Orbit response matrix analysis to quantify skew quadrupole components in the ALS EPUs

The simulations were performed using LOCO for Matlab (James Safranek, Greg Portmann, Christoph Steier), which is programmed on top of the accelerator toolbox AT (Andrei Terebilo).

The orbit response matrizes were measured for five different conditions at 1.9 GeV:

  1. both EPUs open
  2. EPU4 at 14.9 mm gap, -12.5 mm phase; EPU 11 open
  3. EPU4 at 14.9 mm gap, +12.5 mm phase; EPU 11 open
  4. EPU11 at 15.67 mm gap, -12.5 mm phase; EPU 4 open
  5. EPU11 at 15.67 mm gap, +12.5 mm phase; EPU 4 open
The fit was carried out using 109 lattice parameters. 59 normal gradients (24 QF, 24 QD, 4 QFA, 6 QDA, 1 Bend) and 50 skew gradients (24 SF, 24 SD, EPU4, EPU11). The EPUs were modeled as long (1.85 m), homogenous skew quadrupoles. LOCO was iterated twice in each case and to save computation time, BPM coupling and corrector magnet tilt were NOT included in the fit. BPM 62 was excluded because of its cross talk between the horizontal and vertical plane.

The plot shows cases 2-5 with the results from case 1 (the baseline) subtracted. The vertical scale is the k-value in m^(-2), i.e. the gradient divided by B*rho. The blue bars indicate the results for EPU4, the red ones the results for EPU11.

Conclusion: The fit results for the skew quadrupole strength are very consistent with the measured variation of the vertical beamsize. The resolution of the fit is good enough, that it should be possible to localize which part of the EPU (ends, bulk, ...) are causing the effect. The measurements for both devices indicate that there is also a gap dependent skew term, which is stronger in sector 4, whereas the phase dependent skew term is stronger in sector 11.

We later measured orbit response matrizes for the sector 4 EPU for many additional shift parameters (every 5 mm). In addition, we modified the LOCO fit routine, as to split the EPU in 3 sections (first period, core and last period). The following plots show the results.

CSteier@lbl.gov