Octopole correction of geometric aberrations for high-current heavy-ion fusion beams

It is noted that the success of heavy-ion fusion depends critically on the ability to focus heavy-ion beams to millimeter-size spots. Third-order geometric aberrations caused by fringe fields of the final focusing quadrupoles can significantly distort the focal spot size calculated by first-order theory. A method is presented for calculating the locations and strengths of the octopoles that are needed to correct these aberrations. It is shown, to a very good approximation, that in calculating the locations and strengths of the octopoles for high-current beams, the third-order contributions from space-charge force can be neglected. Thus, the procedure becomes almost identical to the treatment for low-current beams except that the data from first-order beam line calculation including the space charge are used to calculate the third-order correction. Calculations indicate that the required octopole pole-tip field strength is very small, e.g. a few percent of the strength of the final quadrupoles