= Solution
For <linear polarization>, $a_0=eE_L/(m_ec\omega_0)$ and $I=\epsilon_0cE_L^2/2$. Substitution gives $a_0\simeq0.855\lambda_{\mu\mathrm m}\sqrt{I/(10^{18}\ \mathrm{W\,cm^{-2}})}\simeq0.64$. Thus the specified peak <electron> quiver motion is at most mildly relativistic, not highly relativistic. Its quiver <Lorentz factor> is of order $\sqrt{1+a_0^2}\simeq1.19$. The supplied 40 TW fixes a focal area through $P/I$, but does not increase $a_0$ once the intensity is specified. This exposes a limitation of assuming a strongly nonlinear, fully wavebreaking wake in the preceding estimates.
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