Abstract
Single bunch instabilities for the $50\mathrm{GeV}\ifmmode\times\else\texttimes\fi{}50\mathrm{GeV}$ muon collider are discussed. An impedance budget of the collider is estimated. A phase-slip factor of $|\ensuremath{\eta}|=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ is desired to avoid excessive rf systems. Potential-well distortion of a smooth bunch can be compensated by rf cavities. Accumulated growth in energy due to imperfections and noises in the muon bunch can be reduced by smoothing the bunch distribution before injection. The growth due longitudinal microwave instability is small because of the compensated rf cavities, the finite lifetime of the muons, and the choice of a small $|\ensuremath{\eta}|$. Beamloadings in the compensating rf cavities are large and suitable feed-forward cancellation is required. Transverse microwave instability can be damped by chromaticities and octupoles. Beam breakup can be cured by Balakin-Novokhatsky-Smirnov damping in principle, but is nontrivial in practice. When beam breakup is small, it can possibly be damped by a betatron tune spread in the beam.
Highlights
Muon colliders offer significant advantage in the production of Higgs bosons over electron colliders
In order to attain the luminosity of 1 3 1032 cm22 s21 for the accumulation of 1.9 3 103 Higgs bosons in a year, each of the colliding m1 and m2 bunches needs to have an intensity of N 4 3 1012 particles, rms bunch length sᐉ 4 cm, and rms momentum spread sd 1.2 3 1023 [1]
Beamstrahlung is not a problem in the muon interaction region; it is possible to have the momentum spread of the muon beams to be as small as sd 3.0 3 1025. There is another mode of operation of the muon collider at this small momentum spread with rms bunch length sᐉ 13 cm for the precision determination of the Higgs boson mass
Summary
Muon colliders offer significant advantage in the production of Higgs bosons over electron colliders. This is because the muon mass is mmme 105.7͞0.5110 206.8 times larger than the electron mass, so that the production cross section is mm2 ͞me2 4.28 3 104 times larger. There is another mode of operation of the muon collider at this small momentum spread with rms bunch length sᐉ 13 cm for the precision determination of the Higgs boson mass. With such a high-intensity bunch and small momentum spreads, the study of beam instabilities becomes a very important task
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