We report on an ytterbium-doped photonic crystal fiber with a core diameter of 60 microm and mode-field-area of ~2000 microm(2) of the emitted fundamental mode. Together with the short absorption length of 0.5 m this fiber possesses a record low nonlinearity which makes this fiber predestinated for the amplification of short laser pulses to very high peak powers. In a first continuous-wave experiment a power of 320 W has been extracted corresponding to 550 W per meter. To our knowledge this represents the highest power per unit length ever reported for fiber lasers. Furthermore, the robust single-transverse-mode propagation in a passive 100 microm core fiber with a similar design reveals the potential of extended large-mode-area photonic crystal fibers.