### Application of the balanced identification method to the reconstruction of the parameters of fast nonlocal heat transfer in a plasma of magnetic thermonuclear fusion

#### Abstract

The method of balanced identification, which consists in finding the optimal (in the sense of minimizing the mean square error of cross-validation) correlation between the complexity of the model and the quantity and quality (error) of experimental data, was used to correctly pose the problem of reconstructing the parameters of fast nonlocal heat transfer (FNHT) in plasma in installations for magnetic thermonuclear fusion. These phenomena manifest themselves in the instantaneous (on the time scale of heat diffusion described by the heat conduction equation) response of the spatial profile of the electron temperature to its local perturbation. The balanced identification method was used to identify the parameters of FNHT models and to verify the models themselves. These models are based on nonlocal heat transfer by electromagnetic (EM) waves with a large mean free path, described by integral (superdiffusion) equations, with respect to space variables, that are not reducible to diffusion-type differential equations. In particular, it was shown that FNHT by the EM waves in a plasma requires too high a reflectivity of the walls of the vacuum chamber to describe the experimental data on tokamaks and stellarator. Here we give a brief overview of the previous results and present the latest results of the FNHT model, which assumes strong internal reflection of waves in plasma and is compatible with the model of “wild cables” for the transfer of TEM waves along magnetically-coupled skeletal nanostructures. It is shown that for superdiffusive physical models of FNHT the balanced identification method is an effective tool for their verification. The calculations are carried out using the optimization modeling services deployed in the Everest distributed computing environment (http://everest.distcomp.org/).

#### Full Text:

PDF (Russian)#### References

A. V. Sokolov and V. V. Voloshinov, 2018 “Choice of mathematical model: balance between complexity and proximity to measurements,” International Journal of Open Information Technologies, vol. 6, no. 9, pp. 33–41, 2018 (in Russian).

A. V. Sokolov, V. V. Voloshinov, “Vybor matematicheskoj modeli: balans mezhdu slozhnost'ju i blizost'ju k izmerenijam” International Journal of Open Information Technologies, t. 6, # 9, s. 33–41, 2018. Dostupna: http://injoit.org/index.php/j1/article/view/612

A. Sokolov and V. Voloshinov, “Balanced Identification as an Intersection of Optimization and Distributed Computing.” arXiv preprint arXiv:1907.13444. 2019.

V. G. Linnik, A. V. Sokolov, and I. V. Mironenko, 2016 “Current trends in the development of biogeochemistry,” Moscow: GEOKHI RAS (in Russian), 2016, pp. 423-434.

A. V. Sokolov, V. V. Mamkin, V. K. Avilov, D. L. Tarasov, J. A. Kurbatova, and A. V. Olchev, “Application of a balanced identification method for gap-filling in CO2 flux data in a sphagnum peat bog,” Somputer Research and Modeling (in Russian) 2019, to be published.

A. V. Sokolov, V. K. Bolondinskij, V. V. Voloshinov, “Tehnologija sbalansirovannoj identifikacii dlja vybora matematicheskoj modeli transpiracii sosny,” Matematicheskaja biologija i bioinformatika, t. 14. # 2. s. 665–682, 2019. doi: 10.17537/2019.14.665.

A. V. Sokolov, L. A. Sokolova, “Postroenie matematicheskih modelej: kolichestvennaja ocenka znachimosti prinjatyh gipotez i ispol'zuemyh dannyh,” Materialy XXI Mezhdunarodnoj konferencii po vychislitel'noj mehanike i sovremennym prikladnym programmnym sistemam (VMSPPS’2019), Alushta, 2019, s. 114.

J. D. Callen and M. W. Kissick, “Evidence and concepts for non-local transport” Plasma Phys. Contr. Fusion, vol. 39, suppl. 12B, p. B173, 1997.

A. B. Kukushkin and K. V. Cherepanov, “Evidences for and the models of fast nonlocal transport of heat in magnetic fusion devices,” in AIP Conf. Proc., vol. 1154, pp. 83-94, 2009.

