Algorithms to get a circulating beam

Two algorithms based on trajectory fitting have been used to obtain rapidly a circulating beam in LEP with strong focusing lattices. A new algorithm called “orbit closure” uses the beam positions measured at the first and the second turn. From their difference, it computes two corrector strengths per plane such that the second turn passes at the same place as the first turn at about ten BPM locations. This produces a closed orbit amplitude with an RMS value close to that of the first turn trajectory. A new `first turn threader´ has been tried. It detects places where an oscillation with an RMS amplitude larger than a specified value starts, and computes two corrector strengths to cancel it. By iterating this process, it should be possible to correct by steps the first turn trajectory so that its RMS amplitude is below a specified value. The orbit closure has been applied with success to a very low emittance lattice (135° in the horizontal plane) in LEP