The Brown-Servranckx matching transformer for simultaneous RFQ to DTL H+ and H- matching

The issue involved in the simultaneous matching of H+ and H- beams between an RFQ and DTL lies in the fact that both beams experience the same electric-field forces at a given position in the RFQ. Hence, the two beams are focused to the same correlation. However, matching to a DTL requires correlation of the opposite sign. The Brown-Servranckx quarter-wave (λ / 4) matching transformer system, which requires four quadrupoles, provides a method to simultaneously match H+ and H- beams between an RFQ and a DTL. The method requires the use of a special RFQ section to obtain the Twiss parameter conditions βx = βy and αx = αy = 0 at the exit of the RFQ. This matching between the RFQ and DTL is described. (author)