The spherically symmetric calculations of a thermonuclear explosion on a neutron star is extended to two dimensions. Assuming a simple dipolar field, accretion will be focused onto a small region at the polar cap. For a suitable accretion rate hydrogen burns stably by the beta-limited CNO cycle, forming a layer of helium; a thermonuclear runaway initiates at a point at the base of the helium layer. The detonation model is hydrodynamically calculated using a two-dimensional hydrodynamic code. The wave is found to propagate across the helium lake at 9000 km/s without dying out, igniting all the helium and liberating 2.4 x 10 to the 39th ergs. The rise time of the burst, determined by the time required to propagate the detonation across the helium layer, is about 50 microseconds.
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Fryxell et al. (1982) studied this question.