summarized in Table 7. Note that the current ramp will follow some curve outside these regions in order to make sure that the revolution harmonics do not land on the fundamental or HOM resonances. Booster breakpoint Maximum dI/dt (kA/s) Maximum inductive voltage Injection 16 80 Transition 17 70 Extraction 1 3 Table : Maximum parameters in the three Booster break points. Coil heating and cooling requirements The coils will need to be cooled because heat will be generated by the current ramp. Using the fictitious ramp shown in in Figure 74, the power loss in the windings is 4.1 kW (derived below). This is a lot of power and so cooling of the windings is imperative. The exact current ramp need only be known in the three regions shown in Figure 73. The current outside these regions will be determined operationally to keep the revolution harmonics of the beam outside the fundamental and the HOM resonances. A fictitious current ramp shown in Figure 74 models the required ramp with sufficient precision for our thermal analysis. The fictitious current ramp starts from 139 A at injection and rises linearly in 20 ms to 592 A. It stays constant until ms before linearly ramping down to 139 A. The rms current,, for this ramp is simply (14) where is the current pulse shown in Figure 74. The resistance of the coils is the sum of the resistances in series from Table 6 and is m. Thus, the rms power, , deposited in the coils from the fictitious ramp is (15)
summarized in Table 7. Note that the current ramp will follow some curve outside these regions in order to make sure that the revolution harmonics do not land on the fundamental or HOM resonances. Booster breakpoint Maximum dI/dt (kA/s) Maximum inductive voltage Injection 16 80 Transition 17 70 Extraction 1 3 Table : Maximum parameters in the three Booster break points. Coil heating and cooling requirements The coils will need to be cooled because heat will be generated by the current ramp. Using the fictitious ramp shown in in Figure 74, the power loss in the windings is 4.1 kW (derived below). This is a lot of power and so cooling of the windings is imperative. The exact current ramp need only be known in the three regions shown in Figure 73. The current outside these regions will be determined operationally to keep the revolution harmonics of the beam outside the fundamental and the HOM resonances. A fictitious current ramp shown in Figure 74 models the required ramp with sufficient precision for our thermal analysis. The fictitious current ramp starts from 139 A at injection and rises linearly in 20 ms to 592 A. It stays constant until ms before linearly ramping down to 139 A. The rms current,, for this ramp is simply (14) where is the current pulse shown in Figure 74. The resistance of the coils is the sum of the resistances in series from Table 6 and is m. Thus, the rms power, , deposited in the coils from the fictitious ramp is (15)