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We investigated the effects of a transverse magnetic field on a volume H.ion source driven by a radio frequency (RF) or a DC filament. We observed an electron cooling and an enhancement of the H.ion extraction efficiency when a transverse magnetic field was applied. The floating potential in the plasma in front of the extractor was found to increase with the magnetic field intensity, implying that a higher voltage on the plasma electrode would be required to extract the H.ions. In addition, the effect of the transverse magnetic field on the filament arc discharge was investigated.