By the presented paper I tried to express my deep appreciation to Vitaly D. Shafranov who was my supervisor, friend and mentor. The great value of his equilibrium theory is widely recognized as one of the pillar of tokamaks. At the same time, it may look like the importance of contribution of founders of tokamak physics is diminishing in favor on new research results and models. The paper shows that this is not the case: after six decades of tokamak fusion, the program is incapable to demonstrate fusion power exceeding the applied plasma heating. In contrast to this situation, the return to fundamentals of tokamak physics suggests much more efficient approach with order of magnitude better confinement, consistent with burning plasma.
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REFERENCES
M. A. Leontovich and V. D. Shafranov, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Pergamon, New York, 1959), Vol. 1, p. 255.
M. Kruskal and M. Schwarzschild, Proc. R. Soc. London, Ser. A 223, 348 (1954).
L. A. Artsimovich and V. D. Shafranov. JETP Lett. 15, 51 (1972).
G. A. Emmert, A. T. Mense, and J. M. Donhowe, The First Topical Meeting on the Technology of Controlled Nuclear Fusion, San Diego CA,1974, Report UWFDM-93.
L. E. Zakharov, W. Blanchard, R. Kaita, H. Kugel, R. Majeski, and J. Timberlake, J. Nucl. Mater. 363–365, 453 (2007).
R. Litunovski, JET Internal Report, Contract No. JQ5/11961 (JET Joint Undertaking, Abingdon, 1995), Pts. 1, 2.
P. Noll, P. Andrew, M. Buzio, R. Litunovski, T. Raimondi, V. Riccardo, and M. Verrecchia, in Proceedings of the 19th Symposium on Fusion Technology, Lisbon,1996, Ed. by C. Varandas and F. Serra (Elsevier, Amsterdam, 1996) Vol. 1, p. 751.
L. E. Zakharov, Phys. Plasmas 15, 062507 (2008).
L. E. Zakharov and X. Li, Phys. Plasmas 22, 062511 (2015).
B. B. Kadomtsev and O. P. Pogutse, Sov. Phys. JETP 38, 283 (1974).
L. E. Zakharov, J. Plasma Phys. 81, 515810609 (2015).
L. E. Zakharov, J. Lewandowski, E. L. Foley, F. M. Levinton, H. Y. Yuh, V. Drozdov, and D. C. McDonald, Phys. Plasmas 15, 092503 (2008).
L. E. Zakharov, E. L. Foley, F. M. Levinton, and H. Y. Yuh, Plasma Phys. Rep. 34, 173 (2008).
K. M. McGuire, H. Adler, P. Alling, C. Ancher, H. Anderson, J. L. Anderson, J. W. Anderson, V. Arunasalam, G. Ascione, D. Ashcroft, C. W. Barnes, G. Barnes, S. Batha, G. Bateman, M. Beer, et al., Phys. Plasmas 2, 2176 (1995).
J. D. Strachan, H. Adler, P. Alling, C. Ancher, H. Anderson, J. L. Anderson, D. Ashcroft, C. W. Barnes, G. Barnes, S. Batha, M. G. Bell, R. Bell, M. Bitter, W. Blanchard, N. L. Bretz, et al., Phys. Rev. Lett. 72, 3526 (1994).
A. Keilhacker, C. Gibson, P. J. Gormezano, P. J. Lomas, P. R. Thomas, M. L. Watkins, P. Andrew, B. Balet, D. Borba, C. D. Challis, I. Coffey, G. A. Cottrell, H. P. L. De Esch, N. Deliyanakis, A. Fasoli, et al., Nucl. Fusion 39, 209 (1999).
JET Team, Nucl. Fusion 39, 1227 (1999).
V. A. Evtikhin, I. E. Lyublinski, A. V. Vertkov, S. V. Mir-nov, and V. B. Lazarev, Fusion Engines Des. 56–57, 363 (2001).
G. M. McCracken and S. K. Ertents, in Proceedings of the B.N.E.S. Nuclear Fusion Reactor Conference, Culham,1969, Paper 4.2.
G. V. Pereverzev and P. N. Yushmanov, Preprint No. IPP 5/98 (Max-Planck-Institut für Plasmaphysik, Garching, 2002).
R. E. Nygren and F. L. Tabarés, Nucl. Mater. Energy 9, 6 (2016)
L. E. Zakharov, Nucl. Fusion 59, 096008 (2019). https://doi.org/10.1088/1741-4326/ab246b
L. E. Zakharov and V. D. Shafranov, in Reviews of Plasma Physics, Ed. by M. A. Leontovich, (New York, Consultant Bureau, 1986), Vol. 11, p. 153.
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Zakharov, L.E. V. D. Shafranov and Necessary Conditions for Fusion Energy. Plasma Phys. Rep. 45, 1087–1092 (2019). https://doi.org/10.1134/S1063780X19120092
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DOI: https://doi.org/10.1134/S1063780X19120092