  Axion helioscopes search for solar axions and axion-like particles via
inverse Primakoff conversion in strong laboratory magnets pointed at the Sun.
Anticipating the detection of solar axions, we determine the potential for the
planned next-generation helioscope, the International Axion Observatory (IAXO),
to measure or constrain the solar magnetic field. To do this we consider a
previously neglected component of the solar axion flux at sub-keV energies
arising from the conversion of longitudinal plasmons. This flux is sensitively
dependent to the magnetic field profile of the Sun, with lower energies
corresponding to axions converting into photons at larger solar radii. If the
detector technology eventually installed in IAXO has an energy resolution
better than 200 eV, then solar axions could become an even more powerful
messenger than neutrinos of the magnetic field in the core of the Sun. For
energy resolutions better than 10 eV, IAXO could access the inner 70% of the
Sun and begin to constrain the field at the tachocline: the boundary between
the radiative and convective zones. The longitudinal plasmon flux from a
toroidal magnetic field also has an additional 2% geometric modulation effect
which could be used to measure the angular dependence of the magnetic field.
