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The off-resonance heating that is observed in hot-electron plasmas is explained in terms of harmonic resonances, appropriately modified to include relativistic and Doppler effects. A theoretical expression for the heating rate is proposed and is found to agree with the results of a computer simulation over a range of parameters. The theoretical heating rate is evaluated numerically for several special cases, including a uniform magnetic field, a mirror field with a 2:1 mirror ratio, and a large-aspect ratio bumpy torus. The enhanced axial loss observed experimentally with heating below the cyclotron frequency is explained by absorption at harmonics of the electron bounce frequency.
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J. C. Sprott (1972) studied this question.
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