Long- and short-lived electrons with anomalously high collision rates in laser-ionized gases

Ultrashort broadband terahertz pulses are applied to probe the electron dynamics of gaseous Ar and ${\mathrm{O}}_2$ following ionization by an intense femtosecond laser pulse. The conductivity in the plasma center is extracted by a modified Wentzel-Kramers-Brillouin approach. It exhibits a nearly perfect Drude-like spectral shape and yields the temporal evolution of the free-electron density and collision rate. While the electron density in the Ar plasma remains nearly constant during the first $200\mathrm{ps}$ after generation, it decays much faster in ${\mathrm{O}}_2$ due to dissociative recombination which is only possible in molecular plasmas. Adding a small amount of the electron scavenger ${\mathrm{SF}}_6$ to Ar reduces the electron lifetime in the plasma dramatically and allows us to determine the electron temperature to about $20000\mathrm{K}$. Furthermore, anomalously high, metal-like electron collision rates of up to $25\mathrm{THz}$ are found. Kinetic plasma theory substantially underestimates these rates pointing towards additional and more complex processes randomizing the total electronic momentum. Our results are relevant to both lightning control and generation of terahertz radiation by intense laser pulses in gases.

Figure 1

Schematic of the sample geometry. The pump beam is focused into the gas cell by two cylindrical lenses in orthogonal orientation. The resulting plasma sheet around the focal plane of lens 2 is probed by the THz beam perpendicular to the pump beam.

Figure 2

(a) Grayscale plot of the intensity profile $I_{\mathrm{pump}}$ of the pump-beam focus as measured with a charge-coupled device (CCD) camera. The THz probe pulse propagates along the $z$ axis. Note the different axis scaling. (b), (c) Line plots of $I_{\mathrm{pump}}$ along the $z$ and $y$ axis in (a), respectively. With a $400\text{−}\mathrm{\mu }\mathrm{m}$ length of the pump focus in $x$ direction, the THz probe beam sees a plasma sheet homogeneous in the $x\text{−}y$ plane.

Figure 3

(a) THz waveforms $S_{\infty }\left(t\right)$ and $S_{\tau }\left(t\right)$ transmitted through unexcited and excited ${\mathrm{O}}_2$, respectively, at a pump-probe delay of $\tau =1\mathrm{ps}$ and a peak pump intensity of about $3\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$. (b) Amplitude spectra of the waveforms $S_{\infty }\left(t\right)$ and $S_{\tau }\left(t\right)$ in panel (a). (c), (d) Same as (a), (b) but for a pump intensity reduced by $\approx 30\%$.

Figure 4

Fraction of the THz pulse energy transmitted through Ar and ${\mathrm{O}}_2$ as a function of the pump-probe delay $\tau$. Note the expanded $\tau$-axis scaling around zero delay.

Figure 5

(a) Pump-induced changes $\mathrm{\Delta }{\epsilon }_{\tau }$ in the dielectric function of Ar at $\tau =1\mathrm{ps}$ and (b) $\tau =100\mathrm{ps}$ after ionization which is nearly identical with (a). (c), (d) Same as (a), (b) for ${\mathrm{O}}_2$. Note the different axis scaling and the strongly decreased dielectric function in (d). In all cases, the Drude model excellently reproduces the experimental data.

Figure 6

(a) Collision rate $\gamma$ of Eq. (9) and weighting factor ${ϵ}^{3∕2}\partial f_{ϵ}$ of the integral in Eq. (8) versus electron energy $ϵ$ for $n_{\mathrm{e}}=3\times {10}^{17}{\mathrm{cm}}^{-3}$ and $T_{\mathrm{e}}=10000\mathrm{K}$. Note that for $ϵ>1\mathrm{eV}$, e-n scattering starts to dominate the total scattering rate $\gamma$. (b) Dielectric function resulting from Eq. (8). Thick solid lines mark a fit according to the Drude formula (7) which excellently reproduces the input electron density.

Figure 7

(a) Temporal evolution of the free-electron density $n_{\mathrm{e}}$ in Ar and ${\mathrm{O}}_2$ following optical ionization. (b) Corresponding dynamics of $1∕n_{\mathrm{e}}$ in ${\mathrm{O}}_2$ with a fit to the dissociative-recombination model of Eq. (11).

Figure 8

Logarithmic plot of $n_{\mathrm{e}}\left(\tau \right)$ for the $9:1\text{−}\mathrm{Ar}:{\mathrm{SF}}_6$ mixture and pure ${\mathrm{SF}}_6$ together with mono-exponential fits. The free-electron decay in ${\mathrm{O}}_2$ deviates considerably from a mono-exponential behavior as demonstrated by comparison to the dashed line. The “O” indicates the value of $n_{\mathrm{e}}\left(\tau \right)$ in the Ar plasma, which is largely constant for $\tau >50\mathrm{ps}$.

Figure 9

(a) Temporal dynamics of the Drude collision rate $\Gamma$ in laser-ionized Ar and ${\mathrm{O}}_2$. (b) Corresponding plots of the Drude relaxation rate $\Gamma$ in ${\mathrm{O}}_2$ and Ar as a function of the electron density $n_{\mathrm{e}}$. Exemplary Drude relaxation rates of Ref. 9 taken for an ${\mathrm{O}}_2$ plasma with lower $n_{\mathrm{e}}$ are appended. Solid lines are modeled collision rates at various electron temperatures according to the theoretical approach of Sec. 3B.

Figure 10

(a) Spectral dependence of the auxiliary quantity $h$ of Eq. (B2) measured in Ar at $5\mathrm{ps}$ after excitation with different pump-pulse energies $W$. The maximum pulse energy of $W_{\max }=0.4\mathrm{mJ}$ corresponds to a maximum intensity of $\approx 2\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ in the center of the pump focus. (b) Dependence of the spectrally averaged $h(W,\omega )$ on the pump intensity together with power law fits in double-logarithmic presentation.