The effect of structure on the stability of detonations I. Role of the induction zone

The linear stability of steady, plane, overdriven detonations is considered when the disturbance wavelength is much larger than the thickness of the wave. In the limit of very long wavelengths, the structure palys no role and we merely recover results of Erpenbeck, Majda, and Rosales, albeit in a more transparent fashion. Otherwise, by (realistically) considering an induction zone behind the lead shock that is very sensitive to the shock temperature, we find that the detonation wave is unstable under all conditions. The neutrally stable modes described by Majda & Rosales (which they claim are responsible for the observed diamond patterns) are found to be either stabilized or nonexistent. Our present analysis does not select a most unstable wave mode, a requirement if the diamond patterns are to be expalined, but a slight modification does. The latter, which takes account of futher reaction (in the burnt gas), will be the subject of Part II.