The consideration of nonextensivity effects is crucial to the accurate diagnosis of plasma parameters; common plasma nonextensive parameters include electron nonextensive parameter and ion nonextensive parameter, and the former can be measured, while the ion nonextensive parameter cannot be measured yet. Here we show the measurement of ion nonextensive parameter of plasma based on the theory of nonextensive geodesic acoustic modes. We assume that the plasma to be measured can be described by nonextensive statistical mechanics, and on this basis, the nonextensive geodesic acoustic mode theory is established. Utilizing this theory, we have measured the ion nonextensive parameter $${{q}_{{{F}_{\mathrm {i}}}}}= 1.565$$ q F i = 1.565 which cannot be diagnosed even by a nonextensive single electric probe. Our research points out that the proposed measurement method of ion nonextensive parameter may play a role in plasma diagnosis and will help us to grasp the nonextensivity of plasma more precisely. We hope the proposed method of ion nonextensive parameter diagnosis based on the nonextensive geodesic acoustic mode theory can be the starting point of more complex ion nonextensive parameter diagnosis methods. In addition, the measurement of ion nonextensive parameter is closely related to the study of various plasma waves, instabilities, turbulence and abnormal transport, and a defined and quantitative test of nonextensive geodesic acoustic mode theory will bound up deeply with such developments.

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Theoretical analysis and a large number of experiments have proved that plasma components do not satisfy Boltzmann–Gibbs statistics and can be well described by nonextensive statistical mechanics, while sheath potential coefficients in plasma with nonextensive distribution are not investigated deeply and comprehensively. Here, we investigate the ion sheath formed around a nonextensive single electric probe in plasma described by nonextensive statistical mechanics, and find that the sheath potential coefficient is related to the electron nonextensive parameter, besides the extensive limit the results return to the case of the Boltzmann–Gibbs statistical framework. The sheath potential coefficient presents different dependences on the electron nonextensive parameters in different regions. We also have calculated the corresponding method error and evaluated with a set of real experiment data, and found that the error is as high as 83.91% indicating that the effect of nonextensive parameters should be considered in the actual measurement.

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