A Novel Method to Determine Magnetic Fields in low-density Plasma e.g. Solar Flares Facilitated Through Accidental Degeneracy of Quantum States in Fe$^{9+}$

TL;DR

This paper introduces a new spectroscopic method using Fe$^{9+}$ ions to measure magnetic fields in astrophysical plasmas, especially solar flares, by analyzing magnetic-field induced electric dipole transitions.

Contribution

The paper proposes a novel technique leveraging accidental degeneracy in Fe$^{9+}$ ions to determine magnetic field strengths in low-density plasmas.

Findings

Theoretical calculations of transition rates induced by magnetic fields.

Proposal for experimental measurement of energy differences between near-degenerate states.

Potential application to direct magnetic field measurements in solar flares.

Abstract

We propose a new method to determine magnetic fields, by using the magnetic-field induced electric dipole transition $3p^43d\,^4\mathrm{D}_{7/2}$ $\rightarrow$ $3p^5\, ^2\mathrm{P}_{3/2}$ in Fe$^{9+}$ ions. This ion has a high abundance in astrophysical plasma and is therefore well-suited for direct measurements of even rather weak fields in e.g. solar flares. This transition is induced by an external magnetic field and its rate is proportional to the square of the magnetic field strength. We present theoretical values for what we will label the reduced rate and propose that the critical energy difference between the upper level in this transition and the close to degenerate $3p^43d\, ^4\mathrm{D}_{5/2}$ should be measured experimentally since it is required to determine the relative intensity of this magnetic line for different magnetic fields.