Collisional redistribution of hydrogen line radiation in low- and moderate-density magnetized plasmas

A computer simulation technique has been applied to the modeling of radiation redistribution functions in low- and moderate-density magnetized hydrogen plasmas. The radiating dipole is described within the Heisenberg picture, and perturbations by the plasma microfield are accounted for through a time-dependent Stark effect term in the Hamiltonian. Numerical applications are presented for the first Lyman and Balmer lines at plasma conditions relevant to tokamak divertors and magnetized white dwarf atmospheres. In both cases, the collisional redistribution of the radiation frequency is shown to be incomplete. Comparisons with a previously developed impact model are performed, and results are discussed.

Figure 1

Plot of the Lyman $\alpha$ line shape function $F\left(\omega \right)$ normalized to unity. A numerical simulation method has been used. Both resonance fluorescence and Rayleigh components are visible in the spectrum, which indicates that the radiation redistribution is incomplete. Only the $\sigma$ components of the spectrum are shown here for the sake of clarity.

Figure 2

Plot of the Lyman $\beta$ line shape function for the same conditions as in Fig. 1. The redistribution is also incomplete. The Zeeman components are broader than those of Lyman $\alpha$ because the Stark effect is more important for this line.

Figure 3

Plot of the Lyman $\alpha$ line shape obtained from the impact model. The Zeeman components have different amplitudes, which is in contrast to the simulation result in Fig. 1. A reason for this is that interferences between the scattering amplitudes are not retained within this model. See the text for explanation.

Figure 4

If the interferences between the scattering amplitudes are removed from the simulation, the two results are in agreement with each other. Here, the Lyman $\alpha$ line shape has been calculated with the same conditions as in Figs. 1 and 3.

Figure 5

The Stark widths obtained from the impact model and the simulation are also in good agreement. Here, the simulation and impact results are plotted for the same plasma conditions. For the sake of clarity, the magnetic field has been set equal to zero.

Figure 6

Plot of the $H\alpha$ and $H\beta$ line shapes in white dwarf atmosphere conditions. The redistribution is incomplete in both cases.

Figure 7

White dwarfs can have a very strong magnetic spectrum, resulting in asymmetric Zeeman spectra. Here, this effect is illustrated in the case of $H\beta$ under a magnetic field of 2 kT. The quadratic Zeeman effect yields a shift of the overall line and splitting of the components. The unperturbed $H\beta$ frequency is shown as reference. The Rayleigh peak is still visible, indicating that redistribution is incomplete.