muons-betatron-oscillations

This repository contains C++ and MATLAB files for simulating the horizontal and vertical betatron oscillations of muons in the g-2 storage ring at KEK, JAPRC. The simulations use the Runge-Kutta 4th Order (RK4) method to solve the equations of motion in a weak focusing storage ring.

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Project Structure

Files Overview

• Horizontal Betatron Oscillation:

  • Horizontal Betatron Oscillation.cpp: A C++ program that simulates horizontal betatron oscillations using RK4 and saves position and velocity data to a text file.
  • Horizontal_Betatron_Oscillation.m: A MATLAB script to visualize the results (position and velocity vs. time).

• Vertical Betatron Oscillation:

  • Vertical Betatron Oscillation.cpp: A C++ program that simulates vertical betatron oscillations using RK4 and saves position and velocity data to a text file.
  • Vertical_Betatron_Oscillation.m: A MATLAB script to visualize the results (position and velocity vs. time).

Output Files

• horizontal_betatron_oscillation_cm.txt: Contains time, position (x), and velocity ((\dot{x})) data for the horizontal oscillation in centimeters and seconds.
• muon_VBO_trajectory_cm.txt: Contains time, position (z), and velocity ((\dot{z})) data for the vertical oscillation in centimeters and seconds.

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Simulation Details

Horizontal Betatron Oscillations

• Equation of Motion:
  x'' + ω₀²(1 - n)x = 0
  Where:

  • ω₀: Theoretical angular frequency.
  • n: Field index (weak focusing strength).

• Initial Conditions:

  • x(0) = 1.0 cm
  • x'(0) = 0.0 cm/s

• Time Step: 1 ns

• Duration: 120 ns

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Vertical Betatron Oscillations

• Equation of Motion:
  z'' + nω₀²z = 0
  Where:

  • ω₀: Theoretical angular frequency.
  • n: Field index.

• Initial Conditions:

  • z(0) = 5.0 cm
  • z'(0) = 0.0 cm/s

• Time Step: 1 ns

• Duration: 10 μs

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Visualization

MATLAB Plots

The MATLAB scripts generate the following visualizations:

1. Position vs. Time:
   • Displays the oscillatory motion of muons in the weak focusing field.
2. Velocity vs. Time:
   • Illustrates the velocity variation corresponding to the oscillations.

Each MATLAB script uses sgtitle to group the plots under a single heading.

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How to Use

1. C++ Programs:

   • Compile the .cpp files using a C++ compiler (e.g., g++).

     g++ Horizontal\ Betatron\ Oscillation.cpp -o horizontal
     ./horizontal

   • The output data will be saved to a text file (e.g., horizontal_betatron_oscillation_cm.txt).

2. MATLAB Scripts:

   • Run the .m files in MATLAB after generating the respective output data from the C++ programs.
   • Example:

     run('Horizontal_Betatron_Oscillation.m')

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Dependencies

• C++:
  • Any standard C++ compiler (e.g., GCC, Clang, MSVC).
• MATLAB:
  • MATLAB version with basic plotting capabilities.

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Applications

These simulations are part of the study of betatron oscillations, which are crucial for understanding:

• The dynamics of stored muons in weak focusing fields.
• The design and analysis of storage rings for high-energy particle experiments like the Muon g-2/EDM experiment at J-PARC.

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