  A first-order model is derived for quasisymmetric stellarators where the
vacuum field due to coils is dominant, but plasma-current-induced terms are not
negligible and can contribute to magnetic differential equations, with $\beta$
of the order of the ratio of induced to vacuum fields. Under these assumptions,
it is proven that the aspect ratio must be large and a simple expression can be
obtained for the lowest-order vacuum field. The first-order correction, which
involves both vacuum and current-driven fields, is governed by a Grad-Shafranov
equation and the requirement that flux surfaces exist. These two equations are
not always consistent, and so this model is generally overconstrained, but
special solutions exist that satisfy both equations simultaneously. One family
of such solutions are the first-order near-axis solutions. Thus, the
first-order near-axis model is a subset of the model presented here. Several
other solutions outside the scope of the near-axis model are also found. A case
study comparing one such solution to a VMEC-generated solution shows good
agreement.
