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In this paper, an irreversible quantum Brayton heat engine cycle model composed of two isomagnetic processes and two irreversible adiabatic processes is established. The quantum heat engine works with non-interacting spin-1/2 systems and has multi-irreversibilities. By using detailed numerical examples, this paper gives the fundamental optimal relationship of the quantum Brayton heat engine, in a general case and at high temperature limits, and analyzes the effects of internal friction and bypass heat leakage on the fundamental optimal relationship. Comparisons of the power output versus efficiency characteristics among this spin quantum heat Brayton engine, a quantum spin Carnot heat engine and a Brayton heat engine working with a classical working medium, are made. Three special cases, such as the endoreversible case, the frictionless case and the case without bypass heat leakage, are discussed

Fundamental optimal relation of a spin 1/2 quantum Brayton heat engine with multi-irreversibilities