injection = 2xT filling - 0.22xTfilling Fixed PETS power TW TW + rec. To maintain the same gradient for the 15% reduced current, the PETS power should be reduced: TW: -3.6% TW + rec.: - 8.3%

5. I. Syratchev, structure team meeting, 19.09.2007 How to integrate into Alexej’s optimization: # 1. For any given structure the RF transmitting efficiency and filling time are calculated. #2. For the given current, the beam induced RF power at the structure output is defined. #3. The input RF power is then taken from Fig.1 : # 4. Calculate loaded gradient. If result < Target value, STOP! # 5. The RF pulse shape (amplitude) is constructed following: -Linear ramp = 2x Filling time (pp #1) -Flat top # 6. Flat top is adjusted then to the P/C or temperature, or… # 7. For the efficiency calculation: Efficiency = (Beam power/Input power/PR) x (Tflat/(Tflat+2xTfill)) where PR (PETS power reduction) is taken from Fig 2. following calculated losses in a structure (pp.#1) #8. Enjoy! Fig.1 Fig.2 TW versus TW + rec. for the fixed gradient and current. Data for the old 30 GHz CLIC structure called TDS TW TW + rec. TDS