The momentum distribution of electrons created by the external field of the form (29) for E 0 ¼ E c , T ¼ 5 m −1 , and various values of δ (points). The solid line represents the LCFA prediction.

Contexts in source publication

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... multiplying them by a factor of 2π=ð2LÞ. After this renormalization, the summation over the x coordinate leads exactly to the infinite-capacitor results discussed in the previous section which are to be compared with the exact values. As an example, we present the longitudinal momentum distributions for E 0 ¼ E c , T ¼ 5 m −1 , and various δ (see Fig. 9). The transversal momentum equals zero, i.e., π ⊥ ¼ m. The graph reveals indeed that the spectra found for the 2D field configuration recover the 1D result as δ → ∞. However, for small δ the effects of spatial finiteness become crucial, which means that the LCFA is well justified only for sufficiently large ...

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... Fig. 9 one observes that in the case δ ¼ 2, the spectrum support is strongly different from that obtained for large δ. This can be understood if one notices that a classical particle in such a field configuration can escape from the region x ∈ ½−L; LŠ before the field gets switched off. The left edge of the spectrum is formed by the particles ...

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... the field parameters from Fig. 9 and π ⊥ ¼ m, it yields δ 0 ≈ 6.52. Using Eq. (33), one can now approximately identify the domain of the LCFA justification. The condition (33) was derived within relativistic mechanics. The nonrelativistic regime appears ...

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... not take into account "dynamical production" of particles due to fast variations of the external field (e.g., rapid switching on and off). However, in the latter case, the LCFA treats the particle as if it were interacting with a uniform and infinite background and thus prevents the particle from escaping, which leads to the overestimation in Fig. 9. Note that these two patterns are clearly seen in our results since we treat here the temporal dependence exactly and therefore disentangle the two ...