BBU threshold current study for 6 GeV beam in 12 GeV beamline setup Ilkyoung Shin and Byung C. Yunn JLAB-TN-09-004 January 12, 2009 1. Introduction The study of BBU threshold current is done for a 6 GeV beam in a 12 GeV beamline because the beam of 6 GeV will be still needed after 12 GeV upgrade. In this work, instead of 6 GeV, 6.6 GeV are considered to compare three beamline setups which are 3-pass 6.6 GeV, 5-pass 6.6 GeV, and 5-pass 11 GeV. 2. Assumption and simplification in simulations The same assumptions, simplification, and treatment as in TN-04-035 and TN-07-069 are used in the simulations. Two interesting quantities are Q l =10 7 and R/Q = 82.5 Ohms. Only 1874 MHz mode is excited in cavities. The 7-cell cavity cryomodules are located at the 21 st ~ 25 th zones in the North linac and the 46 th ~50 th zones in the South linac. The 1874 MHz mode is excited in the 7-cell cavities. Threshold currents are calculated when Q l = 10 7 and R/Q = 83 Ohms. Only the 7-cell cavities are exited with the 1874 MHz mode in each threshold calculation while the other cavities give energy gains without excitation of the HOMs. DBA arc optics are used. The total recirculation path length is 6554(6549, 6547, 6546) RF wavelengths for the 1 st (2 nd, 3 rd, 4 th ) pass of the CEBAF accelerator. 1
3. Two beamline setup for 6 GeV The 12 GeV nominal beamline setup is 5-pass 11 GeV, and each linac has a 1.1 GeV energy gain. On the other hand, the 5-pass 4 GeV setup has a 0.4 GeV energy gain in each linac. 3.1. 3-pass 6 GeV setup 3 passes of the electron beam goes through 6 linacs. If the nominal energy gain of 12 GeV setup, which is 1.1 GeV, is taken into account, the total energy gain is 6.6 GeV. (Energy gain during 3-pass) = (energy gain in a linac) χ (number of linacs during 3-pass) 6.6 GeV = 1.1 GeV χ 6 linacs In this study, 3-pass 6 GeV will beam 3-pass 6.6 GeV. 3.2. 5-pass 6 GeV setup The 60% version of 12 GeV setup is the 5-pass 6.6 GeV setup. The energy gain in linacs and injection energy are reduced to 60% of the 12 GeV setup values. Energy gain during 5 pass = energy gain of 12 GeV nominal setup χ 6.6 GeV = 11 GeV χ As above, 5-pass 6 GeV means 5-pass 6.6 GeV. 3.3. Injection energy Injection energy satisfies the equation (Injection energy) = χ (energy gain of a linac). By substituting the actual values into the formula, injection energies are obtained. Injection energy for 4 GeV setup = Injection energy for 12 GeV setup = χ 400 MeV = 45 MeV χ 1.1 GeV = 123 MeV 2
4. Simulation results 4.1. 3-pass 6.6 GeV Threshold current = 0.537 ma, Injection energy = 123 MeV Figure 1. 3 pass 6.6 GeV 4.2. 5-pass 6.6 GeV Threshold current 0.131 MeV, Injection energy = 73 MeV Figure 2. 5 pass 6.6 GeV 3
4.3. 5-pass 12 GeV This work is done in TN-08-069. Threshold current 0.219 ma, Injection energy 123 MeV Figure 3. 5 pass 12 GeV 5. Comparison of threshold currents with 3-pass and 5-pass setups The simulation results are summarized in the table. 3-pass 6.6 GeV 5-pass 6.6 GeV 5-pass 11 GeV Threshold current 0.537 ma 0.131 ma 0.219 ma Injection energy 123 MeV 73 MeV 123 MeV Table 1. Simulation results The threshold current for the 3-pass 6.6 GeV is greater than for the 5-pass 6.6 GeV. Let us compare the 5-pass 6.6 GeV with the 5-pass 12 GeV. As the beam energy is reduced from 11 GeV to 6.6 GeV, which is 60% reduction, the threshold current and injection energy are also decreased to approximately 60%. The threshold current is proportional to the injection energy while the number of pass is fixed. 4
6. Availability of the maximum current The maximum beam current is limited by the beam dump power. (Beam dump power) (maximum beam current) χ (maximum beam energy e) Applying the maximum beam dump power, 1 MW, to the formula gives 1 MW 0.151 ma χ 6.6 GeV e We have maximum beam current of 0.151 ma. The table below shows the maximum beam current and the threshold currents of the 6.6 GeV setup. Maximum beam current by beam dump power Threshold current for 3-pass 6.6 GeV Threshold current for 5-pass 6.6 GeV 0.151 ma 0.537 ma 0.131 ma Table 2. Comparison of threshold currents with maximum available beam current The maximum beam current is not available in the 5-pass 6.6 GeV setup because the threshold current, 0.131 ma, is less than the maximum beam current, 0.151 ma. Maximum beam current is available for the 3-pass 6.6 GeV setup. 7. Conclusions The threshold current for three setups are: 3-pass 6.6 GeV 5-pass 6.6 GeV 5-pass 11 GeV Threshold current 0.537 ma 0.131 ma 0.219 ma Table 3 Threshold current for three setups The threshold current is proportional to the injection energy at the same number of passes. Therefore, the threshold current for the 5-pass 6 GeV setup will be a factor of 0.55 for 5-pass 11 GeV setup. The maximum beam current is not available in the 5-pass 6.6 GeV setup. 8. Acknowledgement Thanks a lot to Ryan Bodenstein. 5