Abstract
The space-charge potential can be a source of various resonances in high-intensity hadron bunches traveling in linear accelerators at relatively low energy. Those natural resonances, which may occur even without external driving fields, have to be avoided carefully to minimize undesired beam loss. We perform self-consistent multiparticle simulations systematically to locate major resonance stop bands in the tune diagram, starting from equipartitioned and nonequipartitioned beams. Serious excitation of synchrobetatron resonances is confirmed, depending on the emittance condition at injection. It is demonstrated that a synchrobetatron difference resonance of any order can be suppressed strongly by controlling the ratio of the transverse and longitudinal projected emittances. The equipartitioned linac design is shown to broaden the usable operating area in the tune space, though that has almost nothing to do with thermodynamic effects.
Highlights
The natural Coulomb interaction among charged particles plays a crucial role in the performance of modern accelerators that transport high-intensity hadron beams [1,2]
The space-charge-induced effect is severe in an injector linac operating at relatively low energy
The stability of the stationary solution to the 2D envelope equations against perturbation was analyzed in detail by Struckmeier and Reiser [34]. Their perturbative approach was recently applied by Qiang to the 3D envelope equations in order to explore the bunched-beam stability [35]. We here follow his analysis to figure out the region of the linear-mode instability in the so-called “tune diagram.”
Summary
The natural Coulomb interaction among charged particles plays a crucial role in the performance of modern accelerators that transport high-intensity hadron beams [1,2]. According to our past experience, the WARP code has a better convergence with the sinusoidal focusing, which is most likely due to the smooth variation in the envelope functions It is unnecessary in this simple model to adjust the step size of numerical integration at the entrance and exit of each magnet, depending on extra parameters (not very essential to the fundamental feature of resonances) such as the quadrupole occupancy factor. The symmetric focusing is a sort of standard choice in linacs, but in synchrotrons, usually avoided for the reason that the so-called “Montague resonance” may possibly occur at high beam density [23] Such a coupling resonance in the transverse degrees of freedom can, be strongly suppressed by choosing a proper emittance ratio at injection. This is a primary reason why these two types of lattices have almost the same resonance feature
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