Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure

The R&D Program for Targetry at a Neutrino Factory

The need for intense muon beams for muon colliders [1] and for neutrino factories based on muon storage rings [2, 3, 4] leads to a concept of 1-4 MW proton beams incident a moving target that is inside a 20-T solenoid magnet, with a mercury jet as a preferred example. Novel technical issues for such a system include disruption of the mercury jet by the proton beam and distortion of the jet on entering the solenoid, as well as more conventional issues of materials lifetime and handling of activated materials in an intense radiation environment. As part of the R&D program [5] of the Neutrino Factory and Muon Collider Collaboration, R&D effort related to targetry is being performed within the context of BNL E951 [6], first results of which are discussed here and in other contributions to this conference