Abstract
Microbunching instability (MBI) has been one of the most challenging issues in designs of high-brightness beam transport lines for single-pass or recirculating accelerators. Although the intrabeam scattering (IBS) has long been studied in lepton or hadron storage rings as a slow diffusion process or in high-intensity proton linear accelerators as one mechanism for the beam halo, the effects of IBS on single-pass or recirculating electron accelerators have drawn attention only in the recent two decades due to emergence of linac-based or energy-recovery-linac-based fourth-generation light sources, which require high-quality electron beams during the beam transport. In this paper we develop a theoretical formulation of microbunching instability in the presence of IBS for single-pass or recirculation accelerators. To quantify MBI with inclusion of IBS, we start from the Vlasov-Fokker-Planck (VFP) equation, combining both collective interactions and incoherent IBS effects. The linearized VFP equation and the corresponding friction and diffusion coefficients are derived. The evolutions of the resultant density and energy modulations are formulated as a set of coupled integral equations. The theoretical formulation is then applied to a recirculating beamline design. The results from the semianalytical calculation are compared and show good agreement with massive particle tracking simulations.
Highlights
In the last two decades, microbunching instability (MBI) has been recognized as a challenging issue in highbrightness electron beam transport and intensive studies have been done in linear accelerators [1], storagering accelerators [2], and recirculating or energy-recoverylinac (ERL) accelerators [3]
In this paper we develop a theoretical formulation of microbunching instability in the presence of intrabeam scattering (IBS) for single-pass or recirculation accelerators
Several relevant model assumptions are summarized below: (1) the beam particles are nonrelativistic in the beam frame, while ultrarelativistic in the lab frame; (2) the 6-D beam phase space distribution is Gaussian, which is a practical approximation but not always valid, because an interplay of friction and diffusion may not allow for the beam distribution to remain Gaussian during the transport; (3) the transport line is assumed uncoupled
Summary
In the last two decades, microbunching instability (MBI) has been recognized as a challenging issue in highbrightness electron beam transport and intensive studies have been done in linear accelerators (linac) [1], storagering accelerators [2], and recirculating or energy-recoverylinac (ERL) accelerators [3]. There is still lack of a dedicated theoretical formulation of microbunching instability for single-pass or recirculating accelerators to include the six-dimensional (6-D) beam dynamics with inclusion of collective effects and the incoherent IBS effect in a general beam transport line. This serves as a motivation of this work. We believe that the developed formulation shall be generally applicable for linear analysis of 6-D phase space dynamics for single-pass high-brightness beams in the presence of both collective and incoherent effects. Several relevant model assumptions are summarized below: (1) the beam particles are nonrelativistic in the beam frame, while ultrarelativistic in the lab frame; (2) the 6-D beam phase space distribution is Gaussian, which is a practical approximation but not always valid, because an interplay of friction and diffusion may not allow for the beam distribution to remain Gaussian during the transport; (3) the transport line is assumed uncoupled. (4) Since the synchrotron motion is usually neglected in a single-pass accelerator, the following formulas for the longitudinal motion assume a coasting beam, resulting in an additional factor of 2 ahead of the longitudinal IBS growth rate [see Ref. [59] or Eq (1) below]. (5) The average over circumference or path length in CIMP formulas will be removed for the single-pass accelerator and the Coulomb log factor takes into account the variation of optics functions along the beamline, i.e., the instantaneous IBS growth rates are evaluated
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