CERN Accelerating science

Internal Note
Report number	HIE-ISOLDE-PROJECT-Note-0005 ; CERN-BE-2009-RF ; CERN-HIE-ISOLDE-PROJECT-Note-0005
Title	Second-order Transit Time Factors for a Two Gap Resonator
Author(s)	Fraser, MA
Corporate author(s)	CERN. Geneva. HIE-ISOLDE Department
Publication	2009
Imprint	01 Oct 2009
Number of pages	17
Subject category	Accelerators and Storage Rings
Accelerator/Facility, Experiment	not applicable
Keywords	HIE-ISOLDE ; LINAC ; Second-order ; Transit ; Factors ; Two Gap ; Resonator
Abstract	The HIE-ISOLDE linac at CERN will operate independently phased quarter-wave resonators (QWRs) in order to accelerate radioactive ion beams (RIBs), with mass to charge states in the range 2.5 < A/q < 4.5, from 1.2 MeV/u up to an energy of at least 10 MeV/u. The low-β version of the QWR will also be used to decelerate beams below 1.2 MeV/u. The combination of low velocity and high gradient results in a significant change of the ion velocity and a breakdown of the first-order approximation commonly used to calculate the energy gain in accelerating cavities. The first-order transit-time factor for two gaps is briefly reviewed before higher-order transit-time factors are derived and the energy gain expressed, taking into account the variation in velocity, to second-order. The formalism of J.R. Delayen, introduced in [1], is used throughout.
Submitted by	[email protected]