Uniform asymptotic behavior of a field of rectangular radio pulses in a magnetoactive plasma

An asymptotic solution is considered for the problem of transversal propagation of rectangular radio pulses in a homogeneous magnetoactive plasma. Uniform asymptotic behavior of the pulse field is studied in the case when the radio pulse carrier frequency is close to the frequency corresponding to the maximum of the local group velocity of extraordinary wave propagation. The solution is expressed through the generalized Airy function and its two first partial derivatives. The amplitude coefficients and arguments of the corresponding functions are algebraically determined through the amplitudes and phases of the space-time rays passing through the point of observation. It is shown that in various regions the solution goes over asymptotically into the formulas of the ray method and its modifications - the half-shadow and caustic asymptotic analyses. Uniform asymptotic formulas are given for an integral with two fixed points located near a simple pole of the amplitude function.