The design of annular doping region located in the cladding can reduce signal overlap with the doped region in order to reduce saturation and minimize gain compression, which has important applications in EDFAs. Here, we present the design and power scaling characterization of a cladding-pumped amplifier with ytterbium dopant located in an annular region near the ultra low NA core in the cladding, which is found to be a promising way to achieve multi-kilowatt single mode fiber lasers. The ultra low NA ensures that the fiber amplifiers operate in single mode state, which results to that the fiber amplifiers are free of the limitation of the transverse mode instability, and that the mode field of the signal laser extends into the cladding to extract gain amplification. The annular ytterbium-doped region located in the cladding can overcome the contradiction between high doping concentration and ultra-low NA design, which can simultaneously obtain high pump absorption with ultra low NA. The size of annular ytterbium-doped region under different core NA has been studied for various core sizes, which shows that the optimal size of annular ytterbium-doped region is related to the core NA and the core size. Detail analysis of high power amplification of cladding-ring-up-doped ultra low NA single mode fiber amplifier has been presented, which includes various nonlinear effects and thermal effects. It shows that, due to the specific design, the single mode characterization of the fiber is less influenced by the detrimental thermo-optic effect, which means that the cladding-annular-doped ultra-low NA fiber has high mode instability threshold than the ultra-low NA fiber with the core being fully uniformly doped. The cladding-pumped fiber amplifiers based on cladding-annular-doped ultra low NA fiber has the capability to achieve >10kW single mode fiber lasers.