Dogbone Geometry for Recirculating Accelerators∗

Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a “dogbone” shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle’s momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective. 1 THE RACETRACK AND DOGBONE GEOMETRIES A recirculating accelerator accelerates bunches by passing particles through the same linac several times by constructing arcs through which the beam returns to the linac. This is a very effective way of accelerating muons since there is minimal synchrotron radiation from the muons at lower energies, and thus they can be bent, and yet the muons decay and thus must be accelerated very rapidly. There is generally a separate arc for each pass through the linac, since the bunches have widely varying energies due to the large amount of acceleration per pass through the linac, and the circulation time is too short for the magnetic fields to be increased with increasing bunch energy. Due to the very high cost per unit length of a linac, it is generally not cost effective to accelerate muons to the maximum desired energy with a single linac. However, as one increases the number of turns, more arcs are required, and the arc cost rapidly dominates the recirculating accelerator cost as one adds more arcs. One could generally decrease the arcs costs if one could reduce the arc length without significantly increasing the cost of the magnets in that arc. Figure 1 shows the racetrack and dogbone [1] geometries for a recirculating accelerator. In the racetrack geometry, the lower energy arcs are forced to be roughly the same length as the higher energy arcs due to the distance the must traverse from one linac to the other. That distance is determined by the length of the highest energy arc. The dogbone ∗Supported by US Department of Energy contract DE-AC0298CH10886 Figure 1: Racetrack (above) and dogbone (below) geometries. geometry tries to solve this problem by eliminating that distance between the linacs: in fact there is only one linac. The bunch simply returns to that same linac, entering the linac at the same end from which it exited. The minimum arc length for a given bending radius is achieved if there is 420◦ of bending in that arc. Since the minimum bend radius should be roughly proportional to the bunch’s momentum, the lower energy arcs can be significantly smaller than the higher energy arcs. One expects the dogbone geometry to be less costly than the racetrack geometry by the following argument: Start with a given racetrack geometry recirculating accelerator. Take its two linacs and make it into a single long linac for the dogbone geometry. The linac costs of these two machines are the same. To accelerate to the same energy, two 180◦ arcs in the racetrack geometry become one 420◦ arc in the dogbone. However, the average arc length is around half the maximum arc length. Thus, the total length of arc in the dogbone is around 7/12 of the total arc length in the racetrack, and the dogbone should thus cost less. Furthermore, the decays should be substantially reduced since the total length traveled by the muons has been substantially reduced, and in particular reduced at the lowest energies. In another scenario, take only one of the two linacs in the racetrack, and use it in the dogbone. Each 180◦ arc from the racetrack will become 420◦ of arc in the dogbone, but as before the average arc length in the dogbone is half the maximum arc length. Thus the dogbone has around 7/6 of the arc length of the racetrack, but half the linac, and thus should be less expensive. Decays should be nearly the same in this case. 0-7803-7191-7/01/$10.00 ©2001 IEEE. 3323 Proceedings of the 2001 Particle Accelerator Conference, Chicago