Abstract
This paper elucidates the close connections between hydrodynamic models of two-dimensional fluids and reduced models of plasma dynamics in the presence of a strong magnetic field. The key element is the similarity of the Coriolis force to the Lorentz force. The reduced plasma model, the Hasegawa–Mima equation, is equivalent to the two-dimensional ion vortex equation. The paper discusses the history of the Hasegawa–Mima model and that of a related reduced system called the Hasegawa–Wakatani model. The 2D fluid ↔ magnetized plasma analogy is exploited to argue that magnetized plasma turbulence exhibits a dual cascade, including an inverse cascade of energy. Generation of ordered mesoscopic flows in plasmas (akin to zonal jets) is also explained. The paper concludes with a brief explanation of the relevance of the quasi-2D dynamics to aspects of plasma confinement physics.
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References
Biglari, H., P.H. Diamond and P.W. Terry. 1990. Influence of sheared poloidal rotation on edge turbulence. Phys. Plasmas 2: 1–4
Biskamp, D., E. Schwarz and J.F. Drake. 1996. Two-dimensional electron magnetohydrodynamic turbulence. Phys. Rev. Lett. 76: 1264–1268
Charney, J.G. 1948. On the scale of atmospheric motions, Vol. 17. Geofysiske Publikasjoner, Oslo
Davis, M.S., M.E. Mauel, D.T. Garnier and J. Kesner. 2014. Pressure profiles of plasmas confined in the field of a magnetic dipole. Plasma Phys. Control. Fusion 56: 095021
Diamond, P. and Y.-B. Kim. 1991. Theory of mean poloidal flow generation by turbulence. Phys. Plasma 3: 1626–1633
Diamond, P., M. Rosenbluth, E. Sanchez, et al. 2000. In search of the elusive zonal flow using cross-bicoherence analysis. Phys. Rev. Lett. 84: 4842–4845
Diamond, P.H., S.-I. Itoh, K. Itoh and T.S. Hahm. 2005. Zonal flow – a review. Plasma Phys. Control. Fusion 47: R35
Diamond, P.H., A. Hasegawa and K. Mima. 2011. Vorticity dynamics, drift wave turbulence, and zonal flows: a look back and a look ahead. Plasma Phys. Control. Fusion 53: 12001
Fujisawa, A. 2009. A review of zonal flow plasma experiments. Nucl. Fusion 49: 013001
Galtier, S. and A. Bhattacharjee. 2003. Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10: 3065
Hamada, Y., T. Watari, A. Nishizawa, O. Yamagishi, K. Narihara, Y. Kawasumi, T. Ido, M. Kojima, K. Toi and the JIPPT-IIU Group. 2012. Regions of kinetic geodesic acoustic modes and streamers in JIPPT-IIU tokamak plasmas. Nucl. Fusion 52: 063023
Hasegawa, A. 1983. A test of self-organization hypothesis in Jovian and Saturnian wind systems. J. Phys. Soc. Jpn. 52: 1930–1934
Hasegawa, A. 1985. Self-organization processes in continuous media. Adv. Phys. 34: 1–42
Hasegawa, A. 1987. A dipole field fusion reaction. Comm. Plasma Phys. Control. Fusion 11: 147–151
Hasegawa, A. and L. Chen. 1975. Kinetic process of plasma heating due to Alfvén wave excitation. Phys. Rev. Lett. 35: 370–373
Hasegawa, A. and K. Mima. 1977. Stationary spectrum of strong turbulence in magnetized nonuniform plasma. Phys. Rev. Lett. 39: 205–208
Hasegawa, A. and K. Mima. 1978. Pseudo-three-dimensional turbulence in magnetized nonuniform plasma. Phys. Fluids 21: 87–92
Hasegawa, A. and M. Wakatani. 1983. Plasma edge turbulence. Phys. Rev. Lett. 50: 682–686
Hasegawa, A. and M. Wakatani. 1987. Self-organization of electrostatic turbulence in a cylindrical plasma. Phys. Rev. Lett. 59: 1581–1584
