Deformed quadrupole magnets for big-acceptance spectrometer

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In order to design a big-acceptance magnetic spectrometer, we often have to utilize deformed quadrupole magnets. In present research, we treated quadrupole magnets whose bore are tapered along the symmetry axis. We tried to find a suitable trial function to express the magnetic field distribution with as small number of parameters as possible.With the three-dimensional magnetic field calculating program TOSCA, we calculated the field distribution for 60 cases of the geometry and the electric current (3 cases of length, 5 cases of the bore taper, 4 cases of current). 294 data points in the region of interest for each case were compared with the trial function.In the case of the fixed-bore (ordinary) quadrupole magnets, 7 length-independent parameters were extracted by the fit to 882 data point of 3 cases of length.In the case of the tapered-bore (deformed) quadrupole magnets, 10 parameters were necessary to reproduce the 4410 data points of 3 lengths and 5 tapers. Because the parameters are independent not only of the lengths, but also of the tapers, we can reproduce the field distributions of arbitrary lengths and tapers. We were able to extract the current-independent parameters by fitting to 17640 data points of 3 lengths, 5 tapers and 4 currents although the standard deviation became 2 times bigger than the fixed-bore case.