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The atomic interstellar medium (ISM) is observed to be full of linearstructures that are referred to as "fibers". Fibers exhibit similar propertiesto linear structures found in molecular clouds known as striations. Suggestiveof a similar formation mechanism, both striations and fibers appear to beordered, quasi-periodic, and well-aligned with the magnetic field. Theprevailing formation mechanism for striations involves the excitation of fastmagnetosonic waves. Based on this theoretical model, and through a combinationof velocity centroids and column density maps, Tritsis et al. (2018) developeda method for estimating the plane-of-sky (POS) magnetic field from molecularcloud striations. We apply this method in two H\textsc{I} clouds with fibersalong the same line-of-sight (LOS) towards the ultra-high-energy cosmic-ray(UHECR) hotspot, at the boundaries of Ursa Major. For the cloud located closerto Earth, where Zeeman observations from the literature were also available, wefind general agreement in the distributions of the LOS and POS components ofthe magnetic field. We find relatively large values for the total magneticfield (ranging from $\sim$$\rm{10}$ to $\sim$$\rm{20} ~\rm{\mu G}$) and anaverage projection angle with respect to the LOS of $\sim$ 50$^\circ$. For thecloud located further away, we also find a large value for the POS component ofthe magnetic field of $15^{+8}_{-3}~\rm{\mu G}$. We discuss the potential ofour new magnetic-field tomography method for large-scale application. Weconsider the implications of our findings for the accuracy of currentreconstructions of the Galactic magnetic field and on the propagation of UHECRthrough the ISM.

Magnetic field tomography in two clouds towards Ursa Major using HI fibers