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A quasi-linear model of particle, momentum and heat transport in a stochastic magnetic field

Published online by Cambridge University Press:  28 September 2023

P. Zanca Open the ORCID record for P. Zanca [Opens in a new window] ,
I. Predebon ,
R. Paccagnella  and
F. Sattin
P. Zanca*
Affiliation:
Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete Spa), Padova, 35100, Italy
I. Predebon
Affiliation:
Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete Spa), Padova, 35100, Italy
R. Paccagnella
Affiliation:
Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete Spa), Padova, 35100, Italy
F. Sattin
Affiliation:
Consorzio RFX (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete Spa), Padova, 35100, Italy
*
† Email address for correspondence: paolo.zanca@igi.cnr.it
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Abstract

We present a quasi-linear treatment of the drift-kinetic equation in the presence of a stochastic magnetic field, which provides a self-contained description of particle, parallel momentum and heat transport. Explicit analytical expressions, which satisfy the Onsager reciprocal relations, are obtained by approximating the distribution function by a local shifted Maxwellian. This theory completes previous formulations (Harvey et al., Phys. Rev. Lett., vol. 47, 1981, p. 102) by including the momentum transport and by generalizing the derivation from the cylindrical tokamak configuration to an arbitrary cylindrical pinch. Application to the reversed field pinch provides satisfactory results.

Keywords

plasma nonlinear phenomenaplasma instabilitiesplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 5 , October 2023 , 905890509
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

