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Transition from a coherent three wave system to turbulence with application to the fluid closure

Published online by Cambridge University Press:  09 June 2014

Jan Weiland ,
Chuan S. Liu  and
Anatoly Zagorodny
Jan Weiland*
Affiliation:
Chalmers University of Technology and EURATOM-VR Association, S-41296 Gothenburg, Sweden
Chuan S. Liu
Affiliation:
East-West Space Science Center, University of Maryland, College Park, MD, USA
Anatoly Zagorodny
Affiliation:
Bogoliubov Institute for Theoretical Physics, Kiev, Ukraine
*
†Email address for correspondence: elfjw@chalmers.se
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Abstract

We start from a Mattor–Parker system and its generalization to include diffusion and derive the Random Phase equations. It is shown that the same type of fluid closure holds in the coherent and turbulent regimes. This is due to the fact that the Random Phase levels (1/I1 = 1/I2 + 1/I3), where Ij is the intensity of wave packet ‘j’, are attractors for the wave dynamics both in the coherent and incoherent cases. Focus here is on the wave dynamics with phase velocities varying due to nonlinear frequency shifts. Thus a Maxwellian distribution function is kept in all cases.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 905810101
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Chandrasekhar, S. 1943 Stochastic problems in Physics and Astronomy. Rev. Mod. Phys. 15 (1), 1–89.Google Scholar
Dimits, A. M. et al. 2000 Comparison and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas. 7 (3), 969–983.Google Scholar
Dupree, T. H. 1966 A perturbation method for strong plasma turbulence. Phys. Fluids 9, 1773.CrossRefGoogle Scholar
Hasegawa, A. 1975 Plasma Instabilities and Nonlinear Effects. New York: Springer.CrossRefGoogle Scholar
Holod, I., Weiland, J. and Zagorodny, A. 2002 Nonlinear fluid closure: three-mode slab ion temperature gradient problem with diffusion. Phys. Plasmas 9, 1217.Google Scholar
Holod, I., Zagorodny, A. and Weiland, J. 2005 Anisotropic diffusion across an external magnetic field and large-scale fluctuations in magnetized plasmas. Phys. Rev. E 71, 046401.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. New York: Academic Press.Google Scholar
Liu, C. S. 1969 Temperature gradient instabilities in axisymmetric systems. Phys. Fluids 12, 1489.Google Scholar
Mattor, N. and Parker, S. E. 1997 Nonlinear kinetic fluid equations. Phys. Rev. Lett. 79, 3419.Google Scholar
Moestam, R., Shaikh, D. and Weiland, J. 2004 Self consistent theory of zonal flows in ion temperature gradient turbulence. Phys. Plasmas 11, 4801.Google Scholar
Rafiq, T., Kritz, A. H., Weiland, J., Pankin, A. Y. and Luo, L. 2013 Physics basis of multi-mode anomalous transport module. Phys. Plasmas 20, 032506.Google Scholar
Rosenbluth, M. N. and Liu, C. S. 1976 Cross-field energy transport by plasma waves. Phys. Fluids 19, 815.CrossRefGoogle Scholar
Wagner, F. and Stroth, U. 1993 Transport in toroidal devices-the experimentalists view. PPCF 35, 1321.Google Scholar
Waltz, R. E., Kerbel, G. O. and Milovich, J. 1994 Toroidal gyro-Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes. Phys. Plasmas 1, 2229.Google Scholar
Weiland, J. 2010 Turbulence at a pinch. Nature Phys. 6, 167.Google Scholar
Weiland, J. 2012 Stability and Transport in Magnetic Confinement Systems. New York: Springer.Google Scholar
Weiland, J. and Nordman, H. 1993 Drift wave model for inward energy transport in tokamak plasmas. Phys. Fluids B5, 1669.Google Scholar
Weiland, J. and Wilhelmsson, H. 1977 Coherent Nonlinear Interaction of Waves in Plasmas. Oxford: Pergamon Press.Google Scholar
Weiland, J. and Zagorodny, A. 2011 Fluid closure, relation to particle pinches, fluid resonances. In Proceedings of the IFP-CNR – Chalmers Workshop on Nonlinear Phenomena in Fusion Plasmas, Villa Monastero, Varenna, June 8–10 2011, AIP Conference Proceedings Vol 1392, pp. 33.Google Scholar
Zagorodny, A. and Weiland, J. 2009 Non-Markovian renormalization of kinetic coefficients for drift type turbulence in magnetized plasmas. Phys. Plasmas 16, 052308.Google Scholar