Abstract
In ring-ring colliders, the collision frequency determines the bunch structures, e.g. the time between the bunches in both rings should be identical. Because of relatively low relativistic speed of the hadron beam in sub-TeV hadron-hadron- and electron-ions-colliders, scanning the hadron beam's energy would require either a change in the circumference of one of the rings, or a switching of the bunch (harmonic) number in a ring. The later would cause so-called 'gear-changing', i.e. the change of the colliding bunches turn by turn. In this article, we study the difficulties in beam dynamics in this 'gear-changing' scheme.
Highlights
In sub-TeV hadron colliders [1] and the ring-ring scheme for electron-ion colliders [2], scanning the energy of one of the hadron beams is desired
To assure that both beams collide at a fixed interaction point (IP), the circumference of hadron ring must be adjusted when its energy changes
We demonstrated the effective one-turn matrix with a permutation matrix and illustrated the formation of the multibunch resonance and the instability of both beam offsets and beam sizes in an asymmetric collision pattern when the number of bunches in two beams are different
Summary
In sub-TeV hadron colliders [1] and the ring-ring scheme for electron-ion colliders [2], scanning the energy of one of the hadron beams is desired. To reduce or avoid such an adjustment, one can choose to change the rf harmonic number, h, of the ring, i.e., to change the number of bunches in the ring This could allow the hadron beam to scan a discrete set of energies without adjusting the circumference. For the same example of a nominal energy 250 GeV=n, where the rf harmonic number is 2500, one can adjust the hadron beam’s energy to 35.1 GeV=n, 24.9 GeV=n, and 20.4 GeV=n by changing the harmonic number of either ring by 1, 2, and 3 units, respectively, without changing the ring’s circumference If energies between those discrete values are required, a smaller adjustment of the circumference still would be required. The bunch in one ring will collide with multiple bunches in the other ring in different turns of revolution This asymmetric collision pattern could introduce complications with the beam dynamics. We assume that the optics functions at IP of the two rings are the same and the
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