dorsal/arxiv
View SchemaA stochastic model for the semiclassical collective dynamics of charged beams in particle accelerators
| Authors | Salvatore De Martino, Silvio De Siena, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | physics/9803036 |
| URL | https://arxiv.org/abs/physics/9803036 |
Abstract
A recent proposal (see quant-ph/9803068) to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations is applied to the specific instance of charged beam dynamics in particle accelerators. The resulting picture is that the collective beam dynamics, at the leading semiclassical order in Planck constant can be described by a particular diffusion process, the Nelson process, which is time-reversal invariant. Its diffusion coefficient $\sqrt{N}\lambda_{c}$ represents a semiclassical unit of emittance (here $N$ is the number of particles in the beam, and $\lambda_{c}$ is the Compton wavelength). The stochastic dynamics of the Nelson type can be easily recast in the form of a Schroedinger equation, with the semiclassical unit of emittance replacing Planck constant. Therefore we provide a physical foundation to the several quantum-like models of beam dynamics proposed in recent years. We also briefly touch upon applications of the Nelson and Schroedinger formalisms to incorporate the description of collective coherent effects.
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"abstract": "A recent proposal (see quant-ph/9803068) to simulate semiclassical\ncorrections to classical dynamics by suitable classical stochastic fluctuations\nis applied to the specific instance of charged beam dynamics in particle\naccelerators. The resulting picture is that the collective beam dynamics, at\nthe leading semiclassical order in Planck constant can be described by a\nparticular diffusion process, the Nelson process, which is time-reversal\ninvariant. Its diffusion coefficient $\\sqrt{N}\\lambda_{c}$ represents a\nsemiclassical unit of emittance (here $N$ is the number of particles in the\nbeam, and $\\lambda_{c}$ is the Compton wavelength). The stochastic dynamics of\nthe Nelson type can be easily recast in the form of a Schroedinger equation,\nwith the semiclassical unit of emittance replacing Planck constant. Therefore\nwe provide a physical foundation to the several quantum-like models of beam\ndynamics proposed in recent years. We also briefly touch upon applications of\nthe Nelson and Schroedinger formalisms to incorporate the description of\ncollective coherent effects.",
"arxiv_id": "physics/9803036",
"authors": [
"Salvatore De Martino",
"Silvio De Siena",
"Fabrizio Illuminati"
],
"categories": [
"physics.acc-ph",
"physics.plasm-ph"
],
"title": "A stochastic model for the semiclassical collective dynamics of charged beams in particle accelerators",
"url": "https://arxiv.org/abs/physics/9803036"
},
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