  The recent experimental data of anomalous magnetic moments strongly indicate
the existence of new physics beyond the standard model. An energetic $\mu^+$
beam is a potential option to the expected neutrino factories, the future muon
colliders and the $\mu$SR(the spin rotation, resonance and relaxation)
technology. It is proposed a prompt acceleration scheme of the $\mu^+$ beam in
a donut wakefield driven by a shaped Laguerre-Gaussian (LG) laser pulse. The
forward part of the donut wakefield can accelerate and also focus positive
particle beams effectively. The LG laser is shaped by a near-critical-density
plasma. The shaped LG laser has the shorter rise time and can enlarge the
acceleration field. The acceleration field driven by a shaped LG laser pulse is
six times higher than that driven by a normal LG laser pulse. The simulation
results show that the $ \mu^+$ bunch can be accelerated from $200\mathrm{MeV}$
to 2GeV and the transversal size of the $\mu^+$ bunch is also focused from
initial $\omega_0=5\mu m$ to $\omega=1\mu m$ within several picoseconds.
