SOLEIL II instability map

Code to reproduce Fig.3 in [1].

[1] Gamelin, A., Gubaidulin, V., Alves, M. B., & Olsson, T. (2024). Semi-analytical algorithms to study longitudinal beam instabilities in double rf systems. arXiv preprint arXiv:2412.06539.

Imports

import numpy as np
import matplotlib.pyplot as plt
from mbtrack2 import CavityResonator
from albums import scan_psi_I0
from albums import SystemState
from albums import EquilibriumOptions, TheoryOptions
from albums import DEFAULT_FLOWS

Ring and cavity setup

from mbtrack2 import Synchrotron, Electron
from mbtrack2 import Optics

def SOLEIL_II(V_RF=1.7e6):
    """
    SOLEIL II lattice v2366 w/ RF parameters from November 2023 RF budget.

    Parameters
    ----------
    V_RF : float, optional
        Total RF voltage in [V]. 
        The default is 1.7e6.
        
    Returns
    -------
    ring : Synchrotron object
        TDR lattice v2366_v3.

    """
    L = 353.97
    E0 = 2.75e9
    particle = Electron()
    ac = 1.05751e-04
    tune = np.array([54.2, 18.3])
    chro = np.array([1.6, 1.6])
    beta = np.array([3.288, 4.003])
    alpha = np.array([0, 0])
    dispersion = np.array([0, 0, 0, 0])
    h = 416
    particle = Electron()
    mcf_order = np.array([-0.00192226,  0.00061511,  0.00010695])
    U0 = 469e3
    tau = np.array([7.64e-3, 13.83e-3, 11.64e-3])
    sigma_delta = 9.063e-4
    emit = np.array([83.7e-12, 83.7e-12*0.01])
        
    optics = Optics(local_beta=beta, local_alpha=alpha, 
                  local_dispersion=dispersion)
    ring = Synchrotron(h, optics, particle, L=L, E0=E0, ac=ac, U0=U0, tau=tau,
                   emit=emit, tune=tune, sigma_delta=sigma_delta, chro=chro, 
                   mcf_order=mcf_order)
    
    tuneS = ring.synchrotron_tune(V_RF)
    ring.sigma_0 = (ring.sigma_delta * np.abs(ring.eta()) 
                    / (tuneS * 2 * np.pi * ring. f0))
    ring.get_longitudinal_twiss(V_RF)
        
    return ring
ring = SOLEIL_II(V_RF=1.7e6)

MC = CavityResonator(ring, m=1, Rs=5e6, Q=35.7e3, QL=6e3, detune=1e6, Ncav=4)
MC.Vc = 1.7e6
MC.theta = np.arccos(ring.U0/MC.Vc)

HC = CavityResonator(ring, m=4, Rs=30*31e3, Q=31e3, QL=31e3, detune=1e6, Ncav=2)

Harmonic cavity tuning vs beam current scan

psi_HC_vals = np.linspace(59.5, 90, 70) # degree
currents = np.linspace(0.195, 0.505, 50) # A

name = "SOLEIL_II_map"
f_HOM = 1700284550.0060253 # Hz
Z_HOM = 8826.533279079998 # ohm

MC = CavityResonator(ring, m=1, Rs=5e6, Q=35.7e3, QL=6e3, detune=1e6, Ncav=4)
MC.Vc = 1.7e6
MC.theta = np.arccos(ring.U0/MC.Vc)

HC = CavityResonator(ring, m=4, Rs=30*31e3, Q=31e3, QL=31e3, detune=1e6, Ncav=2)

eq_opts = EquilibriumOptions(set_MC_phase_HCpassive=True)
theory_opts = TheoryOptions(f_HOM=f_HOM, Z_HOM=Z_HOM)

result = scan_psi_I0(
            SystemState(ring, [MC, HC]),
            psi_HC_vals,
            currents,
            flow=DEFAULT_FLOWS["Alves"],
            eq_opts=eq_opts,
            theory_opts=theory_opts)

result.plot("xi")
result.plot("bunch_length")
result.plot("Touschek")
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../_images/af6b0db72707a9b13e3c1717c8ec40a685df5390b5778e480928959183b339fb.png ../_images/5a0e5f3a9a36a83c211ef123e8ea271b2e8cdb5975bc145d4b26e475830fb20e.png ../_images/022304628fd3d01ab51510d0e8d07a584f713605a3b97484be78ccfac7b288fe.png