  Solutions of the linearized Vlasov-Poisson equations for the electric field
radiated by a time varying point charge in a three-dimensional, unbounded,
spatially homogeneous plasma with a uniform background magnetic field and a
uniform (static) flow velocity are expressed in terms of an equivalent integral
equation in the time domain. For plasmas characterized by Maxwell distribution
functions with isotropic temperatures, the kernel has a relatively simple
mathematical form consisting only of elementary functions, exponential and
trigonometric functions (sines and cosines), and no infinite sums of Bessel
functions. Consequently, the integral equation is amenable to numerical
solutions and may be useful for the study of the impulse response of magnetized
plasmas and, more generally, the response to arbitrary waveforms.
