The singular behaviour of ambipolar diffusion revealed by 1D Cartesian solutions

Ambipolar diffusion is increasingly recognised as a key process in the lower solar atmosphere. Its highly non-linear behaviour has many non-intuitive aspects. We seek to (a) study 1D Cartesian ambipolar diffusion near null points; (b) characterise the non-linear eigenmodes for ambipolar diffusion; and (c) propose tests for ambipolar diffusion solvers in MHD codes. (a) We employed a direct analysis to obtain analytical solutions for ambipolar diffusion. (b) To study the eigenmodes, we solved the