MuCool Notes

Practical ionization cooling rings could lead to lower cost or improved performance in neutrino factory or muon collider designs. The ring modeled here uses realistic three-dimensional fields The performance of the ring compares favorably with the linear cooling channel used in the second US Neutrino Factory Study. The normalized 6D emittance of an ideal ring is decreased by a factor of approximately 240, compared with a factor of only 15 for the linear channel. We also examine such real-world effects as windows on the absorbers and rf cavities and leaving empty lattice cells for injection and extraction. For realistic conditions the ring decreases the normalized 6D emittance by a factor of 49.

Given their 2.2 μS lifetime, muons must be accelerated fairly rapidly for a neutrino factory or muon collider. Muon bunches tend to be large. Progress in fixed field, alternating gradient (FFAG) lattices to meet this challenge is reviewed. FFAG magnets are naturally wide; low momentum muons move from the low field side of a gradient magnet to the high field side as they gain energy. This can be exploited to do double duty and allow a large beam admittance without unduly increasing the magnetic field volume. If the amount of RF must be reduced to optimize cost, an FFAG ring can accommodate extra orbits. I describe both scaling FFAGs in which the bends in each magnet are energy independent and non-scaling FFAGs in which the bends in each magnet do vary with muon energy. In all FFAG designs the sum of the bends in groups of magnets are constant; otherwise orbits would not close. Ways of keeping the accelerating beam in phase with the RF are described. Finally, a 1 MeV proof of principle scaling FFAG has been built at KEK and began accelerating protons in June 2000 with a 1 kHz repetition rate.

Progress on six dimensional ionization muon cooling with relatively small rings of magnets is described. Lattices being explored include scaling sector cyclotrons with edge focusing and strong focusing, fixed field alternating gradient (FFAG) rings. Ionization cooling is provided by high pressure hydrogen gas which removes both transverse and longitudinal momentum. Lost longitudinal momentum is replaced using radio frequency (RF) cavities, giving a net transverse emittance reduction. The longer path length in the hydrogen of higher momentum muons decreases longitudinal emittance at the expense of transverse emittance. Thus emittance exchange allows these rings to cool in all six dimensions and not just transversely. Alternatively, if the RF is located after the ring, it may be possible to cool the muons by stopping them as they spiral adiabatically into a central swarm. As p→0, Δp→0. The resulting cooled muons can lead to an intense muon beam which could be a source for neutrino factories or muon colliders.

The direct s-channel coupling to Higgs bosons is 40000 times greater for muons than electrons; the coupling goes as mass squared. High precision scanning of the lighter h⁰ and the higher mass H⁰ and A⁰ is thus possible with a muon collider. The H⁰ and A⁰ are expected to be nearly mass degenerate and to be CP even and odd, respectively. A muon collider could resolve the mass degeneracy and make CP measurements. The origin of CP violation in the K⁰ and B⁰ meson systems might lie in the the H⁰/A⁰ Higgs bosons. If large extra dimensions exist, black holes with lifetimes of ~ 10^-26 seconds could be created and observed via Hawking radiation at the LHC. Unlike proton or electron colliders, muon colliders can produce black hole systems of known mass. This opens the possibilities of measuring quantum remnants, gravitons as missing energy, and scanning production turn on. Proton colliders are hampered by parton distributions and CLIC by beamstrahlung. The ILC lacks the energy reach.

Generating magnetic field maps for the RFOFO Muon cooling ring has proven challenging. The problem is divided into several parts: (1) The primary field generator which starts with the coil geometry and computes B(X) for an arbitrary point in the muon-accessible volume of the ring from basic physical principles, (2) A field map builder which uses the primary field generator to compute the field on a lattice of points, stored on disk for later use, and (3) a secondary field generator which loads the field-on-a-lattice into memory and interpolates in the field map to deliver B(X) to simulation programs as quickly as possible. Extensive tests must be performed to validate the results at every stage; these validations took far more time to program and run than did the field generators being checked. The current release of the field map and the software to access it is believed to be correct to about a part in ten thousand.

OPTICOSP is a single-processor reduction of the multi-processor optimization program OPTICOOL[1]. Like its predecessor, OPTICOSP runs a user-supplied apparatus simulation program repeatedly, searching for an apparatus configuration that is optimal, varying operating parameters and evaluating measures of merit as specified by the user. OPTICOSP is written in Fortran-77. There are versions that run on PCs under Linux or Windows; porting to other platforms should be straightforward. This note describes OPTICOSP and gives an example of how it has been used with the ICOOL[2] simulator.

OPTICOSP is a single-processor reduction of the multi-processor optimization program OPTICOOL[1]. Like its predecessor, OPTICOSP runs a user-supplied apparatus simulation program repeatedly, searching for an apparatus configuration that is optimal, varying operating parameters and evaluating measures of merit as specified by the user. OPTICOSP is written in Fortran-77. There are versions that run on PCs under Linux or Windows; porting to other platforms should be straightforward. This note describes OPTICOSP and gives an example of how it has been used with the ICOOL[2] simulator.

Following Don Summers ideas presentation at Nufac02, the paper considers a 4 to 16 GeV pulsed muon synchrotron accelerator for a Muon Collider. The paper discusses: 1) possible acceptance requirements, 2) arc and straight section lattices, 3) optimization of the magnet gradient for minimum stored magnetic energy, 4) the use of a DC offset for the pulsed ring magnets, 5) a preliminary look at the cost of a specific design, and 6) a parametric study of both pulsed synchrotron and RLA costs as a function of acceptances and allowed decay loss.

We conclude that if a decay loss of 25% is acceptable, then a pulsed synchrotron with acceptances required using either one or two cooling rings, should reduce the 4-20 GeV acceleration cost by a factor of two compared with study-2.

The paper discusses the injection and extraction kicker requirements for the first cooling ring in a muon storage ring neutrino factory, or muon collider. It is shown that a kicker’s current and single turn voltage are proportional to the normalized emittance of the beam; and that the stored energy is proportional to the square of that emittance. All three parameters are independent of the energy in the ring.

For a beam with ε_n = 10π mm, as in several current designs, the kicker energy and voltage are both far higher than in any conventional kicker. But a proposed ’induction kicker’, powered by magnetic amplifiers similar to those in induction linacs, might meet the requirements.