On the range of the attenuated magnetic ray transform for connections and Higgs fields

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,\mathrm{\Phi }}$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $\mathrm{\Phi }$. We give a description for the range of $I_{A,\mathrm{\Phi }}$ acting on ${\mathbb{C}}^n$-valued tensor fields.