In the present paper, by using a mathematical model for self-propagating high-temperature synthesis, we reveal the three-dimensional structure of so-called spin combustion wave on the inside of cylindrical sample. It is shown that an isothermal surface of regular spin combustion wave has some wings of which number is the same as that of reaction spots on the cylindrical surface and that the isothermal surface with helical wings rotates down with time. Because of this propagating pattern, in this paper, we adopt the more suitable term "helical wave." We also obtain the following existence conditions of a helical wave: If physical parameters are set so that a pulsating wave exists stably for the one-dimensional problem, then a helical wave takes the place of a pulsating wave when the radius of cylindrical sample becomes large.
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