Oscillating Coulomb chain in a storage ring

Abstract

The dynamic behavior of a bunched one-dimensional crystalline beam is studied theoretically. It is shown that, owing to the existence of momentum dispersion, a Coulomb chain traveling in a storage ring performs a complex periodic oscillation whenever it is exposed to a longitudinal radio-frequency force. The equations of motion are derived to predict the oscillation pattern in an arbitrary lattice structure. The validity of the present theory is confirmed through multiparticle simulations. Various features of an oscillating string beam, such as the lattice-parameter dependence of the orbit, the stability, and critical line density, etc., are also discussed.

Crystalline beams in dispersion-free storage rings

“…Consequently, even a 1D string crystal oscillates periodically on the horizontal plane. 3D shell crystals also execute horizontal head-tail oscillations that have the same periodic pattern as in the case of 1D strings [21,28]. This strongly suggests that rf cavities should be placed symmetrically in every lattice period to stabilize a large bunched crystalline beam.…”

“…As pointed out in previous papers [16,21,28], the dynamic behavior of a bunched Coulomb crystal is much more complicated than that in a Paul ion trap. Since individual particles either gain or lose energy at rf cavities, the transverse motion is seriously affected by the energy modulation through the dispersive coupling, in other words, the cross term xp z in the Hamiltonian.…”

Generating Ultralow-Emittance Ion Beams in a Storage Ring

“…cess advances, this timing for a particular particle gradually becomes nonrandom because the synchrotron motion is more and more suppressed. Finally, the ring dispersion, which forces off-momentum particles to deviate from the design orbit, causes the whole beam to oscillate horizontally [13]. We actually notice that the string beam in Fig.…”

“…In an ultralow-emittance state, the transverse tune of this dispersive oscillation is equal to the round number nearest to the bare betatron tune (provided that the strict lattice superperiodicity including cavities is unity) [13]. Since x ; y 2:067; 1:073 in the present case, we expect that the effective incoherent tunes eventually converge not at zero but at 2.0 in the horizontal direction and 1.0 in the vertical direction [14].…”

Static Criteria for the Existence of Coulomb Strings in Storage Rings

“…As results, the probability of reflection (or transmission) increases (drops) sharply when going to larger average interparticle distances. Recently, even more elaborate calculations with the full lattice of the circular accelerators were performed by Okamoto and co-workers [15], yielding similar results.…”