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Dynamics of positrons during relativistic electron runaway

Published online by Cambridge University Press:  22 October 2018

O. Embréus Open the ORCID record for O. Embréus [Opens in a new window] ,
L. Hesslow Open the ORCID record for L. Hesslow [Opens in a new window] ,
M. Hoppe ,
G. Papp ,
K. Richards  and
T. Fülöp Open the ORCID record for T. Fülöp [Opens in a new window]
O. Embréus*
Affiliation:
Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
L. Hesslow
Affiliation:
Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
M. Hoppe
Affiliation:
Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
G. Papp
Affiliation:
Max-Planck-Institute for Plasma Physics, D-85748 Garching, Garching, Germany
K. Richards
Affiliation:
Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
T. Fülöp
Affiliation:
Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
*
†Email address for correspondence: embreus@chalmers.se
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Abstract

Sufficiently strong electric fields in plasmas can accelerate charged particles to relativistic energies. In this paper we describe the dynamics of positrons accelerated in such electric fields, and calculate the fraction of created positrons that become runaway accelerated, along with the amount of radiation that they emit. We derive an analytical formula that shows the relative importance of the different positron production processes, and show that, above a certain threshold electric field, the pair production by photons is lower than that by collisions. We furthermore present analytical and numerical solutions to the positron kinetic equation; these are applied to calculate the fraction of positrons that become accelerated or thermalized, which enters into rate equations that describe the evolution of the density of the slow and fast positron populations. Finally, to indicate operational parameters required for positron detection during runaway in tokamak discharges, we give expressions for the parameter dependencies of detected annihilation radiation compared to bremsstrahlung detected at an angle perpendicular to the direction of runaway acceleration. Using the full leading-order pair-production cross-section, we demonstrate that previous related work has overestimated the collisional pair production by at least a factor of four.

Keywords

runaway electrons
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 5 , October 2018 , 905840506
Copyright
© Cambridge University Press 2018 

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References

Alwall, J., Frederix, R., Frixione, S., Hirschi, V., Maltoni, F., Mattelaer, O., Shao, H.-S., Stelzer, T., Torrielli, P. & Zaro, M. 2014 The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. J. High Energy Phys. 7, 79.Google Scholar
Anderson, C. D. 1932 The apparent existence of easily deflectable positives. Science 76 (1967), 238–239.Google Scholar
Briggs, M. S., Connaughton, V., Wilson-Hodge, C., Preece, R. D., Fishman, G. J., Kippen, R. M., Bhat, P. N., Paciesas, W. S., Chaplin, V. L., Meegan, C. A. et al. 2011 Electron–positron beams from terrestrial lightning observed with Fermi GBM. Geophys. Res. Lett. 38 (2), l02808.Google Scholar
Charlton, M. & Humberston, J. 2001 Positron Physics. Cambridge University Press.Google Scholar
Chen, H., Wilks, S. C., Bonlie, J. D., Liang, E. P., Myatt, J., Price, D. F., Meyerhofer, D. D. & Beiersdorfer, P. 2009 Relativistic positron creation using ultraintense short pulse lasers. Phys. Rev. Lett. 102, 105001.Google Scholar
Connor, J. & Hastie, R. 1975 Relativistic limitations on runaway electrons. Nucl. Fusion 15, 415.Google Scholar
Dreicer, H. 1959 Electron and ion runaway in a fully ionized gas I. Phys. Rev. 115, 238–249.Google Scholar
Dwyer, J. R. 2012 The relativistic feedback discharge model of terrestrial gamma ray flashes. J. Geophys. Res. 117 (A2), a02308.Google Scholar
Dwyer, J. R. & Uman, M. A. 2014 The physics of lightning. Phys. Rep. 534 (4), 147–241.Google Scholar
Embréus, O., Stahl, A. & Fülöp, T. 2016 Effect of bremsstrahlung radiation emission on fast electrons in plasmas. New J. Phys. 18 (9), 093023.Google Scholar
Embréus, O., Stahl, A. & Fülöp, T. 2018 On the relativistic large-angle electron collision operator for runaway avalanches in plasmas. J. Plasma Phys. 84 (1), 905840102.Google Scholar
Fülöp, T. & Papp, G. 2012 Runaway positrons in fusion plasmas. Phys. Rev. Lett. 108, 225003.Google Scholar
Fülöp, T., Pokol, G., Helander, P. & Lisak, M. 2006 Destabilization of magnetosonic-whistler waves by a relativistic runaway beam. Phys. Plasmas 13 (6), 062506.Google Scholar
Gabrielse, G., Bowden, N. S., Oxley, P., Speck, A., Storry, C. H., Tan, J. N., Wessels, M., Grzonka, D., Oelert, W., Schepers, G. et al. 2002 Background-free observation of cold antihydrogen with field-ionization analysis of its states. Phys. Rev. Lett. 89, 213401.Google Scholar
Gryaznykh, D. 1998 Cross section for the production of electron–positron pairs by electrons in the field of a nucleus. Phys. Atom. Nucl. 61 (3), 394–399.Google Scholar
Guanying, Y., Liu, J., Xie, J. & Li, J. 2017 Detection of tokamak plasma positrons using annihilation photons. Fusion Engng Des. 118, 124–128.Google Scholar
Gurevich, A. V. & Zybin, K. P. 2001 Runaway breakdown and electric discharges in thunderstorms. Phys.-Usp. 44 (11), 1119–1140.Google Scholar
Haug, E. 1975 Bremsstrahlung and pair production in the field of free electrons. Zeitsch. für Natur. A 30 (9), 1099–1113.Google Scholar
Heitler, W. 1954 The Quantum Theory of Radiation, vol. 86. