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

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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!