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Radial Electric Field in Tokamak Plasmas as a Physical Consequence of Ehrenfest’s Paradox

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DOI: 10.4236/jmp.2012.330201    3,811 Downloads   5,909 Views   Citations


A simplified form and some possible theoretical resolutions of the so-called Ehrenfest’s Paradox are described. A relation between physical consequences of this relativistic paradox and charge density ρ of tokamak plasma is shown. Plasma experiments which could resolve the Ehrenfest’s Paradox are presented.

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The authors declare no conflicts of interest.

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R. Alexander, "Radial Electric Field in Tokamak Plasmas as a Physical Consequence of Ehrenfest’s Paradox," Journal of Modern Physics, Vol. 3 No. 10A, 2012, pp. 1639-1646. doi: 10.4236/jmp.2012.330201.


[1] P. Ehrenfest, “Rotation Starrer Korper und Relativit?tstheorie,” Physikalische Zeitschrift, Vol. 10, No. 23, 1909, pp. 918-920.
[2] G. Rizzi and M. L. Ruggiero, “Space Geometry of Rotating Platforms: An Operational Approach,” Foundation of Physics, Vol. 32, No. 10, 2002, pp. 1525-1556. doi:10.1023/A:1020427318877
[3] H. A. Lorentz, “The Michelson-Morley Experiment and the Dimensions of Moving Bodies,” Nature, Vol. 106, No. 2677, 1921, pp. 793-795. doi:10.1038/106793a0
[4] A. S. Eddington, “Mathematical Theory of Relativity,” Cambridge University Press, Cambridge, 1922.
[5] R. D. Klauber, “Rotating Disk and Non-Time-Orthogonal Reference Frames,” Foundation of Physics Letters, Vol. 11, No. 5, 1998, pp. 405-443. doi:10.1023/A:1022548914291
[6] R. D. Klauber, “Spatial Geometry of the Rotating Disk and Its Non-Rotating Counterpart,” American Journal of Physics, Vol. 67, No. 2, 1999, pp. 158-159. doi:10.1119/1.19213
[7] A. Tartaglia, “Lengths on Rotating Platforms,” Foundation of Physics Letters, Vol. 12, No. 1, 1999, pp. 17-28. doi:10.1023/A:1021674620702
[8] A. Grunbaum and A. J. Janis, “The Geometry of the Rotating Disk in the Special Theory of Relativity,” Synthese, Vol. 34, No. 3, 1977, pp. 281-299. doi:10.1007/BF00485879
[9] L. D. Landau and E. M. Lifshitz, “The Classical Theory of Fields,” Pergamon Press, Oxford, 1951.
[10] C. W. Berenda, “The Problem of the Rotating Disk,” Physical Review, Vol. 62, No. 2, 1942, pp. 280-290. doi:10.1103/PhysRev.62.280
[11] A. Einstein, “The Meaning of Relativity,” Princeton University Press, Princeton, 1950.
[12] O. Gron, “Space Geometry in a Rotating Reference Frame: A Historical Appraisal,” American Journal of Physics, Vol. 43, No. 10, 1975, pp. 869-976.
[13] G. Rizzi and A. Tartaglia, “Speed of Light on Rotating Platforms,” Foundation of Physics, Vol. 28, No. 11, 1998, pp. 1663-1683. doi:10.1023/A:1018893609690
[14] N. Rosen, “Notes on Rotation and Rigid Bodies in Relativity Theory,” Physical Review, Vol. 71, No. 1, 1947, pp. 54-58. doi:10.1103/PhysRev.71.54
[15] H. Arzelies, “Relativistic Kinematics,” Pergamon Press, New York, 1966.
[16] H. Nikolic, “Relativistic Contraction and Related Effects in Noninertial Frames,” Physical Review A, Vol. 61, No. 3, 2000, pp. 321091-321098. doi:10.1103/PhysRevA.61.032109
[17] A. Eagle, “Note on Synchronizing’ Clocks in a Moving System by a Connecting Spindle,” Philosophical Magazine, Vol. 28, No.4, 1939, pp. 592-595.
[18] M. Galli, “Contraction of a Rotating Ring,” Rendiconti Academia Lincei, Vol. 12, No. 6, 1952, pp. 569-572.
[19] A. Romannikov, “Ehrenfest’s Paradox and Radial Electric Field in Quasi-Neutral Tokama,” Foundation of Physics, Vol. 41, No. 8, 2011, pp. 1331-1337. doi:10.1007/s10701-011-9551-6
[20] A. Romannikov, “Volume Charge Density and Radial Electric Field Er(r) in a Moving Tokamak Plasma,” Journal of Experimental and Theoretical Physics, Vol. 108, No. 2, 2009, pp. 340-348. doi:10.1134/S1063776109020162
[21] J. Wesson, “Tokamaks,” Oxford University Press, Oxford, 1997.
[22] E. L. Feinberg, “Russian Mozhno Li Rassmatrivat’ Relyativistskoe Izmenenie Masshtabov Dlinni I Vremeni Kak Rezultat Deistviya Sil,” Uspekhi Phizicheskih Nauk, Vol. 116, No. 4, 1975, pp. 709-730.
