Scattering of acoustic waves by a magnetic cylinder

With the aim of studying magnetic effects in time-distance helioseismology, we use the first-order Born approximation to compute the scattering of acoustic plane waves by a magnetic cylinder embedded in a uniform medium. We show, by comparison with the exact solution, that the travel-time shifts computed in the Born approximation are everywhere valid to first order in the ratio of the magnetic to the gas pressures. We also show that, for arbitrary magnetic field strength, the Born approximation is not valid in the limit where the radius of the magnetic cylinder tends to zero.