ABSTRACT

At the energies where MAGNEX should operate (0.5 - 8 MeV/u), straggling phenomena cannot be neglected and the effectiveness of the trajectory reconstruction algorithm could be seriously reduced if a careful shaping of the magnetic fields is not carried out. Indeed, in order to achieve a given momentum resolving power with the trajectory reconstmction algorithm, the effective image size at the focal surface should be less than the product of the dispersion and the given momentum resolution. Applying the standard formulas for the errors propagation, this requirement can be expressed by the following inequality:

(I) Note that the derivatives that appear in the left-hand side of Eq. (I) can be expressed as a function of the aberrations whereas the measurement errors depend both on the straggling effects and finite detector resolution. Such a coupling between the straggling, finite detector resolution and optical aberrations puts severe constraints on these latter once the former two cannot be reduced below certain practical limits. Consequently an appropriate approach [ 6] for the hardware minimisation of aberrations needs to be adopted.