Two-dimensional, collision free, z-independent equilibria of a high- beta plasma in an external magnetic field are studied, using distributions of the form f(H,pz). The charge-neutral approximation then makes the macroscopic moments and the electrostatic potential functions of the magnetic vector potential A only, whereby these quantities assume constant values along the magnetic field lines, and the treatment becomes essentially one-dimensional with the use of flux coordinates. MHD-like equations of simple form for both particle species are obtained, including both an ambipolar electric field, arbitrarily large gyro excursions and lines with zero magnetic field component in the (r, theta ) plane. These equations provide useful interrelations between the macroscopic quantities that may be of value for interpretation of experimental results. A parametrized subclass of distributions gives a flexible tool for constructing solutions corresponding to given macroscopic profiles, and an expression for the smallest obtainable pinch radius is derived. An alternative to free-boundary methods for computing the magnetic field is presented. Intended applications concern linear and large aspect ratio toroidal systems of z pinch and multipole type.