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Title: Quantization of the Coulomb Chain in an External Focusing Field

Abstract

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[1]. 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, 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.

Authors:
Publication Date:
Research Org.:
Stanford Linear Accelerator Center, Menlo Park, CA (US)
Sponsoring Org.:
USDOE Office of Energy Research (ER) (US)
OSTI Identifier:
784850
Report Number(s):
SLAC-PUB-8760
TRN: US0108634
DOE Contract Number:  
AC03-76SF00515
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 24 Jan 2001
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; ACCELERATORS; CHARGED PARTICLES; DECAY; FOCUSING; PHONONS; QUANTIZATION; SCATTERING; BEAM DYNAMICS; QUANTUM MECHANICS

Citation Formats

Kabel, Andreas C. Quantization of the Coulomb Chain in an External Focusing Field. United States: N. p., 2001. Web. doi:10.2172/784850.
Kabel, Andreas C. Quantization of the Coulomb Chain in an External Focusing Field. United States. doi:10.2172/784850.
Kabel, Andreas C. Wed . "Quantization of the Coulomb Chain in an External Focusing Field". United States. doi:10.2172/784850. https://www.osti.gov/servlets/purl/784850.
@article{osti_784850,
title = {Quantization of the Coulomb Chain in an External Focusing Field},
author = {Kabel, Andreas C},
abstractNote = {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[1]. 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, 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.},
doi = {10.2172/784850},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2001},
month = {1}
}

Technical Report:

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