Abstract
At the specific power of electron cyclotron resonance (ECR) heating of 3.2 MW m–3 (plasma density of 2 × 1019 m–3, electron temperature of 0.6 keV), an increase in the plasma energy lifetime by not less than 30% is accompanied by a two-time-decrease in the level of short-wave turbulent density fluctuations. In such a shot, before the beginning of the quasi-stationary confinement stage, the turbulent state of density fluctuations is characterized by the stronger deviation from zero of the coefficient of excess of fluctuation increments than it is in shots without transport transitions. This indicates the stronger deviation of the probability distribution function of density fluctuation increments from the normal law in shots with transport transitions. Based on the analysis of increments of short-wave fluctuations using the special method for separating the continuous components in stochastic processes, a qualitative difference was established between the behaviors of the structural components forming the plasma turbulence in shots with and without transport transitions. In addition, for shots with transport transitions, a change in the shape of the approximating finite mixture of normal distributions and parameters of its component densities is demonstrated.
Similar content being viewed by others
REFERENCES
V. P. Budaev, S. P. Savin, and L. M. Zelenyi, Phys.–Usp. 54, 875 (2011). https://doi.org/10.3367/ufne.0181.201109a.0905
T. S. Hahm and P. H. Diamond, J. Korean Phys. Soc. 73, 747 (2018). https://doi.org/10.3938/jkps.73.747
T. Happel, T. Estrada, E. Blanco, C. Hidalgo, G. D. Conway, U. Stroth, and TJ-II Team, Phys. Plasmas 18, 102302 (2011). https://doi.org/10.1063/1.3646315
B. Ph. van Milligen, B. A. Carreras, I. Voldiner, U. Losada, C. Hidalgo, and TJ-II Team, Phys. Plasmas 28, 092302 (2021). https://doi.org/10.1063/5.0057791
A. Fujisawa, H. Iguchi, T. Minami, Y. Yoshimura, H. Sanuki, K. Itoh, S. Lee, K. Tanaka, M. Yokoyama, M. Kojima, S.-I. Itoh, S. Okamura, R. Akiyama, K. Ida, M. Isobe, et al., Phys. Rev. Lett. 82, 2669 (1999). https://doi.org/10.1103/PhysRevLett.82.2669
D. A. Shelukhin, V. A. Vershkov, and K. A. Razumova, Plasma Phys. Rep. 31, 985 (2005). https://doi.org/10.1134/1.2147644
S. I. Lashkul, S. V. Shatalin, A. B. Altukhov, E. O. Vekshina, V. V. Dyachenko, L. A. Esipov, M. Yu. Kantor, D. V. Kuprienko, A. Yu. Popov, A. Yu. Stepanov, and A. P. Sharpeonok, Plasma Phys. Rep. 32, 353 (2006). https://doi.org/10.1134/S1063780X06050011
S. V. Shatalin, A. V. Pavlov, A. Yu. Popov, S. I. Lashkul, and L. A. Esipov, Plasma Phys. Rep. 33, 169 (2007). https://doi.org/10.1134/S1063780X07030014
T. L. Rhodes, W. A. Peebles, J. C. DeBoo, R. Prater, J. E. Kinsey, G. M. Staebler, J. Candy, M. E. Austin, R. V. Bravenec, K. H. Burrell, J. S. deCrassie, E. J. Doyle, P. Gohil, C. M. Greenfield, R. J. Groebner, et al., Plasma Phys. Control. Fusion 49, B183 (2007). https://doi.org/10.1088/0741-3335/49/12B/S17
T. L. Rhodes, W. A. Peebles, M. A. Van Zeeland, J. S. deCrassie, R. V. Bravenec, K. H. Burrell, J. C. DeBoo, J. Lohr, C. C. Petty, X. V. Nguyen, E. J. Doyle, C. M. Greenfield, L. Zeng, and G. Wang, Phys. Plasmas 14, 056117 (2007). https://doi.org/10.1063/1.2714019
V. Yu. Korolev, Probabilistic-Statistical Methods for Volatility Decomposition of Chaotic Processes (Izd-vo MGU, Moscow, 2011) [in Russian].
