The Methodical Accelerator Design program MAD for circular accelerators is in regular use for the design and modelling of LEP, LHC, PS and SPS at CERN, and in 10 to 20 other laboratories. It includes the following new accelerator physics features: (i) Machine imperfections, e.g. random and systematic errors in the alignment and excitation of the magnetic elements and read-out errors of the beam-position monitors, (ii) closed orbit correction using the MICADO algorithm, (iii) Lie-algebraic techniques for concatenating beam lines, for tracking trajectories and for higher-order orbit functions, (iv) systematic energy loss due to synchrotron radiation and its effects on the closed orbit and the orbit functions in all 3 degrees of freedom, ( v ) spin dynamics in SMILE style. The data describing the machine are held as data modules in a dynamically managed memory pool, including garbage collection and overflow onto external files. Graphics is interfaced to standard GRS and used for plotting orbit functions along the orbit and versus the momentum error, and phase space plots, Fourier spectra of particle orbits, etc. MAD is implemented on Cray, IBM, Nord, and VAX systems and on Apollo and Sun workstations.

We describe the status of our effort to realize a first neutrino factory and the progress made in understanding the problems associated with the collection and cooling of muons towards that end. We summarize the physics that can be done with neutrino factories as well as with intense cold beams of muons. The physics potential of muon colliders is reviewed, both as Higgs factories and compact highenergy lepton colliders. The status and time scale of our research and development effort is reviewed as well as the latest designs in cooling channels including the promise of ring coolers in achieving longitudinal and transverse cooling simultaneously. We detail the efforts being made to mount an international cooling experiment to demonstrate the ionization cooling of muons.

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A major expense and design challenge in carbon/proton cancer therapy machines are the isocentric gantries. The transport elements of the carbon/proton gantry are presently made of standard conducting dipoles. Because of their large weight, of the order of 100 tons, the total weight of the gantry with support structure is 600 tons. The novel gantry design that is described here is made of fixed field superconducting magnets, thus dramatically reducing magnet size and weight compared to conventional magnets. In addition, the magnetic field is constant throughout the whole energy region required for tumor treatment. Particles make very small orbit offsets, passing through the beam line. The beam line is built of combined-function dipoles such as a nonscaling fixed field alternating gradient (NS-FFAG) structure. The very large momentum acceptance NS-FFAG comes from very strong focusing and very small dispersion. The NS-FFAG small magnets almost completely filled the beam line. They first make a quarter (or close to a quarter) of an arc bending upward and an additional half of a circle beam line finishing so that the beam is pointed towards the patient. At the end of the gantry, additional magnets with a fast response are required to allow radial scanning and to provide the required position and spot size. The fixed field combined-function magnets for the carbon gantry could be made of superconducting magnets by using low temperature superconducting cable or by using high temperature superconductors.