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Abstract
Understanding the 3D collective long-term response of beams exposed to resonances is of theoretical interest and essential for advancing high intensity synchrotrons. This study of a hitherto unexplored beam dynamical regime is based on 2D and 3D self-consistent particle-in-cell simulations and on careful analysis using tune spectra and phase space. It shows that in Gaussian-like beams Landau damping suppresses all coherent parametric resonances, which are of higher than second order (the ``envelope instability''). Our 3D results are obtained in an exemplary stopband, which includes the second order coherent parametric resonance and a fourth order structural resonance. They show that slow synchrotron oscillation plays a significant role. Moreover, for the early time evolution of emittance growth the interplay of incoherent and coherent resonance response matters, and differentiation between halo and different core regions is essential. In the long-term behavior we identify a progressive, self-consistent drift of particles toward and across the resonance, which results in effective compression of the initial tune spectrum. However, no visible imprint of the coherent features is left over, which only control the picture during the first one or two synchrotron periods. An intensity limit criterion and an asymptotic formula for long-term rms emittance growth are suggested. Comparison with the commonly used non-self-consistent ``frozen space charge'' model shows that in 3D this approximation yields a fast and useful orientation, but it is a conservative estimate of the tolerable intensity.
Highlights
Beam intensity in operating or future high intensity circular hadron accelerators is limited by space charge effects on resonances [1]
Contrary to low intensity operation, where resonances are single particle phenomena, high intensity requires self-consistent treatment with differentiation between incoherent and coherent resonance effects as well as consideration of Landau damping of nonlinear coherent parametric resonances
In circular accelerators it is common practice to describe the effect of space charge in terms of an incoherent footprint on resonance charts, which depends on the distribution function—besides chromatic and other effects not in the focus here
Summary
Beam intensity in operating or future high intensity circular hadron accelerators is limited by space charge effects on resonances [1]. Minimizing their effects on beam quality; but so far— for cpu and noise related reasons—only non-self-consistent “frozen space charge models” (FSM) have been employed in these campaigns, which require modeling of 105...106 machine turns. Such fully self-consistent 3D simulations using large numbers of simulation particles and many turns of synchrotron lattices are quite possible. For high intensity hadron circular accelerators—different from linear devices—a main beam dynamics challenge is self-consistent and long-term 3D modelling including synchrotron oscillation, which has motivated the present study.
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