*x*corresponds to the vertical direction, while

*y*refers to the horizontal direction

determination_of_angles_and_momentum

**This is an old revision of the document!**

The optical coordinates used in the S800 are described in relation to a central trajectory passing through the center of the S800 magnets, and with the reference momentum given by *p _{0}=qBρ_{0}*, where

With the exception of the sextupole in front of the S800 spectrograph and the trim coils, the aberrations—introduced mostly by the fringe fields of the magnets—are calculated and corrected analytically based on measured field maps. This method ^{2)}) uses the ion optics code COSY Infinity ^{3)} to calculate the transfer matrix *S* from the target to the focal plane, including aberrations up to 5^{th} order. The precision attained with the 5^{th} order is comparable to the resolution of the position-sensitive detectors in the focal plane. The tracking algorithm inverts the matrix *S* before applying it to the coordinates measured at the focal plane on an event-by-event fashion, according to the equation *(a _{t} y_{t} b_{t} d_{t}) = S^{-1} (x_{f} a_{f} y_{f} b_{f})*. The subindexes

Since the energy coordinate *d* is one of the quantities deduced from the inverse map, the beam position x_{t} cannot be calculated and is assumed to be zero. This assumption implies that the final resolution is obtained by folding the finite size of the beam spot in that direction with the size obtained from the reconstruction, itself depending on the detector resolution and the order to which the calculation is performed. Note that this is still the case when the S800 is operated in dispersion-matched mode, where the incoming beam is momentum dispersed—and therefore rather large—on the target. In that case it is the size at the object location that matters since the entire S800 (analysis line + spectrograph) is achromatic. Because the shapes of the fringe fields vary significantly with the absolute strength of the magnets, inverse maps need to be calculated for each magnetic-rigidity setting of the spectrograph. The inverse transfer maps can be calculated online from the currents of the S800 dipoles and quadrupole doublet, magnetic rigidity, and the particle (A,Z) are necessary. The process takes about 20 seconds.

Note that since the S800 bending dipoles are oriented vertically, the coordinate *x* corresponds to the vertical direction, while *y* refers to the horizontal direction

M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, and A. F. Zeller, Phys. Rev. C 47, 537 (1993

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determination_of_angles_and_momentum.1387894425.txt.gz · Last modified: 2013/12/24 09:13 by pereira