Progress in the Development of a 3d Finite Element Computer Program to Calculate Space and Image Charge Effects in RF Quadrupoles

This paper describes the further development of the RFQTRAK computer program. Two RFQ cells, with combined length ß¿, are modelled with finite elements and a ´waterbag´ distribution of particles is tracked through them. Each particle makes about 20 time steps per cell. At each time step the space charge solution is obtained and the field at the particle positions is calculated. These fields are added to the parameterised RF fields for use in the tracking routine. When one complete RF cycle of particles has emerged from the double cell the next pair of cells is modelled in a similar way. This is repeated until the beam has been tracked through the whole RFQ. Estimates of beam loss for the Chalk River RFQ1-B design are compared with results from the PARMTEQ program.