V. D. Pustovitov, “Nonlocal effects in energy balance in an equilibrium plasma during its fast heating/cooling in tokamaks and stellarators,” Plasma Phys. Contr. Fusion, vol. 54, p. 124036, 2012.

M. N. Rosenbluth and C. S. Liu, “Cross‐field energy transport by plasma waves,” Phys. Fluids, vol. 19, p. 815, 1976.

S. Tamor, “Synchrotron radiation loss from hot plasma,” Nucl. Instr. and Meth. Phys. Res. A, vol. 271, p. 37, 1988.

A. B. Kukushkin, V. S. Lisitsa, and Yu. A. Saveliev, “Nonlocal transport of thermal perturbations in a plasma,” JETP Lett., vol. 46, p. 448, 1987.

L. M. Biberman, V. S. Vorob'ev, I. T. Jakubov, “Kinetika neravnovesnoj nizkotemperaturnoj plazmy,” M.: Nauka, 1982.

L. M. Biberman, V. S. Vorob’ev, and I. T. Yakubov, “Kinetics of Nonequilibrium Low Temperature Plasmas,” New York: Consultants Bureau, 1987.

A. N. Starostin, “Perenos rezonansnogo izluchenija,” Jenciklopedija nizkotemperaturnoj plazmy, pod. red. V. E. Fortova. M., «Nauka», 2000, Vvodnyj tom 1, c. 471.

V. I. Kogan, “Zapiranie izluchenija v plazme,” tam zhe, c. 481.

V. A. Abramov, V. I. Kogan, V. S. Lisica, “Perenos izluchenija v plazme”. Voprosy teorii plazmy (pod red. M. A. Leontovicha i B. B. Kadomceva), Vyp. 12, M: Jenergoizdat, 1982, s. 114–155.

V. A. Abramov, V. I. Kogan, and V. S. Lisitsa “Reviews of Plasma Physics,” vol. 12, M. A. Leontovich and B. B. Kadomtsev, Ed., New York: Consultants Bureau, 1987, p. 151.

F. Sattin and D. F. Escande, “Alfvénic Propagation: A Key to Nonlocal Effects in Magnetized Plasmas,” Phys. Rev. Lett., vol. 112, p. 095003, 2014.

F. Sattin and D. F. Escande, “Retraction: Alfvénic Propagation: A Key to Nonlocal Effects in Magnetized Plasmas [Phys. Rev. Lett. 112, 095003 (2014)],” Phys. Rev. Lett., vol. 112, p. 159901, 2014.

A. B. Kukushkin in Proc. 24th EPS Conf. on Plasma Phys. and Contr. Fusion, Berchtesgaden, Germany, 1997, vol. 21A, part II, pp. 849–852.

A. B. Kukushkin, P. A. Sdvizhenskii, V. V. Voloshinov, and A. A. Kulichenko, “A Model of Recovering the Fast Nonlocal Transport Parameters in Magnetic Fusion Plasmas,” in Proc. 42nd EPS Conf. on Plasma Phys., Lisbon, Portugal, 2015, vol. 39E, P5.182

A. B. Kukushkin, A. A. Kulichenko, P. A. Sdvizhenskii, A. V. Sokolov, and V. V. Voloshinov, “Inverse Problem for Fast Nonlocal Heat Transport Events in Magnetic Fusion Plasmas,” in Proc. 43rd EPS Conference on Plasma Phys., Leuven, Belgium, 2016, vol. 40A, P2.028.

A. B. Kukushkin, A. A. Kulichenko, P. A. Sdvizhenskij, A. V. Sokolov, V. V. Voloshinov, “Model' vosstanovlenija parametrov bystrogo nelokal'nogo perenosa tepla v ustanovkah magnitnogo uderzhanija termojadernoj plazmy,” Voprosy atomnoj nauki i tehniki. Serija: Termojadernyj sintez, t. 40, vyp. 1, s. 45–55, 2017.

