starkzee

A Python library implementing a coupled Stark-Zeeman plasma line-shape model for hydrogen-like radiators, based on:

S. Ferri, O. Peyrusse, A. Calisti, et al., “Stark-Zeeman line-shape model for multi-electron ions in hot dense plasmas”, Matter and Radiation at Extremes 7, 015901 (2022).

StarkZee implements the Standard Lineshape Theory for emission lines of hydrogen-like ions in a magnetized plasma. Ions are treated in the quasi-static approximation: the ion microfield at the radiator site is assumed stationary on the timescale of the emitted photon, and the spectral profile is obtained by averaging Stark-Zeeman Hamiltonians over the ion microfield distribution. Electron broadening is represented by weak binary collisions within the Griem–Baranger–Kolb (GBK) binary-collision relaxation model, which accounts for the suppression of broadening at large frequency detunings through a semi-classical exponential-integral factor and a magnetic-field-dependent lower cutoff. The static magnetic field enters the radiator Hamiltonian directly — in the electric-dipole approximation — producing coupled Stark-Zeeman energy levels and polarized π and σ± emission components. Ion dynamics are optionally included via the Frequency Fluctuation Model (FFM), which treats the microfield as a Markovian jump process between quasi-static configurations. The static ion microfield distribution is evaluated using the analytical Hooper screened distribution, parametrized by the electron–ion screening factor a = re / λD (ratio of the mean inter-particle distance to the electron Debye length).

The code computes emission line profiles of hydrogen-like ions in a magnetic field B, accounting for:

  • Quasi-static ion microfield broadening (Holtsmark / Hooper distributions)

  • Electron impact broadening (GBK model with Larmor-frequency cutoff)

  • Ion dynamics via the Frequency Fluctuation Model (FFM)

  • Spin-orbit coupling and the quadratic (diamagnetic) Zeeman term

  • Doppler and instrumental broadening as post-processing convolutions

import numpy as np
from starkzee.line_profile import LineProfile

lp = LineProfile(n_u=3, n_l=2, Z=1, B=5.0, Ne_m3=1e20, Te_ev=5.0)
energies = lp.E0 + np.linspace(-0.005, 0.005, 1000)
lp.compute_profile(energies, num_f=30, num_mu=8)

import matplotlib.pyplot as plt
plt.plot(lp.wavelengths_nm - lp.E0_wavelength_nm, lp.profile_transverse)
plt.xlabel("Δλ (nm)")

Getting started

Background

API reference