Thorsten Hellert studies on orbit response at FLASH Doktorand_innenseminar, 19.08.2011

table of contents motivation linear beam dynamics response matrix measurements simulation conclusion

motivation Linear Optics from Closed Orbits (LOCO) was written for NSLS to fit e.g. Imagnets, BPM gain, steerer gain, BPM displacement ... (1) today LOCO is used in over 30 storage rings (e.g. Petra III) can „LOOO“ be used to understand FLASH optics?

linear beam dynamics

linear beam dynamics transfer matrices

response matrix x s0 s1 beam s

response matrix x s0 s1 s

response matrix measurement x kick BPM s0 s1 s

response matrix measurement kick BPM 1 BPM 2 Θ1 s Θ x Θ1 BPM 1 BPM 2 x dΘ Θ1 dx dx Θ dΘ

measurements one BPM Δx in mm ΔΘ in rad

measurements one BPM Δx in mm ΔΘ in rad

measurements all BPMs systematic mismatch? Orbit response in mm/mrad wrong BPM gain? cross-wired BPM? s in m

simulation formalism Χ2 < 1 Χ2 > 1 find (a1 ... ak) that minimizes χ2

simulation SVD singular value decomposition (SVD) y‘ x‘ y y‘ y δy‘ δx‘ value of interest: δ σx' ≈ 10% σy' ≈ 90% x‘ σx ≈ 45% σy ≈ 55% σtotal ≈ σy‘

simulation numbers of interest mathematical goodness of fit physical goodness of fit

simulation | ΔIsim | number of iteration 'Q1.1UBC2‘ 'Q1.2UBC2‘

simulation | ΔIsim | number of iteration

noise: 1 | ΔIsim | noise: 0 number of iteration

simulation | ΔIsim | number of iteration

improvement of ≈10 after 3 steps

simulation

measurements all BPMs 61 quads changed by < 2% Orbit response in mm/mrad 61 quads changed by < 2% 4 ACCs changed by < 1% errors: 1mm/mrad noise: 1 mm/mrad s in m

conclusion to many free parameters to fit find „golden“ BPMs and steerers precise knowledge of machine is required χ2 is not meaningfull need more physics for algorithm no closed orbit solutions single shot maybe FLASH data is to disturbed for „LOOO“

thanks thanks for your attention

appendix +++ quad sensitivities

appendix +++ simulation +++ a=0,05

appendix +++ simulation +++ a=0,05

appendix +++ measurements +++ bad one!

simulation mean( | ΔIsim | ) number of iteration