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Maps for Electron Clouds

This study presents a simplified approach to model the evolution of electron density in beam pipes influenced by various parameters such as Secondary Electron Yield (SEY) and chamber dimensions. Using cubic mappings, we derive recursive equations to represent electron density changes during bunch passages. By identifying key coefficients for growth, saturation, and decay, we show that the electron density evolution can be consistently described across different bunch patterns. The findings align qualitatively with prior results and offer insights for optimizing beam stability in high-energy physics environments like the LHC.

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Maps for Electron Clouds

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  1. Maps for Electron Clouds • For a given beam pipe characteristics (SEY, Chamber dimensions, etc.) the evolution of the electron density is only driven by the bunch passing by, and the existing electron density before the bunch passed by. • m+1= F(m) • Simplify the Electron Cloud problem into a small number of mathematical parameters

  2. Maps for Electron Clouds U.Iriso, S.Pegg, Phys. Rev. ST-AB8, 024403 (2005) • For the typical parameters of RHIC, the bunch-to-bunch evolution of the electron density can be represented by a cubic map: • m+1= a m+b m2+c m3 • Three sets of coefficients are needed to describe growth saturation and decay of the electron cloud density.

  3. Maps for Electron Clouds: Application to LHC SEY=1.7 N=1.6 1011 Qualitative agreement with previous results (Iriso and Pegg)

  4. Bunch Patterns Number of Bunches = 200 Bunch Pattern (5,5) SEY=1.7; N=1.6 ·1011 Four different sets of map coefficients are needed to describe the electron density evolution

  5. Bunch Patterns cont. Map results do not depend on the initial electron density 0 Relative error under 20% For a given set of the physical parameters (Bunch Intensity, SEY, etc.), differenet Bunch Patterns can be described using the same Map coefficients

  6. Bunch Patterns cont. Number of Bunches = 100 Bunch Pattern (10,10) SEY=1.7; N=1.6 ·1011

  7. Evolution of the Map Coefficients SEY=1.7 Emax=237.125 eV PEY=7.98·10-4

  8. Evolution of the Map Coefficients cont. N=1.0 ·1011 Emax=237.125 eV PEY=7.98·10-4

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