Near-ideal relaxed MHD in slab geometry

We investigate the solutions of the relaxed MHD model (RxMHD) of Dewar \& Qu [J. Plasma Phys. {\bf 88}, 835880101 (2022)]. This model is a generalization of Taylor relaxation that allows the ideal Ohm's law constraint to be included, and this offers a pathway to extend the multi-region relaxed MHD (MRxMHD) model. By constructing solutions numerically, we show that the RxMHD model of Dewar \& Qu is mathematically well-defined and computationally feasible for constructing MHD equilibria. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum (as is done in the case of MRxMHD with flow), and a pressure profile with a small gradient due to the Bernoulli flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.