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Abstract. Skrinsky and Parkhomchuk introduced the concept of ionization cooling in 1981[1] and the muon collider concept was proposed by Neuffer in 1983[2]. Considerable progress has been made on muon collider design, with one baseline design being established by Palmer, et al.[3] in 1995. Present conceptual designs for a muon collider start with a proton beam driver. The protons are directed onto a target wherein they create pions, which then decay into muons. The muons resulting from this process have a very high spread of velocities, making them inappropriate for acceleration in a collider. To reduce the velocity spreads, ionization cooling is proposed in a process termed “6D cooling” in the literature. Analysis to date shows that 6D cooling can achieve significant cooling, but still leaves the transverse emittances over an order of magnitude larger than the desired transverse design emittance of 25 m. (This emittance is one sigma, normalized). To obtain the desired emittance (so that the collider produces enough high energy physics results) a final cooling section has been proposed (see Palmer, Fernow and Lederman [4]) that effectively exchanges emittances: the final cooler allows the longitudinal emittance to grow while reducing the transverse emittance.
A baseline approach to muon cooling was included in a summary report by Palmer in 2014[5] and more recently discussed in the 2021 Snowmass report[6]. These reports have a design that proposes 6D ionization cooling will reach a transverse emittance of 300 m, and that a final ionization cooling will reach the desired goal of 25 m. Both references refer to difficulties in achieving these values, with the Snowmass paper reporting that the values are not yet even achieved in simulations.
There are significant possible advantages of applying low-energy electron-cooling to a muon collider. In this paper one possible nonmagnetized electron cooling scenario for a muon collider is outlined as a theoretical existence-proof of the concept. A conservative and approximate estimate of the system requirements is presented. The issue of stable high current, low energy electron beams is discussed, and a cooler design based upon prior work done on electron cooling collectors is proposed. It is predicted that this system, while complex, is capable of cooling muons from 300 m down to 0.125 m with a muon survival rate of 41.5% in the electron cooling system. Provided such a low emittance can be maintained, a significant reduction in required muon currents is possible while maintaining the design luminosity. This would enable easing of many other system requirements such as those associated with the proton driver, target, beam loading on cavities, required good field aperture in the magnets, and shielding systems. Physics analysis will benefit from a much lower muon decay background, since with far fewer muons in the beams, far fewer high energy muon decays will occur.
[1]. N. Skrinsky and V.V. Parkhomchuk, Sov. J. of Nucl. Physics 12, (1981) 3.
[2] D. Neuffer, Particle Accelerators, 14, (1983) 75.
[3] R. Palmer et al., SLAC-PUB-9921, Presented at 3rd Int’l Conference on Physics Potential and Development of mu+ mu- Colliders, 12/13/1995-12/16/1995, San Francisco, CA, USA
[4] R. Palmer, R. Fernow and J. Lederman, Muon Collider Final Cooling in Solenoids, BNL-94919-2011-CP, Proc. 2011 PAC, New York, NY (2011).
[5] R.B. Palmer, Reviews of Accelerator Science and Technology, Vol. 7 (2014) 137–159.
[6] Cross-Frontier Report Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021) https://arxiv.org/pdf/2209.01318.
