With a circularly polarized (CP) Gaussian laser pulse, we examine theoretically the acceleration of electrons due to a combined effect of laser wakefield (LW) and direct laser (DL) in the plasma bubble regime. The CP laser pulse is ideal for DLA, since it allows for better electron trapping in the plasma bubble regime than a linearly polarized (LP) laser pulse. As a result of a CP laser pulse propagation in z direction, the electrons are accelerated in longitudinal direction by the accelerating field (Wz\documentclass[12pt]{minimal}
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\begin{document}$${\text{W}}_{{\text{z}}}$$\end{document}) and focused in the transverse direction by the focusing fields (Wx\documentclass[12pt]{minimal}
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\begin{document}$${\text{W}}_{{\text{x}}}$$\end{document}, Wy\documentclass[12pt]{minimal}
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\begin{document}$${\text{W}}_{{\text{y}}}$$\end{document}). The density of plasma medium is about ∼1.8×1018cm-3\documentclass[12pt]{minimal}
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\begin{document}$$\sim 1.8 \times 10^{18} {\text{cm}}^{ - 3}$$\end{document} which is from a 99.9%\documentclass[12pt]{minimal}
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\begin{document}$$99.9\%$$\end{document} He / 0.1%\documentclass[12pt]{minimal}
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\begin{document}$$0.1\%$$\end{document} N2 neutral mix, laser pulse duration is 30fs\documentclass[12pt]{minimal}
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\begin{document}$$30{\text{f}}s$$\end{document} and wavelength 0.8μm\documentclass[12pt]{minimal}
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\begin{document}$$0.8 \mu m$$\end{document}. A bubble radius of over 20μm\documentclass[12pt]{minimal}
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\begin{document}$$20{\mu m}$$\end{document} is achieved with a CP laser pulse at an intensity on the order of a0=7\documentclass[12pt]{minimal}
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\begin{document}$${\text{a}}_{0} = 7$$\end{document} (∼2.14×1020W/cm2\documentclass[12pt]{minimal}
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\begin{document}$$\sim 2.14 \times 10^{20} W/{\text{cm}}^{2}$$\end{document}), although the same can be achieved with an LP laser at a significantly higher intensity. The electron energy gain with a CP laser pulse appears to be above 3GeV\documentclass[12pt]{minimal}
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\begin{document}$$3{\text{GeV}}$$\end{document} at this intensity. CP laser pulse appeared with a lower transverse emittance and a higher energy gain than an LP laser pulse of the same intensity. In comparison to LP laser pulse, CP laser pulse appears to have a more effective acceleration mechanism for LWFA with DLA in the plasma-bubble regime.
