| With the exception of the [[Magnets#Spectrograph Sextupole|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 ((M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, and A. F. Zeller, Phys. Rev. C 47, 537 (1993))) uses the ion optics code COSY Infinity ((Ref)) to calculate the transfer matrix //S// from the target to the focal plane, including aberrations up to 5<sup>th</sup> order. The precision attained with the 5<sup>th</sup> 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<sub>t</sub> y<sub>t</sub> b<sub>t</sub> d<sub>t</sub>) = S<sup>-1</sup> (x<sub>f</sub> a<sub>f</sub> y<sub>f</sub> b<sub>f</sub>)//. The subindexes //t// and //f// refer to the positions behind the target and at the focal plane, respectively. The positions measured with the two [[Detectors#Cathode Readout Drift Chambers (CRDC)|CRDCs]] are used to determine the position //x<sub>f</sub>// and //y<sub>f</sub>//, and angles //a<sub>f</sub>// and //b<sub>f</sub>// at the focal plane. The main advantage of this method is the fast processing of the data as it avoids the tracking of each individual particle in the magnetic fields of the spectrograph. The standard S800 [[SpecTcl]] analysis software provides all necessary functions and interfaces to perform these calculations. | With the exception of the [[Magnets#Spectrograph Sextupole|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 ((M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, and A. F. Zeller, Phys. Rev. C 47, 537 (1993))) uses the ion optics code [[http://www.bt.pa.msu.edu/index_cosy.htm|COSY Infinity]] to calculate the transfer matrix //S// from the target to the focal plane, including aberrations up to 5<sup>th</sup> order. The precision attained with the 5<sup>th</sup> 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<sub>t</sub> y<sub>t</sub> b<sub>t</sub> d<sub>t</sub>) = S<sup>-1</sup> (x<sub>f</sub> a<sub>f</sub> y<sub>f</sub> b<sub>f</sub>)//. The subindexes //t// and //f// refer to the positions behind the target and at the focal plane, respectively. The positions measured with the two [[Detectors#Cathode Readout Drift Chambers (CRDC)|CRDCs]] are used to determine the position //x<sub>f</sub>// and //y<sub>f</sub>//, and angles //a<sub>f</sub>// and //b<sub>f</sub>// at the focal plane. The main advantage of this method is the fast processing of the data as it avoids the tracking of each individual particle in the magnetic fields of the spectrograph. The standard [[S800 SpecTcl|S800 SpecTcl]] analysis software provides all necessary functions and interfaces to perform these calculations. |
