  The destabilizing role of neutrino beams on the Trivelpiece-Gould modes is
considered, assuming electrostatic perturbations in a magnetized plasma
composed by electrons in a neutralizing ionic background, coupled to a neutrino
species by means of an effective neutrino force arising from the electro-weak
interaction. The magnetic field is found to significantly improve the linear
instability growth rate, as calculated for Supernova type II environments. On
the formal level, for wave vector parallel or perpendicular to the magnetic
field the instability growth rate is found from the unmagnetized case replacing
the plasma frequency by the appropriated Trivelpiece-Gould frequency. The
growth rate associated with oblique propagation is also obtained.
