instabilities.py

# -*- coding: utf-8 -*-
"""
General calculations about instabilities

@author: Alexis Gamelin
@date: 15/01/2020
"""

from scipy.constants import c, m_e, e, pi, epsilon_0

def MBI_threshold(ring, sigma, R, b):
    """
    Compute the microbunching instability (MBI) threshold for a bunched beam
    considering the steady-state parallel plate model [1][2].
    
    Parameters
    ----------
    ring : Synchrotron object
    sigma : float
        RMS bunch length in [s]
    R : float
        dipole bending radius in [m]
    b : float
        vertical distance between the conducting parallel plates in [m]
        
    Returns
    -------
    I : float
        MBI current threshold
        
    [1] : Y. Cai, "Theory of microwave instability and coherent synchrotron 
    radiation in electron storage rings", SLAC-PUB-14561
    [2] : D. Zhou, "Coherent synchrotron radiation and microwave instability in 
    electron storage rings", PhD thesis, p112
    """

    Ia = 4*pi*epsilon_0*m_e*c**3/e # Alfven current
    chi = sigma*(R/b**3)**(1/2) # Shielding paramter
    xi = 0.5 + 0.34*chi
    N = (ring.L0 * Ia * ring.ac * ring.gamma * ring.sigma_delta**2 * xi *
        sigma**(1/3) / ( c * e * R**(1/3) ))
    I = N*e/ring.T0
    
    return I