  An electrostatic, implicit particle-in-cell (PIC) model for collisionless,
fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced
with exact charge, energy, and magnetic moment conservation properties. The
approach is adaptive in configuration space by the use of mapped meshes, and
exploits the strict conservation of the magnetic moment to reduce the
dimensionality of velocity space. A new particle integrator is implemented,
which allows for particle substepping without the need to stop particle motion
at every cell for charge conservation. Particle suborbits are determined from
accuracy considerations, and are allowed to span multiple cells. Novel particle
injection and expansion-to-infinity boundary conditions are developed,
including a control loop to prevent the formation of spurious sheaths at the
edges of the domain. The algorithm is verified in a periodic magnetic mirror
configuration, a uniform plasma test case (to test particle injection), and a
propulsive magnetic nozzle. The algorithm's computational complexity is shown
to scale favorably with timestep, and linearly with the number of particles and
mesh cells (unlike earlier implicit PIC implementations, which scaled
quadratically with the number of mesh cells in one dimension). Numerical
experiments demonstrate that the proposed algorithm outperforms both explicit
PIC and semi-Lagrangian Vlasov codes by more than an order of magnitude.
