Lattice function measurement with TBT BPM data

At Fermilab Main Ring some of the Beam Position Monitors (BPM) are instrumented with Turn-By-Turn (TBT) capability to record up to 1,024 consecutive turns of BPM data for each given trigger. For example, there are 9 horizontal plane and 8 vertical plane BPM`s in the sector D3 and D4. The BPM data, which records the betatron oscillation, is fitted to obtain beam parameters x, x{prime}, y, y{prime}, and {Delta}p/p, using the calculated beam line transfer matrix. The resulted TBT beam parameters (x, x{prime}) or (y, y{prime}) are fitted to ellipses to obtain the lattice function {beta}, {alpha}, and the emittance associated with the betatron oscillation. The tune of the machine can be calculated from the phase space angles of the successive turns, in the normalized phase space. The beam parameters can also be used to extract transfer matrix to be used for local and global coupling analysis. The process of fitting the BPM data produces information that can be used to diagnose problems such as calibration, noise level and polarity. Being available at every turn and at changing beam position the information carries a lot of statistical power. Since most of the BPM`s are located at high beta location only the x and y beam position information is not simultaneously available. The BPM data fitting processing essentially bridged the gap