N. N. Skvortsova, D. K. Akulina, G. M. Batanov, N. K. Kharchev, L. V. Kolik, L. M. Kovrizhnykh, A. A. Letunov, V. P. Logvinenko, D. V. Malakhov, A. E. Petrov, A. A. Pshenichnikov, K. A. Sarksyan, and G. S. Voronov, Plasma Phys. Control. Fusion 52, 055008 (2010). https://doi.org/10.1088/0741-3335/52/5/055008
J. H. Nicolau, L. Garcia, B. A. Carreras, and B. Ph. van Milligen, Phys. Plasmas 25, 102304 (2018). https://doi.org/10.1063/1.5041495
G. M. Batanov, V. D. Borzosekov, A. K. Gorshenin, N. K. Kharchev, V. Yu. Korolev, and K. A. Sarksyan, Plasma Phys. Control. Fusion 61, 075006 (2019). https://doi.org/10.1088/1361-6587/ab1117
G. M. Batanov, V. D. Borzosekov, D. G. Vasil’kov, I. Yu. Vafin, S. E. Grebenshchikov, E. M. Konchekov, A. A. Letunov, A. I. Meshcheryakov, K. A. Sarksyan, M. A. Tereshchenko, N. K. Kharchev, and Yu. V. Khol’nov, Prikl. Fiz., No. 6, 61 (2015).
D. G. Vasil’kov, G. M. Batanov, V. D. Borzosekov, I. Yu. Vafin, S. E. Grebenshchikov, I. A. Grishina, V. A. Ivanov, A. A. Letunov, V. P. Logvinenko, A. I. Meshcheryakov, M. N. Petrova, V. D. Stepakhin, N. K. Kharchev, and Yu. V. Khol’nov, Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint. 43 (3), 79 (2020). https://doi.org/10.21517/0202-3822-2020-43-3-79-89
G. M. Batanov, V. D. Borzosekov, N. K. Kharchev, A. A. Letunov, D. V. Malakhov, K. A. Sarksyan, and D. G. Vasilkov, in Proceedings of the 46th EPS Conference on Plasma Physics, Milan, 2019, Paper P2.1095. http://ocs.ciemat.es/EPS2019PAP/pdf/P2.1095.pdf.
G. M. Batanov, V. D. Borzosekov, L. V. Kolik, E. M. Konchekov, D. V. Malakhov, A. E. Petrov, K. A. Sarksyan, N. N. Skvortsova, V. D. Stepakhin, N. K. Kharchev, and A. A. Kharchevskii, Plasma Phys. Rep. 46, 955 (2020). https://doi.org/10.1134/S1063780X20100025
Stochastic Models of Structural Plasma Turbulence, Ed. by V. Yu. Korolev and N. N. Skvortsova (MAKS Press, Moscow, 2003; VSP, Leiden, 2006)
D. K. Akulina, E. D. Andryukhina, M. S. Berezhetskii, S. E. Grebenshchikov, G. S. Voronov, I. S. Sbitnikova, O. I. Fedyanin, Yu. V. Kholnov, and I. S. Shpigel, Sov. J. Plasma Phys. 4, 569 (1978).
