1. An inverse treatment planning method for intensity modulated particle therapy for the treatment of a target within a biological system using at least two fields, each field comprising a plurality of Bragg peaks, the at least two fields being planned to place a defined number of beam spots j from different directions with certain weights w j within the target, wherein the inverse treatment planning method optimizes the weights w j of the beam spots for the at least two fields simultaneously in order to produce a prescribed biological effect within the target by minimizing an objective function based on biological effects ε, the biological effects ε being treated in a linear-quadratic model which describes the biological effects in the target by two parameters α and β, where ε=αD+βD 2 , D denoting a dose, and wherein the two parameters α and β for each voxel i of the target α i and β i are calculated as dose-averaged mean values of α i,j - and √{square root over (β i,j )}-components, which relate to all beam spots j contributing to a total dose D i in the voxel i, wherein the two parameters α and β for each voxel i of the target (α i and β i ) are calculated as dose-averaged mean values of the form α i = 1 D i ⁢ ∑ j = 1 N ⁢ w j ⁢ D i , j ⁢ α i , j ⁢ ⁢ and β i = 1 D i ⁢ ∑ j = 1 N ⁢ w j ⁢ D i , j ⁢ β i , j for D i >0, D i = ∑ j = 1 N ⁢ w j ⁢ D i , j with N beam spots contributing to the total dose D j in voxel i.