A magnetic disk drive is disclosed which has a tunnel erase head assembly comprising a read/write head for writing and reading data on a magnetic disk, and a pair of tunnel erase heads for trimming a pair of opposite marginal edges of the record track being formed by the read/write head, with the consequent formation of spaces intervening between the record tracks. The spaces created on the same disk by different disk drives may be of one polarity of magnetization or the other, with the possibility of noise production due to an abrupt change in the polarity of magnetization as the read/write head scans any of the spaces as a result of mistracking. For the reduction of such noise the coil of the tunnel erase heads is connected to an erase current source via a circuit whereby the erase current is made to have a staircase or ramp rise and fall.