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CODD system proposal |
The bucket frequency of the PS accelerator as a function of the field of the main bending magnet obeys the following formula (1):
| (1) |
| Rm | 70.0789 m | PS machine magnetic bending radius |
| R0 | 100.00 m | PS machine radius |
| c | 2.99792458e8 m/s | Lightspeed |
| mp | 1.672685e-27 kg | Proton mass |
| Q0 | 1.6021892e-19 C | Elementary charge |
| B | [T] | Magnetic field |
| h | Harmonic number |
The PS machine consists of 100 bending magnets and as many straight sections. That explains why the total machine radius is 100 m, while the magnetic bending radius is only 70 m. The maximum energy of the PS is limited to 26 GeV by the saturation of the bending magnets. This happens at about 1.2 T. The harmonic number gives the number of RF periods that fit in one revolution. Substitute h=1 to get the revolution frequency. Commonly used harmonic numbers are 7, 8 and 16.
Some beams start out at one harmonic, and then change on the fly to another. For example, beams for the LHC start at h=7, are split into three to run for a while at h=21, to be finally split into two, two times in a row, to end up at h=84. This is colloquially referred to as 'RF gymnastics'. This complicates the task of the trajectory measurement system, which must be able to follow a bunch of particles along the acceleration cycle.
The pages below are some musings about a trajectory measurement synchronisation system that should cleanly deal with RF gymnastics. (The present one doesn't.)