Cogging in the Fermilab Booster∗

The Fermilab Booster is a rapid-cycling synchrotron which accelerates 84 bunches of protons from 401 MeV to 8 GeV for injection into the Fermilab Main Injector. The entire circumference, ie., all RF buckets, of the Booster is filled. At extraction, a kicker deflects the beam into the extraction channel. The kicker risetime is long enough so that several of the bunches do not receive the full kick and are deflected instead into Booster magnets, creating radioactive components in the tunnel and radiation at ground level outside. At future Booster intensities and repetition rates, the radiation levels will be unacceptably high. One way of reducing these losses is to create a “notch” of several consecutive unfilled RF buckets. If the beam can be accelerated while tracking and controlling the position of the notch so that the unfilled buckets are aligned with the rising edge of the extraction kicker, losses will be eliminated. We have studied this process and developed an algorithm to count and control RF cycles during the Booster ramp and move (“cog”) the notch longitudinally so that it is aligned with the kicker at extraction time. We will describe the relevant parts of the Booster hardware, measurements we have made to understand what controls the total number of RF cycles during a Booster ramp, and the algorithm we intend to use for cogging during the Booster cycle. 1 BOOSTER PARAMETERS When the Fermilab Main Injector is in full operation, the Booster must deliver its batch of 84 bunches to a specified RF bucket in the Main Injector. In addition, the notch in the beam must be located at the Booster kickers when they fire. In order to move the notch to the proper location, we must be able to predict the total number of RF cycles in a Booster pulse to within a multiple of 84, the Booster harmonic number. Cogging is done by adding a radial offset to the beam, changing the revolution frequency, to add or subtract the necessary number of RF cycles. This technique has been used routinely at Fermilab in the Main Ring and Tevatron but in these accelerators cogging is done at flattop, ie., at a time when the RF frequency is constant. Cogging in the Booster is more complicated because there is no flattop. In addition, the shape of the Booster ramp (number of RF cycles) changes from pulse to pulse in ways which we do not completely understand. The Booster design ramp is a 15 Hz. sinusoidal ramp in which the gradient magnets ramp at a “15 Hz.” rate determined from the power line frequency. In principle, this ∗Work supported in part by the Department of Energy. † Email: [email protected] Figure 1: Integral cogging for a 1 mm. radial offset. The horizontal axis is in Main Injector marker units. There are roughly 3000 Main Injector revolutions in a single Booster pulse. enables us to calculate the RF ramp exactly. However, the power line frequency is not exactly 60 Hz. but fluctuates by ±30 mHz. A 30 mHz. difference in the line frequency causes a change of about 80 RF cycles from the ideal ramp. One could try to correct for variations in the line frequency by measuring the instantaneous frequency and calculating the change in the ramp, but it is not clear that the calculations could be done in real time. Changes in the radial position of a few mms. over the pulse also effect the number of RF cycles by roughly the same amount. Finally, there may be synchronization differences between the start of the magnet ramp and the start of the RF ramp, adding or subtracting hundreds of RF cycles to a pulse. The Booster harmonic number is 84 so moving the notch to an arbitrary location at extraction requires cogging by ±42 RF buckets. Fig. 1 is a plot of the number or RF buckets cogged for a 1 mm. radial offset whose sign is reversed at transition. The horizontal axis is in Main Injector Marker units where 1 unit represents about 11 μsec., the Main Injector revolution time. Several important features are apparent from this plot. It is “easiest” to cog from about MI markers 200 to 800 (about 2 msec. to 8 msec. in time) in the cycle when the number of buckets cogged/radial offset is maximum. Conversely, the amount of cogging that can be done at the end of the cycle is very small. Of course, there is also 0-7803-5573-3/99/$10.00@1999 IEEE. 1091 Proceedings of the 1999 Particle Accelerator Conference, New York, 1999