A revised version of the Projected Range ALgorithm with numerical solutions

In a previous paper a revised version of the Projected Range ALgorithm (PRAL) was presented. These new equations, called the Kent Range ALgorithm (KRAL), consider fully the motion of the ion in three dimensions. In the current paper we review a simple derivation of the KRAL equations starting from the standard LSS integral equations for moments of the range distribution. The resulting 2nd order ordinary differential equations are difficult to solve using classical numerical techniques. We present a modified set of equations called the Kent Optimised Range ALgorithm (KORAL) which is designed for iterative solution. Finally, we compare results from KORAL and 1st and 2nd order PRAL codes with Monte Carlo data from a TRIM code modified to treat targets of infinite extent. Comparisons are performed using consistent nuclear and electronic energy loss models.