No abstract

No abstract

Electron-positron pair production in spatial inhomogeneous electric fields with sinusoidal phase modu lation is studied within the Dirac-Heisenberg-Wigner formalism. The focus is on discussing the effects of the modulation parameters on the momentum spectrum and the reduced particle number at various spatial scales. For the momentum spectrum, the interference effect becomes more and more remarkable with the increase of modulated amplitude or frequency, while the symmetry is severely destroyed with modulated amplitude. For the reduced particle number, it is greatly enhanced at about a few times and evenly one order of magnitude when modulation parameters are applied. Moreover, the effect of spatial scales on the reduced particle number are carefully examined and found that it increases rapidly at small spatial scales, while it tends to be a constant at large spatial scales. Importantly, two interesting results are revealed for the reduced particle number. One is for the more reduced pair number production which can be achieved at small spatial scales. The other is for the optimal pair production that can be achieved through different modulations. These results can provide a possibility for realizing the optimal pair production by combining the advantages of field spatial inhomogeneity with different choice of phase modulation.