Abel Integral Equation in the Reconstruction of the Helical Magnetic Field Structure by the Polarized Synchrotron Radiation of AGN Jet

This paper is devoted to the mathematical part of the inverse problem of reconstructing the magnetic structure in AGN jets from data on the rotation measure for the polarization angle of synchrotron emission from relativistic electrons. Based on the azimuthal symmetry of the helical field, we show how the reconstruction problem reduces to the integral Abel equation. By giving a solution to this equation, we formulate the constraints on the magnetic field components and thermal electron density under which the problem has a unique and stable solution. These results may be useful to astrophysicists and experts in integral equations and inverse problems.