Determination and Analysis of Joule Heat and Ponderomotive Force in a Hollow Copper Cylinder Under the Action of an Electromagnetic Impulse

• Datum: 2026
• Hauptverfasser: Мусій, Роман, Кунинець, Андрій, Свідрак, Інга, Тимошенко, Надія, Шиндер, Валентин
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Online Zugang: https://mcm-math.kpnu.edu.ua/article/view/360490
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

A physical-mathematical model is proposed for determining and analyzing the patterns of Joule heat and ponderomotive force behavior in a non-ferromagnetic, long, hollow, electrically conductive cylinder under a homogeneous, transient electromagnetic field. An electrodynamic problem is formulated to obtain the determining function – the axial component of the magnetic field intensity vector. An initial-boundary value problem in electrodynamics has been formulated to determine the defining function – the axial component of the magnetic field intensity vector. The initial relations for determining the specific heat densities of Joule heat and the ponderomotive force are derived. These two physical factors arise in the cylinder due to the flow of induced currents and the interaction of these currents with an external non-stationary electromagnetic field. We used a cubic approximation for the distribution of the defining function along the radial coordinate to find the determining function. The coefficients of the cubic approximation polynomial are expressed as a linear combination of the integral characteristics of the determining function with respect to the radial variable and its boundary values on the inner and external surfaces of the cylinder. As a result, the initial-boundary value problem for the determining function is reduced to a Cauchy problem for its integral characteristics. The solution to the Cauchy problem is obtained using the Laplace integral transform with respect to time. We found the expressions for the axial component of the magnetic field intensity vector and for the specific densities, Joule heat, and ponderomotive force under the action of a single electromagnetic impuls. For a hollow copper cylinder, the time evolution of the above quantities and their distributions along the thickness of the cylinder have been numerically analyzed. It has been established that the maximum values of the Joule heat and the radial component of the ponderomotive force vector on the mid-surface of the cylinder are approximately 1000 and 100 times smaller, respectively, than their values on the external surfaces of the cylinder. We found that as the thickness of the hollow cylinder under consideration increases – while the radius of its mid-surface remains constant – the maximum values of the Joule heat and the ponderomotive force decrease (by approximately a factor of 0.6) for every one-millimeter increase in the cylinder’s thickness.