  Background: Type I x-ray bursts are the most frequent thermonuclear
explosions in the galaxy, resulting from thermonuclear runaway on the surface
of an accreting neutron star. The $^{30}$S($\alpha$,p) reaction plays a
critical role in burst models, yet insufficient experimental information is
available to calculate a reliable, precise rate for this reaction. Purpose: Our
measurement was conducted to search for states in $^{34}$Ar and determine their
quantum properties. In particular, natural-parity states with large
$\alpha$-decay partial widths should dominate the stellar reaction rate.
Method: We performed the first measurement of $^{30}$S+$\alpha$ resonant
elastic scattering up to a center-of-mass energy of 5.5 MeV using a radioactive
ion beam. The experiment utilized a thick gaseous active target system and
silicon detector array in inverse kinematics. Results: We obtained an
excitation function for $^{30}$S($\alpha$,$\alpha$) near $150^{\circ}$ in the
center-of-mass frame. The experimental data were analyzed with an $R$-Matrix
calculation, and we observed three new resonant patterns between 11.1 and 12.1
MeV, extracting their properties of resonance energy, widths, spin, and parity.
Conclusions: We calculated the resonant thermonuclear reaction rate of
$^{30}$S($\alpha$,p) based on all available experimental data of $^{34}$Ar and
found an upper limit about one order of magnitude larger than a rate determined
using a statistical model. The astrophysical impact of these two rates has been
investigated through one-zone postprocessing type I x-ray burst calculations.
We find that our new upper limit for the $^{30}$S($\alpha$,p)$^{33}$Cl rate
significantly affects the predicted nuclear energy generation rate during the
burst.
