Studies of high-field sections of a muon helical cooling channel with coil separation

The Helical Cooling Channel (HCC) was proposed for 6D cooling of muon beams required for muon collider and some other applications. HCC uses a continuous absorber inside superconducting magnets which produce solenoidal field superimposed with transverse helical dipole and helical gradient fields. HCC is usually divided into several sections each with progressively stronger fields, smaller aperture and shorter helix period to achieve the optimal muon cooling rate. This paper presents the design issues of the high field section of HCC with coil separation. The effect of coil spacing on the longitudinal and transverse field components is presented and its impact on the muon cooling discussed. The paper also describes methods for field corrections and their practical limits. The magnetic performance of the helical solenoid with coil separation was discussed in this work. The separation could be done in three different ways and the performances could be very different which is important and should be carefully described during the beam cooling simulations. The design that is currently being considered is the one that has the poorest magnetic performance because it presents ripples in all three components, in particular in the helical gradient which could be quite large. Moreover, the average gradient could be off, which could affect the cooling performance. This work summarized methods to tune the gradient regarding the average value and the ripple. The coil longitudinal thickness and the helix period can be used to tune G. Thinner coils tend to reduce the ripples and also bring G to its target value. However, this technique reduces dramatically the operational margin. Wider coils can also reduce the ripple (not as much as thinner coils) and also tune the gradient to its target value. Longer helix periods reduce ripple and correct the gradient to the target value