Abstract
We explore a practical approach for designing ionization cooling channels with periodic solenoidal focusing. We examine the lattice characteristics in terms of the properties of the coils and the cell geometry. The peak magnetic field in the coils is an important engineering constraint in lattice design. We examine the dependence of the peak field, momentum passband locations, and the beta function on the coil parameters. We make a systematic examination of all allowed lattice configurations taking into account the symmetry properties of the current densities and the beta function. We introduce a unique classification for comparing cooling lattice configurations. While solutions with a single coil per cell illustrate most of the effects that are important for cooling channel design, the introduction of additional coils allows more flexibility in selecting the lattice properties. We look at example solutions for the problem of the initial transverse cooling stage of a neutrino factory or muon collider and compare our results with the properties of some published cooling lattice designs. Scaling laws are used to compare solutions from different symmetry classes.
Highlights
Ionization cooling [1,2] is an essential feature of most designs for neutrino factories [3] and muon colliders [4].The phase space of the muon beam that comes from pion decays greatly exceeds the acceptance of downstream accelerator systems, so a cooling channel is usually included to reduce the transverse emittance
The beam is passed through an rf cavity that only restores the lost longitudinal momentum
Solenoid lattice design has traditionally been done by varying the parameters of a few coils at the boundary between lattice cells, such that beta function is preserved over a range of incident momentum values
Summary
Ionization cooling [1,2] is an essential feature of most designs for neutrino factories [3] and muon colliders [4]. Later, following a suggestion by Andrew Sessler, it was found that the performance of these lattices could be improved significantly by the addition of higher harmonic terms to the on-axis fields [6] Lattices of this type were given the name ‘‘super-FOFO’’ or ‘‘SFOFO.’’ By changing the coil configurations and symmetry properties a number of periodic lattice configurations were discovered. A step beyond this was made by Penn [9,10], who examined periodic solenoidal lattices in terms of the addition of second and third harmonics to the fundamental sinusoidal field This analysis introduced a scaling variable Bp0 , where B0 is the peak on-axis field, is the period of the magnetic field, and p is the momentum of the particle. We examine the changes that are introduced as additional coils are added to the cell
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