To achieve stable detonation wave propagation to large-bore pulse detonation engine (PDE) combustors, we investigated an initiator for PDEs that uses a pre-detonator, reflector, and driver gas. In this initiator, a planar detonation wave from the pre-detonator becomes a cylindrical detonation wave after collision with the reflector. Wakita et al. previously posited two hypotheses regarding the dominant factors that determine the threshold of propagation to the target gas, which is a stoichiometric hydrogen-oxygen mixture diluted with nitrogen. This study reveals whether the threshold is determined by w/λ or λ/r. To analyze the effect of channel width w on the transition of the cylindrical detonation wave, experiments were conducted for w = 10 mm and w = 15 mm. However, the results could not elucidate whether the threshold is determined by λ/r or w/λ. To clearly distinguish between the effects of w/λ and λ/r, a narrow channel width w' = 3 mm was chosen and implemented using a torus-shaped obstacle. The results showed that a cylindrical detonation wave propagates without quenching when the nitrogen concentration is above 40%, corresponding to the cell size λ greater than w. Accordingly, the cylindrical detonation propagation threshold was determined to be independent of w/λ.