Ideas on Tune Measurement in EMMA FFAG ring J. Pasternak, Imperial College, London / RAL STFC

1. Ideas on Tune Measurement in EMMA FFAG ring J. Pasternak, Imperial College, London / RAL STFC J. Pasternak

2. Outline • Introduction • Assumptions • Methodology • Some results • Summary and future plans J. Pasternak

3. Introduction • Tune – „number of betatron oscillation per turn” - is usually measured • taking data on many turns. • EMMA – first nonscaling FFAG machine. • In nonscaling FFAGs beam makes only a few turns (5-15). • We should be able to measure the optical parameters (tune, betas) • during this time! • If you have many BPMs (as in the case for EMMA) you can measure • phase advances, betas etc. even in the linac! J. Pasternak

4. Assumptions • In the ordinary synchrotron you take many turns in the single • BPM and make Fourier analysis of the data – it is almost a definition. • Decoherence is very fast in EMMA (a few turns). • Taking data over many turns is almost impossible in EMMA! • EMMA is a very symmetric machine (42 cells), but can we use it? • In this talk I will try not to use it! • Let’s assume we have injected beam, measured the orbit, • made the orbit correction (may be no perfectly?). J. Pasternak

5. Methodology (1) • We have many BPMs in EMMA (more than 80!). • We have injected the beam and measured the • BPM signal in ith BPM is given by the following formula: BPM systematic error BPM reading - Initial phase (it can be different for every shot) Phase advance „amplification factor” J. Pasternak

6. Methodology (2) • Number of variables for every BPM used: • (Ai, µi, δi) + µ0s +x0s – initial phase, different for every shot. • It seems, we need at least 4 turns in EMMA! • Equivalently we can take 4 (or more) independent shots (injections) • and store one turn date 4 (or more) times with different injection conditions. • In order to understand our machine we construct: BPM noise J. Pasternak

7. Methodology (3) • Now we need to find (Ai, µi, δi) + µ0s +x0s , which minimize • the merit function. • We can use various methodes and algorithms • (least squares, Minuit, SVD, others). • We may invest some time to search for the best method • for the EMMA case (SVD?)! • We can make the software in Python, Mathematica, ROOT • (please let us know). J. Pasternak

8. First tests • Test is performed on the candidate lattice for nonscaling PRISM. • The EMMA lattice test is in preparation (no electron tracking • in BeamOptics till now). • We can have FFAG tracking in Mathematica. Zgoubi/BeamOptics comparison in muon FFAG J. Pasternak

9. First look at Non-Scaling Design Short Drift 0.376 m Short Drift 0.376 m Long Drift 1.1 m Long Drift 1.1 m F Quad, 0.376 m B from -0.07 to 0.1 T Defocusing RBend, 0.376 m B from 0.34 to 0.31 T • Some parameters: • Lattice Symmetric FDF triplet • N 10 • p0 68 MeV/c • Circunference 40.84 m • (QH, QV)/cell at p0 (0.276, 0.189) • Drif length 2.2 m J. Pasternak

10. Tunes Tune/cell QH QV MeV/c • Chromaticity is relatively flat in horizontal plane. • Vertical tune excursion is large – edge focusing. • Tunes cross – potential problem! J. Pasternak

11. Tune per cell for 10 cells in PRISM lattive Without BPM noise With BPM noise J. Pasternak

12. Summary and future plans • 7 BPM Fourier analysis by Shinji may turn out to be better in EMMA! • We still need an independent test without assuming the symmetry of • the ring. • We still need to work a lot on understanding the procedure. • We need to have the working system soon! J. Pasternak