  The NASA Magnetospheric Multiscale mission has made in situ diffusion region
and kinetic-scale resolution measurements of asymmetric magnetic reconnection
for the first time, in the Earth's magnetopause. The principal theoretical tool
currently used to model collisionless asymmetric reconnection is
particle-in-cell simulations. Many particle-in-cell simulations of asymmetric
collisionless reconnection start from an asymmetric Harris-type magnetic field
but with distribution functions that are not exact equilibrium solutions of the
Vlasov equation. We present new and exact equilibrium solutions of the
Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric
current sheets, with an asymmetric Harris-type magnetic field profile, plus a
constant nonzero guide field. The distribution functions can be represented as
a combination of four shifted Maxwellian distribution functions. This
equilibrium describes a magnetic field configuration with more freedom than the
previously known exact solution and has different bulk flow properties.
