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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Geodesic acoustic mode (GAM) in collisionless toroidal plasmas with a constant electrostatic potential around a magnetic surface is investigated based on the linear gyrokinetic theory in context of nonextensive statistics mechanics. The damping rate of GAM is shown to be dependent on the nonextensive parameters of ions, and in the extensive limit, the result in Maxwellian distribution plasma is recovered. The damping rate is found to be enhanced as the nonextensive parameter of ion decreases.