The invention comprises a method and apparatus for treating a tumor with positively charged particles, comprising the steps of: (1) transporting the positively charged particles sequentially from an accelerator, along a beam transport path, through a nozzle system, and along a treatment beam path and (2) while scanning the treatment beam path along each of a set of vectors for treating the tumor, on average for the set of vectors, intentionally deviating the treatment beam path from a current vector of the set of vectors off of the current vector by at least one-eighth of a treatment beam diameter at least once for every twenty movements of the treatment beam.