G. M. Batanov, V. I. Belousov, Yu. F. Bondar’, V. D. Borzosekov, D. G. Vasil’kov, S. E. Grebenshchikov, I. A. Ivannikov, L. V. Kolik, E. M. Konchekov, D. V. Malakhov, N. V. Matveev, A. I. Meshcheryakov, A. E. Petrov, K. A. Sarksyan, N. N. Skvortsova, et al., Plasma Phys. Rep. 39, 1088 (2013). https://doi.org/10.1134/S1063780X1307012X
A. I. Meshcheryakov, D. K. Akulina, G. M. Batanov, M. S. Berezhetskii, G. S. Voronov, G. A. Gladkov, S. E. Grebenshchikov, V. A. Grinchuk, I. A. Grishina, L. V. Kolik, N. F. Larionova. A. A. Letunov, V. P. Logvinenko, A. E. Petrov, A. A. Pshenichnikov, et al., Plasma Phys. Rep. 31, 452 (2005). https://doi.org/10.1134/1.1947330
K. Itoh, S.-I. Itoh, and A. Fukuyama, J. Phys. Soc. Jpn. 58, 482 (1989). https://doi.org/10.1143/JPSJ.58.482
U. Stroth, T. Geist, J. P. T. Koponen, H.-J. Hartfuß, P. Zeiler, and ECRH and W7-AS team, Phys. Rev. Lett. 82, 928 (1999). https://doi.org/10.1103/PhysRevLett.82.928
V. Erckmann and U. Gasparino, Plasma Phys. Control. Fusion 36, 1869 (1994). https://doi.org/10.1088/0741-3335/36/12/001
V. F. Andreev, A. A. Borschegovskij, V. V. Chistyakov, Yu. N. Dnestrovskij, E. P. Gorbunov, N. V. Kasyanova, S. E. Lysenko, A. V. Melnikov, T. B. Myalton, I. N. Roy, D. S. Sergeev, and V. N. Zenin, Plasma Phys. Control. Fusion 58, 055008 (2016). https://doi.org/10.1088/0741-3335/58/5/055008
D. K. Akulina, G. A. Gladkov, Y. I. Nechaev, and O. I. Fedyanin, Plasma Phys. Rep. 23, 28 (1997).
A. S. Sakharov, D. K. Akulina, G. A. Gladkov, and M. A. Tereshchenko, Plasma Phys. Rep. 32, 729 (2006). https://doi.org/10.1134/S1063780X06090030
I. Yu. Vafin, PhD Tesis (Prokhorov General Physics Inst., Russ. Acad. Sci., Moscow, 2013).
S. E. Grebenshchikov, B. I. Kornev, N. F. Larionova, and A. V. Novikova, in Plasma Physics and Plasma Electronics, Ed. by L. M. Kovrizhnykh (Nauka, Moscow, 1985; Nova Science, Commack, NY, 1989).
E. D. Andryukhina and O. I. Fedyanin, Sov. J. Plasma Phys. 3, 447 (1977).
S. E. Grebenshchikov, N. K. Kharchev, and D. G. Vasil’kov, Plasma Phys. Rep. 45, 1059 (2019). https://doi.org/10.1134/S1063780X19110047
G. M. Batanov, V. D. Borzosekov, E. M. Konchekov, D. V. Malakhov, K. A. Sarksyan, V. D. Stepakhin, and N. K. Kharchev, Inzh. Fiz., No. 10, 56 (2013).
G. M. Batanov, V. D. Borzosekov, L. M. Kovrizhnykh, L. V. Kolik, E. M. Konchekov, D. V. Malakhov, A. E. Petrov, K. A. Sarksyan, N. N. Skvortsova, V. D. Stepakhin, and N. K. Kharchev, Plasma Phys. Rep. 39, 444 (2013). https://doi.org/10.1134/S1063780X13060019
G. M. Batanov, V. D. Borzosekov, L. V. Kolik, D. V. Malakhov, A. E. Petrov, A. A. Pshenichnikov, K. A. Sarksyan, N. N. Skvortsova, and N. K. Kharchev, Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint. 34 (2), 70 (2011).
A. A. Pshenichnikov, L. V. Kolik, N. I. Malykh, A. E. Petrov, M. A. Tereshchenko, N. K. Kharchev, and Yu. V. Khol’nov, Plasma Phys. Rep. 31, 554 (2005). https://doi.org/10.1134/1.1992582
D. Malakhov, N. Skvortsova, A. Gorshenin, V. Korolev, A. Chirkov, and B. Tedtoev, in XXXII International Seminar on Stability Problems for Stochastic Models, Trondheim, 2014, Book of Abstracts, p. 68.
