Measurements of the $\gamma_{v} p \rightarrow p' \pi^{+} \pi^{-}$ cross section with the CLAS detector for $0.4$ GeV$^{2}$ $< Q^{2} <$ $1.0$ GeV$^{2}$ and $1.3$ GeV $< W <$ $1.825$ GeV

New results on the single-differential and fully-integrated cross sections for the process $\gamma_{v} p \rightarrow p' \pi^{+} \pi^{-}$ are presented. The experimental data were collected with the CLAS detector at Jefferson Laboratory. Measurements were carried out in the kinematic region of the reaction invariant mass $W$ from 1.3 to 1.825 GeV and the photon virtuality $Q^2$ from 0.4 to 1.0 GeV$^2$. The cross sections were obtained in narrow $Q^{2}$ bins (0.05 GeV$^{2}$) with the smallest statistical uncertainties achieved in double-pion electroproduction experiments to date. The results were found to be in agreement with previously available data where they overlap. A preliminary interpretation of the extracted cross sections, which was based on a phenomenological meson-baryon reaction model, revealed substantial relative contributions from nucleon resonances. The data offer promising prospects to improve knowledge on the $Q^{2}$-evolution of the electrocouplings of most resonances with masses up to $\sim$1.8 GeV.