  The filamentation instability occurring when a non relativistic electron beam
passes through a quantum magnetized plasma is investigated by means of a cold
quantum magnetohydrodynamic model. It is proved that the instability can be
completely suppressed by quantum effects if and only if a finite magnetic field
is present. A dimensionless parameter is identified which measures the strength
of quantum effects. Strong quantum effects allow for a much smaller magnetic
field to suppress the instability than in the classical regime.
