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Persistent URL http://purl.org/net/epubs/work/44130
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Record Id 44130
Title Equilibrium fluctuations in an n-particle coasting beam : Schottky noise effects
Abstract We discuss the longitudinal dynamics of an unbunched beam with a collective effect due to the vacuum chamber and with the discreteness of an N-particle beam (Schottky noise) included. We start with the 2N equations of motion (in angle and energy) with random initial conditions. The 2D phase space density (Klimontovich density) for the N particles is a sum of delta functions and satisfies the Klimontovich equation and the Vlasov equation. An arbitrary function of the energy also satisfies the Vlasov equation and we linearize about a convenient equilibrium density taking the initial conditions to be independent, identically distributed random variables with the equilibrium distribution. The linearized equations can be solved using a Laplace transform in time and a Fourier series in angle. The resultant stochastic process for the phase space density is analyzed and compared with a known result. Work is in progress to study the full nonlinear problem.
Organisation CI
Keywords physics
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Related Research Object(s): 34176194
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Language English (EN)
Type Details URI(s) Local file(s) Year
Preprint CI Preprints Cockcroft 07-17 2007. Submitted to: Particle Accelerator Conference 2007 (PAC07), Albuquerque, New Mexico, USA, 25-29 Jun 2007 Cockcroft-07-17.pdf 2007