Numerical computation of arbitrary order transfer maps and reconstructive correction of aberrations in the large acceptance spectrometer MAGNEX

The large angular (∼50 msr) and momentum (∼20%) acceptance spectrometer MAGNEX is under construction at the South National Laboratories INFN. In the spectrometer, positions of ions in two planes near the focal plane and their vertical positions near the target are measured. The energy resolution of about 1000 is achieved due to the use of the reconstruction of trajectories and reconstructive correction of aberrations. Main features of the spectrometer ion optics are considered.A numerical method of calculation of an arbitrary order transfer map is proposed. In this method, a transfer map is calculated using, as input, initial and final coordinates of a set of rays in an ion-optical system. The rays start at the nods of a regular multi-dimensional mesh in the particle phase space. Rays of the set are chosen automatically according to the order and dimension of the map to be calculated. Final coordinates of the rays are calculated with a regular numerical integration. The proposed is, in fact, a general (ray tracing based) method of calculation of a transfer map, of any order and dimension, for an arbitrary ion-optical system. The method has been used for numerical simulations of the reconstructive correction of aberrations in the MAGNEX spectrometer. Simulation results are considered.A C++ class library has been developed to realize the proposed transfer map calculation method. Elementary operations with vectors and maps, both being C++ objects, are realized as C++ operator functions. The map order is defined by a user at the moment of initialization of the corresponding map object. Its maximum value is limited only by an available computer memory. Computational aspects of the method are discussed in brief. [Copyright &y& Elsevier]