A TAMR (Thermally Assisted Magnetic Recording) write head is formed with a narrow pole tip, a trailing edge magnetic shield and, optionally, a plasmon shield. The narrow pole tipped write head uses the energy of laser generated edge plasmons, formed in a plasmon generating layer, to locally heat a PMR magnetic recording medium slightly below its Curie temperature, Tc. When combined with the effects of the narrow tip, this local heating to a temperature below Tc is sufficient to create good transitions and narrow track widths in the magnetic medium. The write head is capable of writing effectively on state-of-the-art PMR recording media having Hk of 20 kOe or more.