  As an extension of the previous work [arXiv: 1512.02411], we have
investigated the role of circularly polarized (CP) laser pulses while keeping
other conditions the same. It is found that in the presence of large scale
pre-formed plasmas, super-high energetic electrons can be generated at
relativistic CP laser-solid interactions. For laser of intensity $10^{20}\
\text{W}/\text{cm}^2$ and pre-plasma scale-length $10\ \mu\text{m}$, the
cut-off energy of electron by CP laser is $120\ \text{MeV}$ compared with $100\
\text{MeV}$ in the case of linearly polarized (LP) laser. The unexpected
super-high energetic electron acceleration can also be explained by the
two-stage acceleration model, {by taking into account the envelop modulation
effects of the reflected CP laser pulse.} The underlying physics of this
envelop modulation is figured out, and a modified first-stage electron
acceleration scaling law in the presence of the modulated-CP laser is also
obtained.
