Lattices with minimal space charge effects for crystalline beams

摘要

There are numerous techniques for cooling beams of charged particles including stochastic cooling, electron beam cooling, ionization (foil) cooling (for lepton beams only), and laser cooling which works only with ions with some electrons still attached. The successful implementation of laser cooling at Aarhus, has led to interest in crystalline beams, and it certainly seems that crystallization of small numbers of stored particles should be possible. There are limits, however, that may restrict the total number of charged particles stored; these include the limit on the space-charge tune shift, (vert bar)(triangle)(nu)(vert bar) < 0.25 (though the precise number is subject to debate) and intrabeam scattering. In this paper we will be concerned with the possibility of intense crystalline beams; for simplicity we treat only the nonrelativistic case, though the relativistic case is a simple extension of this work. In the next section we review the limits on the number of particles stored and observe that the beam size scaling with beam temperature is the important dependence that determines the limits on the stored current as a function of beam temperature. In section 3 we use a general formalism to determine the beam size scaling and apply it to various kinds of focusing lattices and determine the relevant limits. In section 4 we use simulations that include lattice elements, a cooling model, and an N-body space-charge model to confirm the predictions of section 3 and to explore the details of various schemes. In the final section we summarize and discuss our results.