For the wire system to properly simulate a beam, two conditions are necessary from fundamental principles:
1) The wire system must produce magnetic fields the same as those of the corresponding beam so that magnetic effects are equivalent, i.e. the wire current must be the same as the beam current.
2) The wire system must produce electric fields the same as those of the corresponding beam so that electric effects are equivalent, i.e. the line charge density on the wire must be the same as that of the beam.