Correction of Field Errors in ISAC RFQ

This paper is an abridged version of a TRIUMF design note[1]. The most important effect of using a non-ideal vane geometry is that the longitudinal field can depart substantially from the value calculated from the usual analytic formulae; and this may lead to beam loss due to inadequate acceleration. The effect is enhanced at low particle speed and low radio-frequency, as occurs at injection into the TRIUMF ISAC heavy ion RFQ. An exact and self-consistent procedure has been invented that may be applied to any practical vane geometry, to recalculate the vane profile parameters, modulation index (m) and minimum bore radius (a), so as to give the ideal acceleration and focusing fieldcoefficients at every RFQ cell. The procedure has two steps. First, make a numerical map, for each field coefficient, of the dependence on cell parameters m, a and cell length. Second, for given, desired fields at the synchronous particle, to invert the map numerically to find the required values of m and a. We have applied this technique to the TRIUMF ISAC RFQ accelerator design.