[23] A. Romannikov, “Relativistic Theory of Radial Electric Field Er(r) in Non-Periphery Tokamak Plasma,” Procee- ding of the 36th EPS, Sofia, 2009, pp. 75-79.
[24] T. S. Taylor, “Physics of Advanced Tokamaks,” Plasma Physics and Controlled Fusion, Vol. 39, No. 12B, 1997, pp. B47-B73. doi:10.1088/0741-3335/39/12B/005
[25] ITER Expert Group on Disruption, Plasma Control, and MHD, ITER Physics Basis Editors, “MHD Stability, Operational Limits and Disruptions,” Nuclear Fusion, Vol. 39, No. 12, 1999, pp. 2251-2389.
[26] P. H. Rutherford, “Collisional Diffusion in an Axisymmetric Torus,” Physics of Fluids, Vol. 13, No. 2, 1970, pp. 482-489. doi:10.1063/1.1692943
[27] R. D. Hazeltine, “Rotation of a Toroidally Confined, Collisional Plasma,” Physics of Fluids, Vol. 17, No. 5, 1974, pp. 961-968. doi:10.1063/1.1694838
[28] J. S. deGrassie, “Tokamak Rotation Sources, Transport and Sinks,” Plasma Physics and Controlled Fusion, Vol. 51, No. 12, 2009, pp. 1240471-1240717. doi:10.1088/0741-3335/51/12/124047
[29] W. Stacey, “Neoclassical Theory for Rotation and Impurity Transport in Tokamaks with Neutral Beam Injection,” Physics of Plasmas, Vol.8, No. 1, 2001, pp. 158-166. doi:10.1063/1.1324664
[30] M. N. Rosenbluth, P. H. Rutherford, J. B. Taylor, et al., “Radial Particle Flux in Tokamak,” Proceedings of the 4th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Madison, 1971, Vol. 1, pp. 495-508.
[31] T. E. Stringer, “Effect of the Magnetic Field Ripple on Diffusion in Tokamaks,” Nuclear Fusion, Vol. 12, No. 6, 1972, pp. 689-694. doi:10.1088/0029-5515/12/6/010
[32] J. W. Connor and R. J. Hastie, “Neoclassical Diffusion Arising from Magnetic-Field Ripples in Tokamaks,” Nuclear Fusion, Vol. 13, No. 2, 1973, pp. 221-226. doi:10.1088/0029-5515/13/2/011
[33] P. Monier-Garbet, K. Burrell, F. Hinton, et al., “Effects of Neutrals on Plasma Rotation in DIII-D,” Nuclear Fusion, Vol. 37, No. 3, 1997, pp. 403-412. doi:10.1088/0029-5515/37/3/I09
[34] F. Hinton and Y.-B. Kim, “Poloidal Rotation in Tokamak with Large Electric Field Gradients,” Physics of Plasmas, Vol. 2, No. 1, 1995, pp. 159-166. doi:10.1063/1.871105
[35] V. Rozhansky and M. Tendler, “The Effect of the Radial Electric Field on the L-H Transitions in Tokamaks,” Physics of Fluids B, Vol. 4, No. 7, 1992, pp. 1877-1888.
[36] B. P. Duval, A. Bortolon, A. Karpushov, et al., “Bulk Plasma Rotation in the TCV Tokamak in the Absence of External Momentum Input,” Plasma Physics and Controlled Fusion, Vol. 49, No. 12B, 2007, pp. B195-B210. doi:10.1088/0741-3335/49/12B/S18
[37] H. Meister, A. Kallenbach, A. G. Peeters, et al., “Measurement of Poloidal Flow, Radial Electric Field and E x B Shearing Rates at ASDEX Upgrade,” Nuclear Fusion, Vol. 41, No. 11, 2001, pp. 1633-1644. doi:10.1088/0029-5515/41/11/313
[38] G. T. Hoang, P. Monier-Garbet, T. Aniel, et al., “An H Minority Heating Regime in Tore Supra Showing Improved L Mode Confinement,” Nuclear Fusion, Vol. 40, No. 5, 2000, pp. 913-922. doi:10.1088/0029-5515/40/5/304
[39] A. N. Romannikov, C. Bourdelle, J. Bucalossi, et al., “Measurement of Central Toroidal Rotation in Ohmic Tore Supra Plasmas,” Nuclear Fusion, Vol. 40, No. 3, 2000, pp. 319-324. doi:10.1088/0029-5515/40/3/303
[40] H. Shirai, M. Kikuchi, T. Takizuka, et al., “Reduced Transport and Er Shearing in Improved Confinement Regimes in JT-60U,” Nuclear Fusion, Vol. 39, No. 11, 1999, pp. 1713-1722. doi:10.1088/0029-5515/39/11Y/311
[41] A. Romannikov, “Certain Considerations Concerning the Nature of Radial Electric Field and Toroidal Rotation Velocity Profile in Tokamak Plasma,” Plasma Physics and Controlled Fusion, Vol. 49, No.4, 2007, pp. 641-647. doi:10.1088/0741-3335/49/5/006
[42] S. Neudatchin, T. Takizuka, N. Hayashi, et al., “Role of Low Order Rational q-Values in the ITB Events in JT-60U Reverse Shear Plasmas,” Nuclear Fusion, Vol. 44, No. 9, 2004, pp. 945-953. doi:10.1088/0029-5515/44/9/002

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