Linear analysis of the momentum cooling Fokker-Planck equation

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In order to optimize the extraction scheme used to take antiprotons out of the accumulator, it is necessary to understand the basic processes involved. At present, six antiproton bunches per Tevatron store are removed sequentially by RF unstacking from the accumulator. The phase space dynamics of this process, with its accompanying phase displacement deceleration and phase space dilution of portions of the stack, can be modelled by numerical solution of the longitudinal equations of motion for a large number of particles. We have employed the tracking code ESME for this purpose. In between RF extractions, however, the stochastic cooling system ... continued below

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Pages: 13

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Rosenzweig, J.B. May 4, 1989.

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Description

In order to optimize the extraction scheme used to take antiprotons out of the accumulator, it is necessary to understand the basic processes involved. At present, six antiproton bunches per Tevatron store are removed sequentially by RF unstacking from the accumulator. The phase space dynamics of this process, with its accompanying phase displacement deceleration and phase space dilution of portions of the stack, can be modelled by numerical solution of the longitudinal equations of motion for a large number of particles. We have employed the tracking code ESME for this purpose. In between RF extractions, however, the stochastic cooling system is turned on for a short time, and we must take into account the effect of momentum stochastic cooling on the antiproton energy spectrum. This process is described by the Fokker-Planck equation, which models the evolution of the antiproton stack energy distribution by accounting for the cooling through an applied coherent drag force and the competing heating of the stack due to diffusion, which can arise from intra-beam scattering, amplifier noise and coherent (Schottky) effects. In this note we examine the aspects of the Fokker-Planck in the regime where the nonlinear terms due to Schottky effects are small. This discussion ultimately leads to solution of the equation in terms of an orthonormal set of functions which are closely related to the quantum simple-harmonic oscillator wave-functions. 5 refs.

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Pages: 13

Notes

NTIS, PC A03/MF A01 - OSTI; 1.

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  • Other Information: Portions of this document are illegible in microfiche products

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  • Other: DE89013724
  • Report No.: FNAL-TM-1590
  • Grant Number: AC02-76CH03000
  • DOI: 10.2172/5995242 | External Link
  • Office of Scientific & Technical Information Report Number: 5995242
  • Archival Resource Key: ark:/67531/metadc1095689

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  • May 4, 1989

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  • Feb. 18, 2018, 3:59 p.m.

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  • May 9, 2018, 6:48 p.m.

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Rosenzweig, J.B. Linear analysis of the momentum cooling Fokker-Planck equation, report, May 4, 1989; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc1095689/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.