Abstract
A radio frequency (rf) quadrupole has been considered as a potential alternative device for Landau damping in circular hadron colliders. The objective of this study is to benchmark and confirm its stabilizing effect predicted by stability diagram theory by means of numerical tracking simulations. To that end, two complementary models of the device are implemented in pyheadtail, a 6D macroparticle tracking code designed to study the formation and mitigation of collective instabilities. The rf quadrupole model is applied to a slow head-tail instability observed experimentally in the Large Hadron Collider to show that such a device can in principle provide beam stability similarly to magnetic octupoles. Thereafter, alternative usage schemes of rf quadrupoles also in combination with magnetic octupoles are proposed, discussed, and benchmarked with simulations.
Highlights
To improve the luminosity of future machines like the High Luminosity Large Hadron Collider (HL-LHC) or the Future Circular Collider (FCC), the brightness of the particle beams will be significantly increased [1,2]
The rf quadrupole model is applied to a slow head-tail instability observed experimentally in the Large Hadron Collider to show that such a device can in principle provide beam stability to magnetic octupoles
The major one is that the incoherent betatron tune spread is dependent on the longitudinal action spread which is several orders of magnitude larger than the transverse ones for the beams of LHC, HL-LHC, and FCC-hh
Summary
To improve the luminosity of future machines like the High Luminosity Large Hadron Collider (HL-LHC) or the Future Circular Collider (FCC), the brightness of the particle beams will be significantly increased [1,2]. Future hadron colliders will operate with beams of smaller transverse emittances making the Landau octupoles significantly less effective due to the reduced spread in ðJx; JyÞ This effect is even more pronounced at higher beam energies as a result of adiabatic damping and may eventually lead to a loss of Landau damping of potentially performance-limiting collective instabilities. Analytical calculations predict that the maximum RMS betatron tune spread generated by the LHC Landau octupoles can theoretically be achieved with a few metres long superconducting rf device operating in a transverse magnetic quadrupolar mode. This is for LHC nominal beam and machine parameters at top energy of 7 TeV. The schemes are partially motivated by stability diagram theory and are benchmarked with tracking simulations
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