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

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