Revision 1

Accepted · first revision · record

Title: Effect of space charge on the transverse mode-coupling instability threshold
Plain: The beam's own repulsion shifts its oscillation frequencies, and theories disagree on whether this raises or lowers the intensity at which bunches start to shake apart.
Precise: For a single proton bunch with transverse impedance $Z$ and incoherent space-charge tune shift $\Delta Q_{\mathrm{sc}}$ comparable to or larger than the synchrotron tune $Q_s$, compute the transverse mode-coupling instability threshold intensity as a function of $\Delta Q_{\mathrm{sc}}/Q_s$, wake shape (broadband, resonator, resistive wall) and longitudinal profile. Reconcile with CERN SPS measurements in which TMCI is suppressed but other instabilities appear at high space charge.
Settled by: A self-consistent theory or converged simulation that reproduces the measured SPS thresholds versus space-charge strength without free parameters.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: contested
Status note: Models published 2016-2018 give thresholds rising or falling with space charge depending on wake sign and phase advance; SPS experiments reported in 2022 saw TMCI replaced by other instabilities at high space charge.
Posed since: 1998