Quantization of the Coulomb Chain in an External Focusing Field

Details Quantization of the Coulomb Chain in an External Focusing Field Quantization of the Coulomb Chain in an External Focusing Field

2001-01-30

arxiv.org/abs/physics/0101102v1

Physics

Accelerator Physics

9 Pages, 6 figures

Scientific paper

With the appropriate choice of parameters and sufficient cooling, charged particles in a circular accelerator are believed to undergo a transition to a highly-ordered crystalline state. The simplest possible crystalline configuration is a one-dimensional chain of particles. In this paper, we write down the quantized version of its dynamics. We show that in a low-density limit, the dynamics is that of a theory of interacting phonons. There is an infinite sequence of $n$-phonon interaction terms, of which we write down the first orders, which involve phonon scattering and decay processes. The quantum formulation developed here can serve as a first step towards a quantum-mechanical treatment of the system at finite temperatures.

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