Fundamental cavity impedance and longitudinal coupled-bunch instabilities at the High Luminosity Large Hadron Collider

Abstract

The interaction between beam dynamics and the radio frequency (rf) station in circular colliders is complex and can lead to longitudinal coupled-bunch instabilities at high beam currents. The excitation of the cavity higher order modes is traditionally damped using passive devices. But the wakefield developed at the cavity fundamental frequency falls in the frequency range of the rf power system and can, in theory, be compensated by modulating the generator drive. Such a regulation is the responsibility of the low-level rf (llrf) system that measures the cavity field (or beam current) and generates the rf power drive. The Large Hadron Collider (LHC) rf was designed for the nominal LHC parameter of 0.55 A DC beam current. At 7 TeV the synchrotron radiation damping time is 13 hours. Damping of the instability growth rates due to the cavity fundamental (400.789 MHz) can only come from the synchrotron tune spread (Landau damping) and will be very small (time constant in the order of 0.1 s). In this work, the ability of the present llrf compensation to prevent coupled-bunch instabilities with the planned high luminosity LHC (HiLumi LHC) doubling of the beam current to 1.1 A DC is investigated. The paper conclusions are based on the measured performances of the present llrf system. Models of the rf and llrf systems were developed at the LHC startup. Following comparisons with measurements, the system was parametrized using these models. The parametric model then provides a more realistic estimation of the instability growth rates than an ideal model of the rf blocks. With this modeling approach, the key rf settings can be varied around their set value allowing for a sensitivity analysis (growth rate sensitivity to rf and llrf parameters). Finally, preliminary measurements from the LHC at 0.44 A DC are presented to support the conclusions of this work.

FCC-ee: The Lepton Collider

“…One of the ways to eliminate the shift of a collision point due to beam phase modulation is matching of abort gap transients. The direct RF feedback with the overall loop delay of 700 ns (similar to the LHC [322]) can also mitigate the transient beam loading at the cost of an additional power generator. For the example shown in Figure 3.20, about a 5% increase of the generator power (the right plot) is sufficient to reduce the bunch-by-bunch phase modulation by 20% (the left plot).…”

Beam gap transient analysis and mitigations in high-current storage rings for an electron-ion collider

“…These equations use the macroparticle model and apply to the electron ring. For the ion beam, these equations provide an approximation to the more exact expressions presented in [33,34]. This summation over frequencies acts to fold all the impedance effects down into the single band of modes spanning half the rf frequency spaced by the revolution frequency.…”

Transient beam loading and rf power evaluation for future circular colliders

“…This has been used in most high-intensity accelerators since the 1980s [19]. In addition to regulation of the cavity field in the presence of amplifier drifts and rf noise, it counteracts the longitudinal coupled-bunch instability driven by the fundamental cavity impedance Z b [8,16,20]. The direct rf feedback reduces the cavity fundamental mode impedance seen by the beam such that the impedance of the closed loop is…”

“…The comparison of amplitude modulations of the cavity voltage with the direct rf feedback (τ d ¼ 700 ns, similar to the loop delay in the LHC [20]) for k ¼ 0.3 and k ¼ 0 [see Eq. (34)] is shown in Fig.…”