rms dynamic simulation for electron cooling using betacool
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
RMS Dynamic Simulation for Electron Cooling Using
BETACOOL
He Zhang
Journal Club Talk, 04/01/2013
He Zhang ---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, εi is the emittance in horizontal or vertical direction
• In longitudinal direction,coasting beam;
bunched beam;
Ωs is 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, imput emittance, 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, Runge Kutta model Integration steps (for Euler model and Runge Kutta model) Lattice: β, α, η, and η 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 modelTransversely,
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!