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.
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.
The trapped electron dynamics is considered in general tokamak magnetic field with positive or reversed shear. Starting from the continuity, energy-evolution, and motion equations of the trapped electron fluid and the definition of Lagrangian invariant, the Lagrangian invariants hidden in the dynamics are strictly found: L=ln[(n/B)c1(T/B2/3)c2], where c1 and c2 are dimensionless changeable parameters and c1∝c2. It yields n/B=const and T3/2/B=const. Further, based on them it is shown that 〈n〉ψq(ψ)=const and 〈T3/2〉ψq(ψ)=const. The former invariant qualitatively fits the experimental data in many tokamaks; the latter may be used to explain the steady-state hollow T-profile (the corresponding hollow j-profile) observed in reversed shear tokamak plasmas.
In the field of plasma diagnosis, the measurement of the distribution function is significant because the distribution function is the basis for the use of plasma kinetic theory and it is the prerequisite for analyzing many physical phenomena, such as Landau damping (wave-particle resonance phenomenon) and ion sheath. Theoretical analysis and a large number of experiments have proved that plasma components do not obey Boltzmann–Gibbs statistics and can be well described by nonextensive statistical mechanics. The field of nonextensive electric probe has also made great progress, and the invention of the nonextensive single electric probes has developed and strengthened the power of plasma diagnostics. The nonextensive electric probe can not only measure the electron nonextensive parameter of plasma that cannot be measured by traditional probes but can also measure more accurate plasma parameters that can also be measured by traditional probes, such as Te, Φp, ne, Φf, and αqFe. However, diagnosing the plasma distribution function by the nonextensive electric probe has not been thoroughly and systematically analyzed and discussed. Here, we show the measurement of the plasma distribution function with a nonextensive single electric probe. This work expands the diagnostic capabilities of the nonextensive single electric probe. We utilize the nonextensive single electric probe theory to analyze the experimental data points of the I–V curve, measure the plasma electron distribution function fvx, and display the distribution curve (figure f-vx), and we also measure the plasma parameters of qFe, Te, Φp, ne, Φf, αqFe, etc. The proposed method provides a new approach to the diagnosis of the plasma distribution function and contributes to a more accurate and comprehensive grasp of plasma, which creates better conditions for us to take advantage of plasma. These initial results illustrate the potential of the nonextensive electric probe in the field of plasma diagnosis and, more generally, in accelerating the progress of fusion-energy science and helping to understand complex physical systems.
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