Orthogonal Correctors in ILC Main Linac

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Presentation transcript:

Orthogonal Correctors in ILC Main Linac Nikolay Solyak – Fermilab Sergey Glukhov – summer student, Novosibirsk State University

Previous works Proposed by P. Eliasson and D.Schulte at “CLIC Tuning Bump Strategies”, Daresbury LET face-to-face meeting, Jan. 2007 Daniel Schulte and Andrea Latina are working on similar BUMPS for ILC linac (this meeting) Our first look for ILC Main Linac

Correctors For a given seed the final beam after BBA can be represented by a vector where n - number of particles (11x11x9 in our case) The effect of knobs (correctors) can be represented by matrix (mx2n) where: si - contains the particle positions and angles at the end of the linac kj - contains changes in particle positions and angles for a unit change of knob j Matrix K is defined by lattice (independent of misalignment)

SVD To minimize final emittance for each seed s one should find a vector x of amplitudes of correctors, which minimize: Singular value decomposition (SVD) on K represents it as a product of orthogonal matrices U and V and diagonal matrix Ksvd: Then Column Ui is the weights of all correctors in j - th orthogonal bump. Vi - corresponding changes of particle coordinates and angle xj – amplitude of j – th orthogonal bump

Example: Straight ML Lattice Regular straight FODO lattice, 114 cells X/Y phase advance per cell = 75/60 8 cavities per cryomodule (CM) 4 CM per quadrupole (TESLA-like) Quadrupole package = BPM, quadrupole, Xcorr, Ycorr. Accelerating gradient = 31.5 GeV/m BPM resolution = 1 μm BPM offset wrt CM = 300 μm Quad offset wrt CM = 300 μm Quad roll angle wrt CM = 300 μrad Structure offset wrt CM = 300 μm Structure pitch wrt CM = 300 μrad CM offset wrt survey line = 200 μm CM pitch wrt survey line = 20 μm

Singular value of matrix K Zoom Singular values for all 100 seeds (some small difference caused by wakes):

Weights of real correctors in orthogonal correctors. Weights are the same for all seeds => Can be calculated for perfectly aligned lattice ones and later used for orthogonal correctors

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

Straight Linac, Regular Lattice Dispersion, Coupling, Wakefields

With wakefields turned off

With wakefields turned off (2)

Straight Linac, Regular Lattice Dispersion Only No Wakes, No coupling (Quad roll)

Straight Linac, Regular Lattice Dispersion Only

Straight Linac, Regular Lattice Dispersion Only

Straight Linac, Regular Lattice Dispersion Only

Straight Linac, Regular Lattice Dispersion Only

Straight Linac, Regular Lattice Dispersion Only

Straight Linac, Regular Lattice Dispersion Only

Summary and Plans Orthogonal correctors was implemented in Lucretia It works good in straight linac. Coupling and wakes cann’t be corrected. Future work: Perform the same study for irregular curved ILC ML lattice as for straight linac