Hasegawa, A., C.G. Maclennan and Y. Kodama. 1979. Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. Phys. Fluids 22: 2122–2129
Hoppensteadt, F. 2006. Predator-prey model. Scholarpedia 1: 1563
Kawazura, Y., Z. Yoshida, M. Nishiura, H. Saitoh, Y. Yano, T. Nogami, N. Sato, M. Yamasaki, A. Kashyap and T. Mushiake. 2015. Observation of particle acceleration in laboratory magnetosphere. Phys. Plasmas 22: 112503
Kikuchi, M. and M. Azumi. 2015. Frontier in fusion research II: introduction to modern tokamak physics. Springer International Publishing, Switzerland
Kolmogorov, A.N. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30: 299–303
Kraichnan, R.H. 1967. Inertial range in two-dimensional turbulence. Phys. Fluids 10: 1417–1423
Mazzucato,E. 1976. Small-scale density fluctuations in the adiabatic toroidal compressor. Phys. Rev. Lett. 36: 792–795
Mima, K. and Y.C. Lee. 1980. Modulational instability of strongly dispersive drift waves and formation of convective cells. Phys. Fluids 23: 105–108
Nagashima, Y., S.-I Ito, S. Shinohara, M. Fukao, A. Fujisawa, K. Terasaka, Y. Kawai, G.R. Tynan, P.H. Diamond, M. Yagi, S. Inagaki, T. Yamada and K. Itoh. 2009. Observation of the parametric-modulational instability between the drift-wave fluctuation and azimuthally symmetric sheared radial electric field oscillation in a cylindrical laboratory plasma. Phys. Plasmas 16: 020706
Onsager, L. 1949. Statistical hydrodynamics. Nuovo Cim. 6: 279–287
Rosenbluth, M.N. and F.L. Hinton. 1998. Poloidal flow driven ion-temperature-gradient turbulent in tokamaks. Phys. Rev. Lett. 80: 724–727
Rossby, C.-G. 1939. Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Mar. Res. 2: 38–55
Sagdeev, R.Z. and A.A. Galeev. 1969. Nonlinear plasma theory (T.M. O’Neil and D.L. Book, eds.). W.A. Benjamin, New York
Schrödinger, E. 1944. What is life? The physical aspect of the living cell. Cambridge University Press, Cambridge
Slusher, R.E. and C.M. Surko. 1978. Study of density fluctuations in the absorption of oxygen on silicon. Phys. Rev. Lett. 40: 400–403
Surko, C.M. and R.E. Slusher. 1976. Study of the density fluctuations in the adiabatic toroidal compressor scattering tokamak using CO2 laser. Phys. Rev. Lett. 37: 1747–1750
Taniuti, T. and H. Washimi H. 1968. Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma. Phys. Rev. Lett. 21: 209–212
Tynan G.R., R.A. Moyer, M.J. Burin and C. Holland. 2001. On the nonlinear turbulentdynamics of shear-flow decorrelation and zonal flow generation. Phys. Plasmas 8: 2691–2699
Wakatani, M. and A. Hasegawa. 1984. A collisional drift wave description of plasma edge turbulence. Phys. Fluids 27: 611–618
Williams, G.P. 1978. Planetary circulations: 1. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci. 35: 1399–1426
Xiao, Y., I. Holod, W. Zhang, S. Klasky and Z. Lin. 2010. Fluctuation characteristic and transport properties of collisionless trapped electron mode turbulence. Phys. Plasmas 17: 022302
Zakharov, V.E. 1972. Collapse of Langmuir waves. Sov. Phys. JETP-USSR 35: 908–914
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Hasegawa, A., Mima, K. Strong turbulence, self-organization and plasma confinement. EPJ H 43, 499–521 (2018). https://doi.org/10.1140/epjh/e2018-90033-4
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DOI: https://doi.org/10.1140/epjh/e2018-90033-4