\noindent
\textit{1. Background}


During last decade laser-plasma methods of terahertz radiation generation were investigated intensively [1, 2]. These methods are characterized by using of femtosecond laser pulses ionizing neutral media and exciting electron currents which radiates broadband terahertz pulses. A number of experimental techniques were proposed in this area [2]. Most of theoretical interpretations focus on low frequency current excitation process, while spectral and spatial properties of terahertz radiation depends on nonlinear dynamics of femtosecond pulse propagating in media. From experiments [3] it is known that spectrum maxima could exceed inverse envelope time. In work [4] it is stated that terahertz radiation pattern produced by two color laser pulses (coherent admixture of laser pulse and its second harmonic usually generated in BBO crystal) has a hollow in the center. These features can not be interpreted without thoroughly investigation of nonlinear laser pulse dynamic peculiarities. On the other hand terahertz radiation features can bring some information about laser pulse propagation. In this work we investigated low frequency current (residual current excited in plasma by laser pulse) properties calculated in numerical simulations of nonlinear two color laser pulse propagation in gas. Using calculated currents we concluded some properties of terahertz radiation and compared them to experimental observations.


\noindent
\textit{2. Model}


We used scalar wave equation for electric field of laser pulse in paraxial approximation (similar approach was used in relativistic plasma wake field studies [5]). According to our estimations ionization supposed to be of tunneling type. Ionization rate formula was adopted from [6]. We used hydrodynamic model for current: $\partial j/\partial \tau=n E$, where $j$ is electric current (both optical and low frequency), $n$ is plasma density, $E$ is laser pulse electric field, $\tau=t-z/c$ is a time in co-moving laser pulse coordinates.

\noindent
\textit{3. Results}


In our simulations we used real experimental parameters. We found that a region exciting low frequency currents shrinks in time due to refraction of laser pulse on breakdown plasma. This effect can significantly shift the upper bound of terahertz spectra. Despite of our expectations we saw no oscillations of low frequency current excitation efficiency due to phase detuning of first and second optical harmonics on plasma. Instead of changing the sign the source of low frequency current decays before the end of nonlinear interaction of laser pulse and gas. The source of low frequency current exists only in areas where breakdown is taking place. The most efficient low frequency current generation occurs at very first sub-front of breakdown plasma, where phase between first and second harmonic is yet preserved. According to our estimations the hollow structure of terahertz radiation pattern can be interpreted by superluminal velocity of breakdown front. \\


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\textbf{References} \\
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\textbf{3}. K. Y. Kim , A. J. Taylor, J. H. Glownia, and G. Rodriguez, \textit{``Coherent control of terahertz supercontinuum generation in ultrafast laser ?gas interactions,''} Nature Photonics \textbf{2}, 605-609 (2008) \\
\textbf{4}. H. Zhong, N. Karpowicz, and X.-C. Zhang, \textit{``Terahertz emission profile from laser-induced air plasma,''} Appl. Phys. Lett. \textbf{88}, 261103 (2006) \\
\textbf{5}. A. A. Balakin, A. G. Litvak, V. A. Mironov, and S. A. Skobelev, \textit{``Compression of femtosecond petawatt laser pulses in a plasma under the conditions of wake-wave excitation,''} Phys Rev. A \textbf{88}, 023836 (2013) \\
\textbf{6}. A. Talebpour, J. Yang, S.L. Chin, \textit{``Semi-empirical model for the rate of tunnel ionization of $\mathrm{N_2}$ and $\mathrm{O_2}$ molecule in an intense Ti:sapphire laser pulse,''} Opt. Commun. \textbf{163}, 29?32 (1999)