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Available energy and ground states of collisionless plasmas

Part of: Frontiers in Plasma Physics Conference Focus on Fusion

Published online by Cambridge University Press:  06 July 2017

Per Helander
Per Helander*
Affiliation:
Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is ‘available’ for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a ‘ground state’ in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plasma with small density and temperature fluctuations, the available energy is proportional to the mean square of these quantities, and exceeds the corresponding energy in ideal or resistive magnetohydrodynamics. If the first or second adiabatic invariant is conserved, ground states generally have inhomogeneous density and temperature. Magnetically confined plasmas are usually not in any ground state, but certain types of stellarator plasmas are so with respect to fluctuations that conserve both these adiabatic invariants, making the plasma linearly and nonlinearly stable to such fluctuations. Similar stability properties can also be enjoyed by plasmas confined by a dipole magnetic field.

Keywords

plasma confinementplasma energy balancemagnetized plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 4 , August 2017 , 715830401
Copyright
© Cambridge University Press 2017 

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References

Barnes, M., Abiuso, P. & Dorland, W.2017 Turbulent heating in an inhomogeneous, magnetized plasma slab. J. Plasma Phys. (submitted).CrossRefGoogle Scholar
Boxer, A. C., Bergmann, R., Ellsworth, J. L., Garnier, D. T., Kesner, J., Mauel, M. E. & Woskov, P. 2010 Turbulent inward pinch of plasma confined by a levitated dipole magnet. Nat. Phys. 6, 207–212.Google Scholar
Brizard, A., Fowler, T. K., Hua, D. & Morrison, P. J. 1991 Comments on Plasma Physcis and Controlled Fusion 14 (5), 263–273.Google Scholar
Dodin, I. Y. & Fisch, N. J. 2005 Variational formulation of Gardner’s restacking algorithm. Phys. Lett. A 341 (1–4), 187–192.Google Scholar
Dubin, D. H. E., Krommes, J. A., Oberman, C. & Lee, W. W. 1983 Nonlinear gyrokinetic equations. Phys. Fluids 26 (12), 3524–3535.Google Scholar
Dunkel, J. & Hilbert, S. 2014 Consistent thermostatistics forbids negative absolute temperatures. Nat. Phys. 10 (1), 67–72.CrossRefGoogle Scholar
Fisch, N. J. & Rax, J.-M. 1993 Free energy in plasmas under wave-induced diffusion. Phys. Fluids B 5 (6), 1754–1759.Google Scholar
Fletcher, L., Dennis, B. R., Hudson, H. S., Krucker, S., Phillips, K., Veronig, A., Battaglia, M., Bone, L., Caspi, A., Chen, Q. et al. 2011 An observational overview of solar flares. Space Sci. Rev. 159, 19–106.Google Scholar
Fowler, T. K. 1968 Thermodynamics of unstable plasmas. In Advances in Plasma Physics, Volume 1 (ed. Simon, A. & Thompson, W. B.), vol. 1, pp. 201–225. Interscience Publishers.Google Scholar
Garbet, X., Idomura, Y., Villard, L. & Watanabe, T. H. 2010 Gyrokinetic simulations of turbulent transport. Nucl. Fusion 50, 043002.Google Scholar
Garbet, X., Mantica, P., Angioni, C., Asp, E., Baranov, Y., Bourdelle, C., Budny, R., Crisanti, F., Cordey, G. & Garzotti, L. 2004 Physics of transport in tokamaks. Plasma Phys. Control. Fusion 46, B557–574.Google Scholar
Gardner, C. S. 1963 Bound on the energy available from a plasma. Phys. Fluids 6 (6), 839–840.Google Scholar
