1. Scaling Gas-filled Muon Ring Coolers Al Garren, UCLA Ringcooler Mini-workshop Tucson, December 15-16, 2003

2. 2 Ring types considered o Weak Focusing Scaling Rings: Radial sectors with uniform magnetic fields ie zero gradients. o Strong Focusing FFAG Scaling Rings: Radial sectors with alternating field direction and magnetic field strength determined by the field exponent k.

3. 3 Weak Focusing Scaling Rings Parameters o Horizontal and vertical focusing is given by the combination of body and edge focusing of the sector magnets. The essential parameters are: o Muon momentum of reference orbit, ie momentum of cooled beam o Number of magnet sectors o Magnetic field o Relative angular width of magnets and drifts

4. 4 The parameter  = Rc/  is a critical parameter which determines , the angular width of the half drift, and , the angular width of the half dipole when measured from the ring center. When = 1 the tunes are equal, and cooling is optimal;  is also the edge angle.

5. 5 Weak Focusing Scaling Rings Examples Studied  4 sector ring,  =   4 sector ring,  = 3/4  6 sector ring,  =1

6. 6 Strong Focusing Scaling Rings Parameters o Assumptions: o Inward and outward bending magnets have identical field profiles except the signs are opposite. Outward bends are horizontally focusing, inward bends are vertically focusing. o Horizontal and vertical focusing is given by body and edge focusing of the sector magnets and by their gradients. o The essential parameters are: o Muon momentum o Number of magnet sectors o Magnetic fields on reference orbit o Relative angular widths of F and D magnets and drifts (if any). o The geometry including edge angles can be derived from the above.

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8. 8 FFAG with drifts o This example shows a triplet cell structure.