Radiation from a particle with constant velocity and time-varying charge, with applications to ultrashort pulsed laser filament microwave emission

A charged particle with constant velocity and time-varying charge $Q\left( t\right) $ resulting from charge-exchange with an otherwise stationary medium emits electromagnetic radiation despite lack of acceleration of the particle itself. This occurs regardless of whether the particle is real, such as a heavy ion traversing an electron stripper, or the electromagnetic equivalent, such as when charge equals the time integral of a short current pulse caused by an ultrashort pulse laser (USPL) wave packet after it has self-focused via the Kerr effect. The pulse width of the radiation is the time interval over which $Q\left( t\right) $ varies times $\left( 1-\beta \cos \theta \right) $, assuming the particle dimensions are negligible relative to $\beta c$ times this pulse width. Here, $\beta $ is the particle speed relative to the speed of light in the medium $c$, and $\theta $ is the emission angle relative to the direction of motion. The violation of this assumption for small $\theta $ for $\beta \approx 1$, such as occurs for USPL filamentation in a gas, provides the basis for estimating the time scale of the current pulse, a parameter of great interest for understanding its physical mechanism.