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RMS Dynamic Simulation for Electron Cooling Using BETACOOL

RMS Dynamic Simulation for Electron Cooling Using BETACOOL. He Zhang Journal Club Talk, 04/01/2013. Outline. Basic idea of the RMS Dynamic Simulation Model of the ion beam Model of the electron beam Model of the cooler How BETACOOL performs the simulation

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RMS Dynamic Simulation for Electron Cooling Using BETACOOL

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  1. RMS Dynamic Simulation for Electron Cooling Using BETACOOL He Zhang Journal Club Talk, 04/01/2013

  2. Outline • Basic idea of the RMS Dynamic Simulation • Model of the ion beam • Model of the electron beam • Model of the cooler • How BETACOOL performs the simulation • A brief description of the simulation process • From emittances to coordinates to invariants • Friction force calculation • Transfer map of the cooler • Characteristic time/rate calculate • Emittance calculation He Zhang

  3. Basic idea of the RMS Dynamic Simulation • Ion bunch has Gaussian distribution in all directions • Solve this equation: • In transverse direction, εiis the emittance in horizontal or vertical direction • In longitudinal direction, coasting beam; bunched beam; Ωsis the synchrotron frequency. He Zhang

  4. Model of the ion beam • Two models: • Single particle model • Monte Carlo model • Parameters for ion beam: • Horizontal emittance • Vertical emittance • Momentum spread • Number of particles • Model particles (only for Monte Carlo model) He Zhang

  5. Model of the electron beam • According to different geometry and different charge distribution, BETACOOL provides the following models: • Uniform cylinder, Gaussian cylinder, Hollow beam, Uniform bunch, Gaussian bunch, Electron array, Parabolic, File. • Set up the Gaussian bunch model One way: Input bunch size and angle, input number of electrons The other way: Input bunch size and choose from model, imputemittance, temperature, or r.m.s. velocity, input number of electrons. He Zhang

  6. Model of the cooler • Parameters for the cooler: • Cooler length • Magnetic field • Section number • Bunch number • Distance between bunches • Cooler model: thin lens, Euler model, RungeKutta model • Integration steps (for Euler model and RungeKutta model) • Lattice: β, α, η, and ή • Shifts He Zhang

  7. How BETACOOL performs the simulation He Zhang

  8. Emittances to Coordinates to Invariants • Single particle model: Transversely, Longitudinally, He Zhang

  9. Emittances to Coordinates to Invariants • Monte Carlo model Transversely, Longitudinally, Invariants are calculated statistically. He Zhang

  10. Friction Force Calculation • Many friction force models: Consider Non-magnetic Meshkov model as an example Besides the constants, we need He Zhang

  11. Friction Force Calculation • We have found • Many models for electron bunch distribution. Consider the Gaussian bunch as an example: Plug in the ion coordinates into the function above to get ne . • Define directly, or define temperature, emittance, velocity spread for the electron bunch, and the program will calculate • Now the friction force can be calculated. He Zhang

  12. Calculate the New Emittance He Zhang

  13. Thanks for your time! He Zhang

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