N. N. Skvortsova, A. Yu. Chirkov, A. A. Kharchevsky, D. V. Malakhov, A. K. Gorshenin, and V. Yu. Korolev, J. Phys.: Conf. Ser. 666, 012007 (2016). https://doi.org/10.1088/1742-6596/666/1/012007
A. Gorshenin and V. Korolev, in Proceedings of the 27th European Conference on Modelling and Simulation, ECMS 2013, Ålesund, Norway, May 27–30, 2013, Ed. by W. Rekdalsbakken, R. T. Bye, and H. Zhang (Digitaldruck Pirrot GmbHP, Dudweiler, 2013), p. 569.
G. M. Batanov, A. K. Gorshenin, V. Yu. Korolev, D. V. Malakhov, and N. N. Skvortsova, Math. Models Comput. Simul. 4, 10 (2012). https://doi.org/10.1134/S2070048212010048
A. K. Gorshenin, AIP Conf. Proc. 1648, 250008 (2015). https://doi.org/10.1063/1.4912512
A. K. Gorshenin, V. Yu. Korolev, and A. A. Shcherbinina, Inf. Ee Primen. 14 (3), 3 (2020). https://doi.org/10.14357/19922264200301
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Fizmatlit, Moscow, 2004; Martino Publishing, Mansfield Centre, CT, 2012).
E. Z. Gusakov and A. Yu. Popov, JETP Lett. 91, 655 (2010). https://doi.org/10.1134/S0021364010120088
S. K. Nielsen, M. Salewski, E. Westerhof, W. Bongers, S. B. Korsholm, F. Leipold, J. W. Oosterbeek, D. Moseev, M. Stejner, and the TEXTOR Team, Plasma Phys. Control. Fusion 55, 115003 (2013). https://doi.org/10.1088/0741-3335/55/11/115003
E. Z. Gusakov and A. Yu. Popov, JETP Lett. 94, 277 (2011). https://doi.org/10.1134/S0021364011160053
E. Z. Gusakov and A. Yu. Popov, Plasma Phys. Control. Fusion 62, 025028 (2020). https://doi.org/10.1088/1361-6587/ab5ba8
E. Z. Gusakov and A. Yu. Popov, Phys. Plasmas 27, 082502 (2020). https://doi.org/10.1063/5.0011949
E. Z. Gusakov and A. Yu. Popov, Plasma Phys. Control. Fusion 63, 125017 (2021). https://doi.org/10.1088/1361-6587/ac301c
E. Z. Gusakov and A. Yu. Popov, Phys. Plasmas 23, 082503 (2016). https://doi.org/10.1063/1.4959849
A. S. Sakharov, Plasma Phys. Rep. 45, 289 (2019). https://doi.org/10.1134/S1063780X19030085
ACKNOWLEDGMENTS
Statistical analysis of ensembles of experimental data was performed by A.K. Gorshenin using the infrastructure of the Shared Research Facilities “High Performance Computing and Big Data” (CKP “Informatics”) of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (Moscow). The authors express their gratitude to the sc-ientific team of the L-2M stellarator represented by I.Yu. Vafin, A.I. Meshcheryakov, I.A. Grishina, D.G. Vasilkov, S.E. Grebenshchikov, and Yu.V. Kholnov for providing measurement data on the mean plasma density, electron temperature, plasma energy content, and limiter voltage.
Funding
The article was prepared with partial financial support from the Ministry of Education and Science of the Russian Federation as part of the implementation of the program of the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2022-284).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by I. Grishina
Rights and permissions
About this article
Cite this article
Batanov, G.M., Borzosekov, V.D., Gorshenin, A.K. et al. Changes in Statistical Characteristics of Turbulent Plasma Density Fluctuations During a Transport Transition in the L-2M Stellarator. Plasma Phys. Rep. 48, 740–753 (2022). https://doi.org/10.1134/S1063780X2270026X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063780X2270026X