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References

Antoni, V., et al. 1998 Particle and energy transport in the RFX experiment. In Proceedings of the 17th IAEA Fusion Energy Conference, Yokohama, Japan. Fusion Energy, 1998, vol. 1, p. 871, EXP3/15.Google Scholar
Bragiinkii, S.I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics (ed. M.A. Leontovich), vol. 1, p. 205. Consultants Bureau.Google Scholar
Carraro, L., Gazza, E., Marrelli, L., Martin, P., Puiatti, M.E., Scarin, P., Valisa, M., Zaccaria, P., Zaniol, B. & the RFX Team 2005 Impurity behaviour and radiation pattern in the RFX-mod reversed field pinch. In Proceedings of the 32nd EPS Conference on Plasma Physics, Tarragona, Spain. Europhysics Conference Abstracts, vol. 29C, P-2.003. European Physical Society (EPS).Google Scholar
D'Angelo, F. & Paccagnella, R. 1996 The stochastic diffusion process in reversed-field pinch. Phys. Plasmas 3 (6), 2353.CrossRefGoogle Scholar
Fiksel, G., Almagri, A.F., Chapman, B.E., Mirnov, V.V., Ren, Y., Sarff, J.S. & Terry, P.W. 2009 Mass-dependent ion heating during magnetic reconnection in a laboratory plasma. Phys. Rev. Lett. 103, 145002.CrossRefGoogle Scholar
Finn, J.M., Guzdar, P.N. & Chernikov, A.A. 1992 Particle transport and rotation damping due to stochastic magnetic field lines. Phys. Fluids B 4, 1152.CrossRefGoogle Scholar
Fitzpatrick, R. 1999 Formation and locking of the “slinky mode” in reversed-field pinches. Phys. Plasmas 6, 1168.CrossRefGoogle Scholar
Frindström, R., Chapman, B.E., Almagri, A.F., Frassinetti, L., Brunsell, P.R., Nishizawa, T. & Sarff, J.S. 2018 Dependence of perpendicular viscosity on magnetic fluctuations in a stochastic topology. Phys. Rev. Lett. 120, 225002.CrossRefGoogle Scholar
Gobbin, M., et al. 2022 Ion heating and energy balance during magnetic reconnection events in the RFX-mod experiment. Nucl. Fusion 62, 026030.CrossRefGoogle Scholar
Guo, S.C., Paccagnella, R. & Romanelli, F. 1994 lon-temperature-gradient-driven instability and anomalous ion heating in reversed-field pinches. Phys. Plasmas 1, 2741.CrossRefGoogle Scholar
Harvey, R.W., McCoy, M.G., Hsu, J.Y. & Mirin, A.A. 1981 Electron dynamics associated with stochastic magnetic and ambipolar electric fields. Phys. Rev. Lett. 47, 102.CrossRefGoogle Scholar
Hinton, F.L. & Hazeltine, R.D. 1976 Theory of plasma transport in toroidal confinement systems. Rev. Mod. Phys. 48, 239.CrossRefGoogle Scholar
Innocente, P., Alfier, A., Canton, A. & Pasqualotto, R. 2009 Plasma performance and scaling laws in the RFX-mod reversed-field pinch experiment. Nucl. Fusion 49, 115022.CrossRefGoogle Scholar
Innocente, P., Lorenzini, R., Terranova, D. & Zanca, P. 2017 FLiT: a field line trace code for magnetic confinement devices. Plasma Phys. Control. Fusion 59, 045014.CrossRefGoogle Scholar
Ishihara, O., Xia, H. & Hirose, A. 1992 Resonance broadening theory of plasma turbulence. Phys. Fluids B 4 (2), 349.CrossRefGoogle Scholar
Krommes, J.A., Oberman, C. & Kleva, R.G. 1983 Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion. J. Plasma Phys. 30, 11.CrossRefGoogle Scholar
Lorenzini, R., et al. 2009 Self-organized helical equilibria as a new paradigm for ohmically heated fusion plasmas. Nat. Phys. 5, 570.CrossRefGoogle Scholar
Lorenzini, R., Auriemma, F., Canton, A. & Carraro, L. 2006 Particle transport in reversed field pinch helium plasmas. Phys. Plasmas 13, 112510.CrossRefGoogle Scholar
McChesney, J.M., Stern, R.A. & Bellan, P.M. 1987 Observations of fast stochastic ion heating by drift waves. Phys. Rev. Lett. 59, 1436.CrossRefGoogle ScholarPubMed
Onsager, L. 1931 Reciprocal relations in irreversible processes. Phys Rev. 37, 405.CrossRefGoogle Scholar
Predebon, I. & Paccagnella, R. 2007 Influence of slow particle dynamics on transport in stochastic plasmas. Phys. Plasmas 14, 082310.CrossRefGoogle Scholar
Predebon, I., Paccagnella, R., Puiatti, M.E. & Valisa, M. 2009 Transport simulations of reversed field pinch plasmas: an integrated model coupling magnetohydrodynamics and impurity physics. Phys. Plasmas 16, 102501.CrossRefGoogle Scholar
Rechester, A.B. & Rosenbluth, M.N. 1978 Electron heat transport in a tokamak with destroyed magnetic surfaces. Phys. Rev. Lett. 40, 38.CrossRefGoogle Scholar
Rechester, A.B., Rosenbluth, M.N. & White, R.B. 1979 Calculation of the Kolmogorov entropy for motion along a stochastic magnetic field. Phys. Rev. Lett. 42, 1247.CrossRefGoogle Scholar
Rice, J.E., Molvig, K. & Helava, H.I. 1982 Continuum x-ray emission from the Alcator a tokamak. Phys. Rev. A 25, 1645.CrossRefGoogle Scholar
Sattin, F., Garzotti, L., Paccagnella, R. & Terranova, D. 2005 Scaling of energy confinement time in RFX with magnetic fluctuations: comparison of experimental data with turbulent transport models. In Proceedings of the 32nd EPS Conference on Plasma Physics, Tarragona, Spain. Europhysics Conference Abstracts, vol. 29C, P-4.029. European Physical Society (EPS).Google Scholar
Scime, E., Cekic, M., Den Hartog, D.J., Hokin, S., Holly, D.J. & Watts, C. 1992 Ion heating and magnetohydrodynamic dynamo fluctuations in the reversed-field pinch. Phys. Fluids B 4, 4062.CrossRefGoogle Scholar
Spizzo, G., White, R.B. & Cappello, S. 2007 Chaos generated pinch effect in toroidal confinement devices. Phys. Plasmas 14, 102310.CrossRefGoogle Scholar
Spolaore, M., Antoni, V., Spada, E., Bergsåker, H., Cavazzana, R., Drake, J.R., Martines, E., Regnoli, G., Serianni, G. & Vianello, N. 2004 Vortex-induced diffusivity in reversed field pinch plasmas. Phys. Rev. Lett. 93, 215003.CrossRefGoogle ScholarPubMed
Trubnikov, B.A. 1965 Particle interactions in a fully ionized plasma. In Reviews of Plasma Physics (ed. M.A. Leontovich), vol. 1, p. 105. Consultants Bureau.Google Scholar
Vianello, N., Spada, E., Antoni, V., Spolaore, M., Serianni, G., Regnoli, G., Cavazzana, R., Bergsåker, H. & Drake, J.R. 2005 Self-regulation of E×B flow shear via plasma turbulence. Phys. Rev. Lett. 94, 135001.CrossRefGoogle Scholar
Wesson, J.A. 2004 Tokamaks, 3rd edn. Clarendon Press.Google Scholar
Zanca, P. & Terranova, D. 2004 Reconstruction of the magnetic perturbation in a toroidal reversed field pinch. Plasma Phys. Control. Fusion 46, 1115.CrossRefGoogle Scholar
Zaniol, B., Bolzonella, T., Cavazzana, R., Innocente, P., Zanca, P. & Zuin, M. 2015 Studies on RFX-mod discharges with spontaneous rotation. In Proceedings of the 42nd EPS Conference on Plasma Physics, Lisbon, Portugal, P4.153. European Physical Society (EPS).Google Scholar
Zuin, M., et al. 2017 Overview of the RFX-mod fusion science activity. Nucl. Fusion 57, 102012.CrossRefGoogle Scholar