Limit on a horizontal emittance in high energy muon colliders due to synchrotron radiation . ∗

It is shown that at a 100 TeV muon collider the synchrotron radiation in the ring will determine the minimum horizontal emittance. In all ee storage ring the horizontal emittance is determined by quantum nature of the synchrotron radiation. Emission of photons in regions with non-zero dispersion leads to growth of the horizontal emittance while the average energy loss leads to the cooling. As the result, some equilibrium emittance is reached. This is well known and corresponding formulae can be found elsewhere [1]. At muon colliders, the synchrotron radiation power is much smaller than that at ee storage rings due to higher particle mass: P ∝ (EB)/m; however this suppression is compensated by the much higher energy and magnetic field. In general, emittance in a storage ring depends on time in the following way ǫx = ǫD(1− e ) + ǫ0e , (1) where ǫ0 is the initial emittance, ǫD is the equilibrium emittance, τ is the damping time. One can check (see also the B.King’s table) that for the 2E=100 TeV muon collider γμτμ ≈ τD ≈ 1 sec, so the emittance will be close to the equilibrium one. The equilibrium normalized (ǫn = γǫ) horizontal emittance in a damping ring [1] ǫD = 55h̄ 32 √ 3mc γ Jx 〈H〉 ρ , (2) Talk at the Workshop Studies on Colliders and Collider Physics at the Highest Energies: Muon Colliders at 10 TeV to 100 TeV, 27 September 1 October, 1999 Montauk, New York, USA, be published by the American Institute of Physics. email:[email protected]