  The run-and-tumble walk, consisting in randomly reoriented ballistic
excursions, models phenomena ranging from gas kinetics to bacteria motility. We
evaluate the mean time required for this walk to find a fixed target within a
2D or 3D spherical confinement. We find that the mean search time admits a
minimum as a function of the mean run duration for various types of boundary
conditions and run duration distributions (exponential, power-law,
deterministic). Our result stands in sharp contrast to the pure ballistic
motion, which is predicted to be the optimal search strategy in the case of
Poisson distributed targets.
