  The $^{18}$Ne($\alpha$,$p$)$^{21}$Na reaction provides a pathway for breakout
from the hot CNO cycles to the $rp$-process in type I x-ray bursts. To better
determine this astrophysical reaction rate, the resonance parameters of the
compound nucleus $^{22}$Mg have been investigated by measuring the resonant
elastic scattering of $^{21}$Na+$p$. An 89 MeV $^{21}$Na radioactive ion beam
was produced at the CNS Radioactive Ion Beam Separator and bombarded an 8.8
mg/cm$^2$ thick polyethylene target. The recoiled protons were measured at
scattering angles of $\theta_{c.m.}$$\approx 175 {^\circ}$ and 152${^\circ}$ by
three $\Delta E$-$E$ silicon telescopes. The excitation function was obtained
with a thick-target method over energies $E_x$($^{22}$Mg)=5.5--9.2 MeV. The
resonance parameters have been determined through an $R$-matrix analysis. For
the first time, the $J^{\pi}$ values for ten states above the alpha threshold
in $^{22}$Mg have been experimentally determined in a single consistent
measurement. We have made three new $J^{\pi}$ assignments and confirmed seven
of the ten tentative assignments in the previous work. The
$^{18}$Ne($\alpha$,$p$)$^{21}$Na reaction rate has been recalculated, and the
astrophysical impact of our new rate has been investigated through one-zone
postprocessing x-ray burst calculations. We find that the
$^{18}$Ne($\alpha$,$p$)$^{21}$Na rate significantly affects the peak nuclear
energy generation rate and the onset temperature of this breakout reaction in
these phenomena.
