We present an electromagnetic design of 325 MHz superconducting single-spoke resonators (SSRs) to accelerate the H$^−$ ions from 3 to ∼160 MeV for the proposed Indian Facility for Spallation Research project. The geometrical parameters of SSRs have been optimised to maximise the achievable acceleration gradient, and to minimise the multipacting growth rate, keeping a reasonably low value of heat dissipation on the cavity surface. For the geometrical optimisation of SSR cavities, we followed a one-dimensional procedure, where we vary and fix the geometrical parameters one by one in a sequential manner. We explain the behaviour of various RF parameters of the SSR with respect to its geometrical parameters, based on which the optimum value of each of the geometricalparameters has been chosen. For the optimised geometry of SSRs, we performed the higher-order mode (HOM) analysis and estimated the transverse and longitudinal kicks imparted to the beam by HOMs. The effect of azimuthala symmetry of the electromagnetic field is also analysed and presented for the adopted design. A holistic design approach is described in the paper that addresses the interlinked optimisation requirements.

The performance of a radiofrequency quadrupole (RFQ) is known to be sensitive to its geometric errors, as well as to the amplitude and phase errors of the input RF. Extensive statistical simulations are typically performed using the available computer codes, for assessing the effect of various errors, to fix the tolerances on these errors. Each of the statistical simulation requires beam dynamics calculations to be performed with a modified electromagnetic(EM) field configuration corresponding to the particular set of geometric errors. Although modified EM field due to geometrical errors should be accurately obtained using EM codes such as CST-MWS, such an approach is time consuming. It is therefore common practice to obtain the EM fields, under quasistatic approximation, which is faster. Such an approach is routinely followed in codes such as TRACEWIN. In this paper, we first present extensive errorstudies, using this approach, for a 325 MHz, 3MeV RFQ, which has been designed as a front-end accelerator for the envisaged Indian Facility for Spallation Research. The validity of quasistatic approximation for such error analysisis explicitly checked in this paper by comparing the results obtained using TRACEWIN, with those obtained using the EM fields derived from the CST-MWS code. To the best of our knowledge, such a comparison has not been reported before. Also, since the available computer codes do not give the option to study the effect of RF phase jitter in an RFQ, techniques evolved for this study are also described in this paper.