Abstract
064001-1 Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the Large Hadron Collider (LHC) at CERN, particles circulate at the injection energy, when multipole errors are most significant, for more than 107 turns, but systematic tracking studies are limited to a small fraction of this total time — even on modern computers. A considerable speedup is expected by replacing element-by-element tracking with the use of a symplectified one-turn map. We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.
Highlights
Since 1982, when maps were first introduced to the accelerator community [1], the question has been, ‘‘Can they be used to replace element-by-element tracking?’’ It became clear that in the presence of strong multipolar fields, maps can be used only if one applies some kind of symplectification scheme [2]
One such scheme was proposed by Irwin [3] in 1989 and later tested for the CERN
It was found to be (i) only a factor of 2 faster and (ii) insufficiently precise for determining the dynamic aperture. The application of this technique was discontinued, until recently, when a significant improvement was proposed [5,6]. This improved scheme produces a symplectic map, called a Cremona map, that is guaranteed to agree with element-by-element tracking through a given Taylor order with minimal additional terms
Summary
Since 1982, when maps were first introduced to the accelerator community [1], the question has been, ‘‘Can they be used to replace element-by-element tracking?’’ It became clear that in the presence of strong multipolar fields, maps can be used only if one applies some kind of symplectification scheme [2]. We apply Cremona map tracking to a realistic model of the LHC to see if this new technique can yield a sufficiently precise determination of the dynamic aperture, but with a tenfold gain in speed compared to direct tracking. To this end we study 60 different configurations (called ‘‘seeds’’ in the following) of randomly distributed multipole errors.
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