  We consider the effect of general neutrino interactions (scalar, vector,
pseudoscalar, axial vector and tensor) in neutrino-electron scattering at the
DUNE near detector. Those interactions can be associated with heavy new physics
and their effect is to cause distortions in the recoil spectrum of the
electrons. We show that for some cases energy scales up to 9 TeV are accessible
after a 5 year run and that current bounds on interaction parameters can be
improved by up to an order of magnitude. The full set of general interactions
includes the usually considered neutrino-electron non-standard matter
interactions, and the near detector will give limits comparable but
complementary to the ones from the analysis of neutrino oscillations in the far
detector.
