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Alternative limit of validity
In the one-dimensional case, another sufficient condition for the SVEA validity is


 * $$ l_g \gg \lambda $$ and  $$l_p \gg \lambda (1-v/c) $$  ,with  $$\lambda = \frac{2\pi}{k_0}$$  and  $$ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} $$

where lg is the length over which the radiation pulse is amplified, lp is the pulse width and v is the group velocity of the radiating system. These conditions are much less restrictive in the relativistic limit when v/c is close to 1, as in a Free-electron laser, compared to the usual conditions required for the SVEA validity.