IntraBeam Scattering

Analytical Growth Rates

The following example illustrates how to obtain IntraBeam Scattering growth rates in Xsuite. The functionality is exposed through the TwissTable and can make use of two different formalism, Nagaitsev and Bjorken-Mtingwa. The former provides a computationally efficient approach but does not account for vertical dispersion, while the latter accounts for it but is slower.

See also: xtrack.twiss.TwissTable.get_ibs_growth_rates()

import json

import numpy as np
import xtrack as xt

from xfields.ibs import get_intrabeam_scattering_growth_rates

##########################
# Load xt.Line from file #
##########################

fname_line_particles = "../../../xtrack/test_data/lhc_no_bb/" \
                       "line_and_particle.json"

with open(fname_line_particles, "r") as fid:
    input_data = json.load(fid)

line = xt.Line.from_json(fname_line_particles)
line.particle_ref = xt.Particles.from_dict(input_data["particle"])
tw = line.twiss(method="4d")

#####################
# Define parameters #
#####################

# Line is for LHC protons at top energy
bunch_intensity: int = int(1.8e11)
nemitt_x: float = 1.8e-6
nemitt_y: float = 1.8e-6
sigma_delta: float = 4.71e-5
bunch_length: float = 3.75e-2

###################################
# Get growth rates with Nagaitsev #
###################################

nag_growth_rates = tw.get_ibs_growth_rates(
    formalism="nagaitsev",
    total_beam_intensity=bunch_intensity,
    nemitt_x=nemitt_x,
    nemitt_y=nemitt_y,
    sigma_delta=sigma_delta,
    bunch_length=bunch_length,
    bunched=True,
)

#########################################
# Get growth rates with Bjorken-Mtingwa #
#########################################

bm_growth_rates = tw.get_ibs_growth_rates(
    formalism="bjorken-mtingwa",  # also accepts "b&m"
    total_beam_intensity=bunch_intensity,
    nemitt_x=nemitt_x,
    nemitt_y=nemitt_y,
    sigma_delta=sigma_delta,
    bunch_length=bunch_length,
    bunched=True,
)


##########################################################
# Compare: we expect Nagaitsev to be wrong in horizontal #
##########################################################

print()
print("Computed from normalized emittances:")
print("------------------------------------")
print(f"Nagaitsev:       {nag_growth_rates}")
print(f"Bjorken-Mtingwa: {bm_growth_rates}")

#####################
# Define parameters #
#####################

gemitt_x: float = 2.598e-10
gemitt_y: float = 2.598e-10

###################################
# Get growth rates with Nagaitsev #
###################################

nag_growth_rates2 = tw.get_ibs_growth_rates(
    formalism="nagaitsev",
    total_beam_intensity=bunch_intensity,
    gemitt_x=gemitt_x,
    gemitt_y=gemitt_y,
    sigma_delta=sigma_delta,
    bunch_length=bunch_length,
    bunched=True,
)

#########################################
# Get growth rates with Bjorken-Mtingwa #
#########################################

bm_growth_rates2 = tw.get_ibs_growth_rates(
    formalism="bjorken-mtingwa",  # also accepts "b&m"
    total_beam_intensity=bunch_intensity,
    gemitt_x=gemitt_x,
    gemitt_y=gemitt_y,
    sigma_delta=sigma_delta,
    bunch_length=bunch_length,
    bunched=True,
)

##########################################################
# Compare: we expect Nagaitsev to be wrong in horizontal #
##########################################################

print()
print("Computed from geometric emittances (rough equivalent):")
print("------------------------------------------------------")
print(f"Nagaitsev:       {nag_growth_rates2}")
print(f"Bjorken-Mtingwa: {bm_growth_rates2}")

# Complete source: xfields/examples/005_ibs/001_growth_rates_from_parameters_with_vdisp.py