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Current long-baseline neutrino-oscillation experiments such as NO$\nu$A andT2K are mainly sensitive to physics in the neighbourhood of the firstoscillation maximum of the $\nu_\mu \to \nu_e$ oscillation probability. Thefuture Deep Underground Neutrino Experiment (DUNE) utilizes a wide-band beamtune optimized for CP violation sensitivity that fully covers the region of thefirst maxima and part of the second. In the present study, we elucidate therole of second oscillation maximum in addressing issues pertaining to unknownsin the standard three flavour paradigm. We consider a new DUNE beam tuneoptimized for coverage of the region of the second oscillation maxima whichcould be realized using proposed accelerator upgrades that provide multi-MW ofpower at proton energies of 8 GeV. We find that addition of the multi-MW 8 GeVbeam to DUNE wide-band running leads to modest improvement in sensitivity to CPviolation, mass hierarchy, the octant of $\theta_{23}$ as well as theresolution of $\delta$ and the Jarlskog invariant. Significant improvements tothe DUNE neutrino energy resolution yield a much larger improvement inperformance. We conclude that the standard DUNE wide-band beam when coupledwith excellent detector resolution capabilities is sufficient to resolve$\delta$ to better than $\sim 12^\circ$ for all values of $\delta$ in a decadeof running. For second maxima (8 GeV 3MW) beam running concurrently with thestandard wide-band (80 GeV 2.2 MW) beam for 5 of the 10 years, it is found that$\delta$ can be further resolved better than $\sim 10^\circ$ for all values of$\delta$.

Physics prospects with the second oscillation maximum at Deep Underground Neutrino Experiment