Previous work on the emission from isolated old neutron stars ( IONS ) accreting the inter-stellar medium ( ISM ) focussed on gravitational capture – Bondi accretion . We propose a new class of sources which accrete via magnetic interaction with the ISM . While for the Bondi mechanism , the accretion rate \dot { M } _ { Bondi } decreases with increasing NS velocity , in magnetic accretors ( MAGACs ) \dot { M } _ { MAGAC } increases with increasing NS velocity ( \dot { M } _ { Bondi } \propto v ^ { -3 } vs . \dot { M } _ { MAGAC } \propto v ^ { 1 / 3 } ) . MAGACs will be produced among high velocity ( \gtrsim 100 km s ^ { -1 } ) high magnetic field ( B > 10 ^ { 14 } G ) radio pulsars – the “ magnetars ” – after they have evolved first through magnetic dipole spin-down , followed by a “ propeller ” phase ( when the object sheds angular momentum on a timescale \lesssim 10 ^ { 10 } yr ) . The properties of MAGACS may be summarized thus : dipole magnetic fields of B \gtrsim 10 ^ { 14 } G ; minimum velocities relative to the ISM of > 25–100 km s ^ { -1 } , depending on B , well below the median in the observed radio-pulsar population ; spin-periods of > days to years ; accretion luminosities of 10 ^ { 28 } – 10 ^ { 31 } erg \mbox { $ s$ } ^ { -1 } ; and effective temperatures kT _ { eff } =0.3 – 2.5 keV if they accrete onto the magnetic polar cap . We find no examples of MAGACs among previously observed source classes ( anomalous X-ray pulsars , soft-gamma-ray repeaters or known IONS ) . However , MAGACs may be more prevelant in flux-limited X-ray catalogs than their gravitationally accreting counterparts .