Hasegawa, A., Chen, L. & Mauel, M. E. 1990 A deuterium-helium-3 fusion reactor based on a dipole magnetic field. Nucl. Fusion 30 (11), 2405–2413.CrossRefGoogle Scholar
Hay, M. J., Schiff, J. & Fisch, N. J. 2015 Maximal energy extraction under discrete diffusive exchange. Phys. Plasmas 22 (10), 102108.CrossRefGoogle Scholar
Helander, P. 2014a Microstability of magnetically confined electron–positron plasmas. Phys. Rev. Lett. 113, 135003.CrossRefGoogle ScholarPubMed
Helander, P. 2014b Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77 (8), 087001.Google Scholar
Helander, P. & Connor, J. W. 2016 Gyrokinetic stability theory of electron–positron plasmas. J. Plasma Phys. 82 (3), 905820301.Google Scholar
Helander, P., Proll, J. H. E. & Plunk, G. G. 2013 Collisionless microinstabilities in stellarators. I. Analytical theory of trapped-particle modes. Phys. Plasmas 20 (12), 122505.Google Scholar
Helander, P., Strumik, M. & Schekochihin, A. A. 2016 Constraints on dynamo action in plasmas. J. Plasma Phys. 82, 905820601.Google Scholar
Isichenko, M. B., Gruzinov, A. V., Diamond, P. H. & Yushmanov, P. N. 1996 Anomalous pinch effect and energy exchange in tokamaks. Phys. Plasmas 3 (5), 1916–1925. 37th Annual Meeting of the Division-of-Plasma-Physics of the American-Physical-Society Location: Louisville, KY, Nov. 6–10, 1995.Google Scholar
Jackson, J. D. 1975 Classical Electrodynamics, 2nd edn. John Wiley and Sons.Google Scholar
Kesner, J. & Hastie, R. J. 2002 Electrostatic drift modes in a closed field line configuration. Phys. Plasmas 9 (2), 395–400.Google Scholar
Kotschenreuther, M., Rewoldt, G. & Tang, W. M. 1995 Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun. 88 (2–3), 128–140.CrossRefGoogle Scholar
Lorenz, E. N. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7 (2), 157–167.CrossRefGoogle Scholar
Proll, J. H. E., Helander, P., Connor, J. W. & Plunk, G. G. 2012 Resilience of quasi-isodynamic stellarators against trapped-particle instabilities. Phys. Rev. Lett. 108 (24), 245002.CrossRefGoogle ScholarPubMed
Rosenbluth, M. N. 1968 Low-frequency limit of interchange instability. Phys. Fluids 11, 869–872.Google Scholar
Schekochihin, A. A. 2017 Lecture Notes on Kinetic Theory and Magnetohydrodynamics of Plasmas. Oxford University.Google Scholar
Schmidt, G. 1965 Extended stability criterion for minimum-b geometries. Phys. Fluids 8 (4), 754–754.Google Scholar
Schuller, F. C. 1995 Disruptions in tokamaks. Plasma Phys. Control. Fusion 37, A135.Google Scholar
Simakov, A. N., Hastie, R. J. & Catto, P. J. 2002 Long mean-free path collisional stability of electromagnetic modes in axisymmetric closed magnetic field configurations. Phys. Plasmas 9, 201–211.CrossRefGoogle Scholar
Taylor, J. B. 1963 Some stable plasma equilibria in combined mirror-cusp fields. Phys. Fluids 6 (11), 1529–1536.Google Scholar
Taylor, J. B. 1964 Equilibrium and stability of plasma in arbitrary mirror fields. Phys. Fluids 7 (6), 767–773.Google Scholar
Taylor, J. B. & Newton, S. L. 2015 Special topics in plasma confinement. J. Plasma Phys. 81, 205810501.Google Scholar
Yankov, V. V. & Nycander, J. 1997 Description of turbulent transport in tokamaks by invariants. Phys. Plasmas 4 (8), 2907–2919.Google Scholar
Yoshida, Z., Saitoh, H., Morikawa, J., Yano, Y., Watanabe, S. & Ogawa, Y. 2010 Magnetospheric vortex formation: self-organized confinement of charged particles. Phys. Rev. Lett. 104, 235004.Google Scholar