A system comprising: a magnetic domain refining device configured to perform a magnetic domain refining process on an electrical steel sheet, the magnetic domain refining device including at least a first electron gun and a second electron gun; and an electron gun abnormality detecting device configured to detect an abnormality in electron guns of the magnetic domain refining device based on an electrical steel sheet magnetic domain structure detected by the electron gun abnormality detecting device in an inspection region (R 1) of the electrical steel sheet that has been processed by the magnetic domain refining device, wherein the inspection region (R 1) includes a boundary between a magnetic domain discontinuity generated by irradiation of a surface of the electrical steel sheet with an electron beam by the first electron gun and a magnetic domain discontinuity generated by irradiation thereof with an electron beam by the second electron gun, the electron gun abnormality detecting device comprising: a magneto-optic element; a light source configured to irradiate the magneto-optic element with linearly polarized light, wherein the magneto-optic element comprises a magneto-optic film provided with a reflective film for reflecting the linearly polarized light back through the magneto-optic film after it has been transmitted through the magneto-optic film, the magneto-optic film being configured to rotate the plane of polarization of the linearly polarized light in the presence of a magnetic field generated by a domain structure of the electrical steel sheet; a polarizing filter; and a detector configured to detect linearly polarized light having been back-reflected through the magneto-optic film and passed through the polarizing filter. a magnetic domain refining device configured to perform a magnetic domain refining process on an electrical steel sheet, the magnetic domain refining device including at least a first electron gun and a second electron gun; and an electron gun abnormality detecting device configured to detect an abnormality in electron guns of the magnetic domain refining device based on an electrical steel sheet magnetic domain structure detected by the electron gun abnormality detecting device in an inspection region (R 1) of the electrical steel sheet that has been processed by the magnetic domain refining device, wherein the inspection region (R 1) includes a boundary between a magnetic domain discontinuity generated by irradiation of a surface of the electrical steel sheet with an electron beam by the first electron gun and a magnetic domain discontinuity generated by irradiation thereof with an electron beam by the second electron gun, the electron gun abnormality detecting device comprising: a magneto-optic element; a light source configured to irradiate the magneto-optic element with linearly polarized light, wherein the magneto-optic element comprises a magneto-optic film provided with a reflective film for reflecting the linearly polarized light back through the magneto-optic film after it has been transmitted through the magneto-optic film, the magneto-optic film being configured to rotate the plane of polarization of the linearly polarized light in the presence of a magnetic field generated by a domain structure of the electrical steel sheet; a polarizing filter; and a detector configured to detect linearly polarized light having been back-reflected through the magneto-optic film and passed through the polarizing filter.