  We present a new, completely Lagrangian magnetohydrodynamics code that is
based on the SPH method. The equations of self-gravitating hydrodynamics are
derived self-consistently from a Lagrangian and account for variable smoothing
length (``grad-h''-) terms in both the hydrodynamic and the gravitational
acceleration equations. The evolution of the magnetic field is formulated in
terms of so-called Euler potentials which are advected with the fluid and thus
guarantee the MHD flux-freezing condition. This formulation is equivalent to a
vector potential approach and therefore fulfills the
$\vec{\nabla}\cdot\vec{B}=0$-constraint by construction. Extensive tests in
one, two and three dimensions are presented. The tests demonstrate the
excellent conservation properties of the code and show the clear superiority of
the Euler potentials over earlier magnetic SPH formulations.
