Scientists explain how the SPIDER code is transforming the approach to nuclear fusion.
The work is published in the journal Physics of Plasmas. Nuclear fusion is one of the most promising technologies for generating clean and virtually inexhaustible energy. The plasma beta (βp) and internal inductance (ℓi) parameters are crucial for characterizing tokamak operations and determining plasma equilibrium. The challenge of separating these parameters arose over 60 years ago when V. D. Shafranov (corresponding member of the USSR Academy of Sciences since 1981, academic of the Russian Academy of Sciences since 1997) demonstrated in his work that their combination naturally appears in the integral consequences of equilibrium equations. Since then, researchers have been striving to find effective methods for their separation, which is an important task for plasma diagnostics and theory.
Scientists from MIPT, the M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, and the Kurchatov Institute conducted three series of plasma equilibrium calculations in a tokamak: at low, medium, and high pressures. In each series, they used an elliptical cross-section with an elongation varying from K = 1 (circular plasma) to K = 2.4.
They employed numerical methods to calculate the integrals that define the right-hand sides of standard virial relations for elongated plasma in tokamaks. The study was conducted using the SPIDER code, which enables modeling various plasma configurations with elliptical cross-sections. In each series of calculations, they analyzed the dependencies of the integrals on plasma parameters, the elongation of magnetic surfaces, and the radial derivatives of displacement and elongation.
The results indicated that the deviation of the integrals from analytical estimates does not exceed 10 percent, confirming the accuracy of the proposed analytical expressions. Specifically, it was established that the integral S2 shows a weak dependence on elongation, which is an important discovery for further research.
“Our study highlights the importance of considering parameters such as elongation and internal inductance for accurately describing plasma behavior in tokamaks. This opens up new possibilities for real-time plasma diagnostics and control,” said Vladimir Pustovito, a researcher in the Plasma Energy Department at MIPT.
The novelty of this research lies in its provision of numerical estimates for integrals for which compact analytical expressions were previously obtained.
The work of Russian scientists paves the way for new opportunities in nuclear fusion research. In particular, it can be utilized to optimize the operations of tokamaks like ITER and to develop new plasma diagnostic methods. The application of the results obtained will enhance plasma control and improve the efficiency of nuclear reactors.
The research findings can be applied to optimize tokamak operations, develop new precise methods for measuring plasma parameters, and deepen scientific understanding of plasma behavior under various conditions, potentially leading to new discoveries in the field of nuclear fusion.