Profiles and polarizations of the Balmer-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>line from high-temperature hydrogen atoms in strong magnetic fields

Abstract

Energies and eigenstates are obtained for the $n=2$ and $n=3$ levels of hydrogen atoms moving in strong magnetic fields. The Hamiltonian of the system includes the interaction with the Lorentz field, $\stackrel{\ensuremath{\rightarrow}}{E}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{B}$, as well as the magnetic interaction, $\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{B}$. These results are utilized together with the Doppler shifts in order to obtain profiles and polarizations of the Balmer-$\ensuremath{\alpha}$ line in tokamak-like environments under the assumption that the velocity distributions are Maxwellian.