Repeated plasma outbursts were recognized at our analyzing currents of the fast carbon and fluorine ions produced with the sub-nanosecond PALS laser beam (λ0 = 1.315 µm, τL = ≈350 ps, Imax ≈ 6 × 1015 W/cm2) focused onto polytetrafluoroethylene and polyethylene targets. This study deals with a repetitive occurrence of doublets of C6+-C5+ and F9+-F8+ ion peaks in the time-of-flight (TOF) spectra, whose TOF can be related to the same accelerating voltage: . The repeated occurrence of ion outbursts containing fully ionized ions can be characterized by a set of discrete voltages Ui, where the subscript i ∈ (1, N) labels the outbursts of ions from the fastest one (i = 1) up to the slowest and in the TOF spectrum yet distinguishable outburst (i = N). These discrete values could indicate plasma pulsations followed by repetitive outbursts of ions. The ions expand with a velocity up to ≈9 × 108 cm/s. The corresponding values of the accelerating voltage of ≈800 kv, and the temperature of ≈1.1 keV were determined by revealing partial ion currents based on the shifted Maxwell-Boltzmann velocity distribution. Characteristics of fast ion outbursts depend on the focus position with respect to the target surface.