The relevance At present, the issues of creating an original design of a highly efficient explosive magnetic (magnetocumulative) generator, developing its mathematical model and conducting experimental research in this direction are topical in science and technology. Aim of research Consider the possibility of building new aircraft fuel ignition devices based on a double-helix magnetic-cumulative generator, solving the problem of confirming its advantages over known and proven methods by creating a mathematical model. Research methods Literature review and patent study, obtaining a mathematical model with experimental studies on full-scale samples in real operating conditions. In the course of the work, methods of the theory of electrical circuits, magnetic field, elements of mathematical analysis and the theory of electrical oscillatory processes (beats, resonance, etc.) in complex circuits were used. Results As a result, a relation was obtained that determines the maximum value of the beat frequency between two electrical circuits connected by a weak capacitive coupling, which makes it possible to carry out the calculations necessary when creating a magnetocumulative generator with high microwave radiation and during its regulation. Thus, the mathematical model of a magnetocumulative generator presented in the article is based on a fundamentally new combination of the application of the laws of electrodynamics and the theory of electrical oscillatory processes. On the basis of this model, proposals have been developed for using the proposed design with the original circuit design. The results of the work can be used in the ignition system of aircraft at an altitude of more than 20 km, which is a world problem, as well as to improve the efficiency of a shunt reactor, an installation for de-icing, mechanical engineering, medicine, military equipment, radio physics, etc.