RMS Dynamic Simulation for Electron Cooling Using BETACOOL
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Transcript of RMS Dynamic Simulation for Electron Cooling Using BETACOOL
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RMS Dynamic Simulation for Electron Cooling Using
BETACOOL
He Zhang
Journal Club Talk, 04/01/2013
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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
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Basic idea of the RMS Dynamic Simulation
• Ion bunch has Gaussian distribution in all directions• Solve this equation:
• In transverse direction, εi is the emittance in horizontal or vertical direction
• In longitudinal direction,coasting beam;
bunched beam;
Ωs is the synchrotron frequency.
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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)
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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, imput emittance, temperature, or r.m.s. velocity, input number of electrons.
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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, Runge Kutta model Integration steps (for Euler model and Runge Kutta model) Lattice: β, α, η, and η Shifts
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How BETACOOL performs the simulation
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Emittances to Coordinates to Invariants
• Single particle model:Transversely,
Longitudinally,
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Emittances to Coordinates to Invariants
• Monte Carlo modelTransversely,
Longitudinally,
Invariants are calculated statistically.
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Friction Force Calculation
• Many friction force models: Consider Non-magnetic Meshkov model as an example
Besides the constants, we need
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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.
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Calculate the New Emittance
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Thanks for your time!