Analysis in the instantaneous frequency forms of a chirped laser pulse

We analyze two forms of the instantaneous frequency of a linearly chirped laser pulse. Using a 3D test particle simulation, numerical results are presented for electrons accelerated by a chirped laser pulse with these two linearly chirped forms of the instantaneous frequency. We summarize that the linearly chirped frequency, ω(t) = ω₀ [1 -α (t - z / c)] is reasonable, ω₀ is laser frequency at z = 0 and t = 0, αand is the frequency chirp parameter.