  We extend previous studies of the conformal 0+1d kinetic non-equilibrium
attractor in relaxation time approximation by enforcing number conservation
through the introduction of a dynamical fugacity (chemical potential). We
derive two coupled integral equations for the effective temperature and
fugacity which are then solved numerically to obtain the exact solution. The
resulting solutions exhibit convergence to a unique non-equilibrium attractor
when the scaled moments of the distribution function are plotted as a function
of the rescaled time w = tau/tau_eq. This occurs even though the system is out
of chemical equilibrium at late times. In addition, compared to the case where
number conservation was not imposed, we find that the moments converge to their
respective attractors more quickly, particularly for moments with m=0. Finally,
we compare the resulting attractor moments with predictions from different
hydrodynamic frameworks.
