= Solution
The laser driver should occupy at most roughly half a <plasma (physics)>[plasma] period to excite the accelerating <density> response effectively. Interpreting pulse length as full significant spatial duration gives $\boxed{\ell_{\max}\sim\lambda_p/2\simeq8.35\ \mu\mathrm m,\quad\tau_{\max}\sim27.8\ \mathrm{fs}}$. If the source's $\sigma$ denotes the rms width of a Gaussian envelope instead, the resonant scale is commonly $k_p\sigma\sim1$, or $\sigma\sim2.66\ \mu$m and $8.9$ fs; full duration and rms width cannot be assigned the same numerical value without a pulse-shape convention. The robust condition is a sub-plasma-period pulse.
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