ION OPTICS IN LONG, MULTISTAGE ACCELERATOR TUBES

The recurrence formulae for the cardinal elements of a multistage accelerator tube are derived. The calculated results for an equidiameter cylinder lens obtained by the consecutive applications of the formulae are not so different from those obtained by assuming a uniform acceleration and still show the appreciable deviations from the experimental data. The errors would, therefore, become large, unless the experimental values are used for the cardinal elements of an individual accelerating lens on which the calculation for multistage accelerator tube is based. As an example, the cardinal elements for a 12-stage accelerator tube is shown. The comparison with those obtained by the assumption of a uniform acceleration shows that the latter results are not satisfactorily accurate for such a multistage accelerator.