Numerical Optimization of 6D Cooling Solenoids for a Muon Collider

In the current most evolved design concept of a machine for accelerating and colliding muons, there exists two long ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 1km) channels for cooling newly created muons and anti-muons. Termed the ‘6D cooling channels’, the beam is cooled in momentum and position space using a series of alternating polarity solenoids which create an oscillating field in the beam direction, absorbers and radio-frequency cavities. In total there are around 3000 solenoids per channel, contributing to a significant portion of the cost and engineering demands of the entire machine. The integration of the requirements of the field profile with feasible solenoid configurations is a difficult and unique problem, without analytic descriptions to readily relate these. We have addressed this problem in two ways: in the first we constrain the optimization studies of the optics by setting limits on solenoid parameters; in the second we have developed a numerical optimization routine to find the best configuration given a desired field profile, in terms of cost and engineering complexity. The following paper reviews semi-analytic descriptions of solenoids, select operating limits considering HTS, followed by the numerical optimization approach and subsequent results. This procedure is applicable to any solenoid or set of solenoids and can be an extremely useful optimization tool, running much quicker than current commercial softwares.