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We numerically model the performance of high-power 977-nm fiber lasers and amplifiers pumped at 915 nm, in which the Yb is doped in a ring inside the core of a high-order-mode (HOM) fiber. Light in the spatially coherent LP07 mode is amplified in the fiber, and then coupled to the LP01 mode by long-period gratings. For the laser, it is found that parasitic oscillation on the 1023-nm four-level transition is much less likely when the ring position coincides with a low-intensity point in the LP07 mode pattern. For the amplifier, the maximum extractable energy is found to increase as the pump power is increased up to around 20 W, and then it becomes limited by amplified spontaneous emission to a few millijoules. This limit is not related to the use of HOM fiber, apart from the required fiber numerical aperture, and is independent of the core radius, Yb concentration, and doping profile. The HOM fiber does have the advantage of increasing the efficiency of energy extraction in the amplifier, when the doped ring position coincides with a maximum in the HOM intensity pattern.