RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. The transformation peculiarities that the electromagnetic pulses get when heading towards a boundary that performs uniformly accelerated relativistic motion are the present paper concern. A smooth non-stationarity case when the boundary velocity gradually changes from zero to the pulse velocity value is considered, with a focus on the spacetime distribution and evolution of the electromagnetic Airy pulse field.

Methods and methodology. The study and analysis are carried out by the method of Volterra integral equations which can describe electromagnetic wave propagation in a heterogeneous time-varying medium. In terms of this method, the basic initial boundary value electrodynamical problem on the electromagnetic source radiation in a heterogeneous time-varying medium is formulated, taking into account the boundary and initial conditions. The resolvent method for solving the Volterra integral equation of the second kind is described. Its advantage is analytical solution capabilities and a versatility as to the primary field choice.

Results. Analytical solutions to the original integral equation have been obtained. By analysis, it has been found that the secondary field expressions have singularities that can be controlled well enough by a proper choice of numerical modeling parameters. The revealed singularities have been analytically studied. Their action on the Airy pulse was examined and illustrated through simulation modeling using the starting parameter that locates the Airy pulse at any moment in time.

Conclusions. In this work, the electromagnetic Airy pulse interaction with a boundary perfoming uniformly accelerated relativistic motion was examined using the Volterra integral equations method. The obtained analytical solutions revealed significant spacetime changes in the Airy pulses. Our analysis indicated possibilities for controlling the secondary field characteristics by a proper choice of modeling parameters. The results have been confirmed by numerical simulations. They provide a basis for further research in this area.

Keywords: Airy pulse; electromagnetic waves; Volterra integral equations; resolvent; relativistic motion; uniformly accelerated motion

Manuscript submitted  25.03.2024

Radio phys. radio astron. 2024, 29(4): 271-280

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