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Gyrokinetic stability theory of electron–positron plasmas

Published online by Cambridge University Press:  04 May 2016

P. Helander*
Affiliation:
Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
J. W. Connor
Affiliation:
Culham Centre for Fusion Energy, Abingdon OX14 3DB, UK
*
Email address for correspondence: per.helander@ipp.mpg.de

Abstract

The linear gyrokinetic stability properties of magnetically confined electron–positron plasmas are investigated in the parameter regime most likely to be relevant for the first laboratory experiments involving such plasmas, where the density is small enough that collisions can be ignored and the Debye length substantially exceeds the gyroradius. Although the plasma beta is very small, electromagnetic effects are retained, but magnetic compressibility can be neglected. The work of a previous publication (Helander, Phys. Rev. Lett., vol. 113, 2014a, 135003) is thus extended to include electromagnetic instabilities, which are of importance in closed-field-line configurations, where such instabilities can occur at arbitrarily low pressure. It is found that gyrokinetic instabilities are completely absent if the magnetic field is homogeneous: any instability must involve magnetic curvature or shear. Furthermore, in dipole magnetic fields, the stability threshold for interchange modes with wavelengths exceeding the Debye radius coincides with that in ideal magnetohydrodynamics. Above this threshold, the quasilinear particle flux is directed inward if the temperature gradient is sufficiently large, leading to spontaneous peaking of the density profile.

Type
Research Article
Copyright
© Cambridge University Press 2016 

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References

Baltenkov, A. S. & Gilerson, V. B. 1985 Measurement of the temperature of a dense plasma by means of positron annihilation. Sov. J. Plasma Phys. 10, 632634.Google Scholar
Birmingham, T. 1969 Convection electric fields and the diffusion of trapped magnetospheric radiation. J. Geophys. Res. 74, 21692181.Google 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, 207212.CrossRefGoogle 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), 24052413.Google Scholar
Heitler, W. 1953 The Quantum Theory of Radiation, 3rd edn. Oxford University Press.Google 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; (The relevant equation is to be found on page 24 and should have $B$ in the numerator rather than in the denominator.).Google Scholar
Helander, P. & Ward, D. J. 2003 Positron creation and annihilation in tokamak plasmas with runaway electrons. Phys. Rev. Lett. 90, 135004.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2006 Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651 (1), 590614.Google Scholar
Kesner, J. & Hastie, R. J. 2002 Electrostatic drift modes in a closed field line configuration. Phys. Plasmas 9, 395400.Google Scholar
Pedersen, T. S., Boozer, A. H., Dorland, W., Kremer, J. P. & Schmitt, R. 2003 Prospects for the creation of positron–electron plasmas in a non-neutral stellarator. J. Phys. B 36 (5), 10291039.Google Scholar
Pedersen, T. S., Danielson, J. R., Hugenschmidt, C., Marx, G., Sarasola, X., Schauer, F., Schweikhard, L., Surko, C. M. & Winkler, E. 2012 Plans for the creation and studies of electron–positron plasmas in a stellarator. New J. Phys. 14 (3), 035010.Google Scholar
Rosenbluth, M. N. & Longmire, C. L. 1957 Stability of plasmas confined by magnetic fields. Ann. Phys. 1 (2), 120140.Google Scholar
Saitoh, H., Stanja, J., Stenson, E. V., Hergenhahn, U., Niemann, H., Pedersen, T. S., Stoneking, M. R., Piochacz, C. & Hugenschmidt, C. 2015 Efficient injection of an intense positron beam into a dipole magnetic field. New J. Phys. 17 (10), 103038.Google Scholar
Saitoh, H., Yoshida, Z., Morikawa, J., Yano, Y., Mizushima, T., Ogawa, Y., Furukawa, M., Kawai, Y., Harima, K., Kawazura, Y. et al. 2011 High-beta plasma formation and observation of peaked density profile in RT-1. Nucl. Fusion 51, 063034.Google Scholar
Sarri, G., Poder, K., Cole, J. M., Schumaker, W., Di Piazza, A., Reville, B., Dzelzainis, T., Doria, D., Gizzi, L. A., Grittani, G. et al. 2015 Generation of neutral and high-density electron–positron pair plasmas in the laboratory. Nat. Commun. 6, 6747.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, 201211.Google Scholar
Tang, W. M., Connor, J. W. & Hastie, R. J. 1980 Kinetic-ballooning-mode theory in general geometry. Nucl. Fusion 20 (11), 14391453.Google Scholar
Tsytovich, V. & Wharton, C. B. 1978 Laboratory electron–positron plasma – a new research object. Comments Plasma Phys. Control. Fusion 4 (4), 91100.Google Scholar