A. B. Kukushkin, A. A. Kulichenko, P. A. Sdvizhenskii, A. V. Sokolov, and V. V. Voloshinov, “A model of recovering the parameters of fast nonlocal heat transport in magnetic fusion plasmas,” Problems of Atomic Science and Technology, Series Thermonuclear Fusion, vol 40, no. 1, pp. 45–55, 2017 (in Russian).

A. B. Kukushkin, A. A. Kulichenko, P. A. Sdvizhenskii, A. V. Sokolov, and V. V. Voloshinov, “A model of recovering the parameters of fast nonlocal heat transport in magnetic fusion plasmas”, J. Phys. Conf. Series, vol. 941, paper 012008 (6 pp), 2017, doi:10.1088/1742-6596/941/1/012008. Available:

http://iopscience.iop.org/article/10.1088/1742-6596/941/1/012008/pdf

N. Tamura, et al, “Impact of nonlocal electron heat transport on the high temperature plasmas of LHD,” Nucl. Fusion, vol. 47, p. 449, 2007.

N. Tamura et al, “Edge-Core Interaction Revealed with Dynamic Transport Experiment in LHD,” in Proc. 23rd IAEA Fusion Energy Conf., Daejeon, Republic of Korea, 2010, EXC/P8-16.

M. W. Kissick, J. D. Callen, E. D. Fredrickson, A. C. Janos, and G. Taylor, “Non-local component of electron heat transport in TFTR,” Nucl. Fusion, vol. 36, p. 1691, 1996.

A. B. Kukushkin, “Analytic description of energy loss by a bounded inhomogeneous hot plasma due to the emission of electromagnetic waves,” JETP Lett., vol. 56, p. 487, 1992.

A. B. Kukushkin, “Heat transport by cyclotron waves in plasmas with strong magnetic field and highly reflecting walls” in 14th IAEA Conference on Plasma Physics and Controlled Nuclear Fusion Research, Vienna, 1992, vol. 2, pp. 35–45.

A. B. Kukushkin and P. V. Minashin, “Influence of Magnetic Field Inhomogeneity on Electron Cyclotron Power Losses in Magnetic Fusion Reactor,” in Proc 36th EPS Conference on Plasma Physics, 2009, ECA vol. 33E, P-4.136.

P. Mantica, et al, “Perturbative transport experiments in JET low or reverse magnetic shear plasmas,” Plasma Phys. Control. Fusion, vol. 44, pp. 2185–2215, 2002.

A. B. Kukushkin, P. A. Sdvizhenskii, A. V. Sokolov, and P. V. Minashin, “Recoveru of parameters of fast nonlocal heat transport in magnetic fusion plasmas: testing a model of waves with high internal reflections,” preprint arXiv:1901.03789 [physics.plasm-ph], 2019.

A. B. Kukushkin and V. A. Rantsev-Kartinov, “Long-lived filaments in fusion plasmas: review of observations and status of hypothesis of microdust-assembled skeletons,” in Current Trends in International Fusion Research — Proceedings of the Fourth Symposium. Eds. C. D. Orth, E. Panarella, NRC Research Press, Ottawa, Ontario, Canada, 2007, pp. 75–92.

A. B. Kukushkin and V. A. Rantsev-Kartinov, “Wild cables in tokamak plasmas (theoretical view),” in Proc 27th EPS Conference on Contr. Fusion and Plasma Phys., Budapest, 2000, 12-16 June, ECA vol 24B, pp. 568-571.

A. N. Tihonov, “O matematicheskih metodah avtomatizacii obrabotki nabljudenij” V: Problemy vychislitel'noj matematiki. M.: Izd-vo MGU, 1980. c. 3-17.

O. Sukhoroslov, S. Volkov, A. Afanasiev, “A Web-Based Platform for Publication and Distributed Execution of Computing Applications,” in Parallel and Distributed Computing: Proc. 14th International Symposium on IEEE, Cambridge, USA, 2015, p. 175–184.

### Refbacks

- There are currently no refbacks.

Abava Absolutech Fruct 2020

ISSN: 2307-8162