Experimental validation for the compensation method of nonlinearities in periodic magnets

Nonlinearities from any periodic magnet in accelerators may strongly degrade the dynamics of the beams. This may be especially critical for magnets where the beam excursions are comparable to the good field region, as for example in wigglers, since the beam trajectory can be of the order of the pole width. A general method based on alternately shifting the magnetic axis of each pole to compensate this effect was proposed and applied to the $\mathrm{DA}\mathrm{\Phi }\mathrm{NE}$ wigglers, where an important integrated octupole was measured. This approach has been optimized by multipolar analyses and the effect on the beam dynamics verified by tracking studies. In this paper we report about the experimental validation of the magnetic model and the verification of the method by beam based measurements. The latter were performed after all the wigglers in the $\mathrm{DA}\mathrm{\Phi }\mathrm{NE}$ main rings had been modified according to the optimal configuration. These measurements were in agreement with the expectations and allowed experimentally proving the method.

Figure 1

Schematic top view of the wiggler. The terminal (HC) and the central (FC) coils are indicated in red and in blue respectively. The reference trajectory $x_T$ is also indicated in black.

Figure 2

Simulated $I_3^T$ as a function of the shift of the magnetic axis position.

Figure 3

Simulated $b_3^T$ along the longitudinal position for the optimal case of $\pm 7.3\mathrm{mm}$ axis shift.

Figure 4

Simulated exit angle and position as a function of the entrance shift $\mathrm{\Delta }x$ with respect to the reference trajectory before (aligned) and after (shifted) the modification.

Figure 5

Top view of the bottom half of the spare wiggler during the modification.

Figure 6

Measured vertical component of the magnetic field of the modified wiggler compared to the simulations at the center of the wiggler in the midplane.

Figure 7

Coefficients of the field expansion calculated from the measured field map on the spare wiggler after the modification and comparison with the simulation expectations (fourth order polynomial fit applied in a range of $\pm 4\mathrm{cm}$ around the reference beam trajectory).

Figure 8

Exit angle as a function of the orbit displacement at the entrance of the wiggler computed using the measured field maps after the modification. In the small graph the comparison with the aligned poles case (Before) is also shown. The results correspond to the first measured wigglers of the positrons (PL101, PS201, PS101) and electrons (EL201, ES101) ring.

Figure 9

Measured tune shift as a function of the closed orbit bump amplitude before (aligned poles) and after (shifted poles) the modification. For the case after the modification the line shows the predictions from the tracking analysis, for the case before the modification a polynomial fit to the experimental data is applied.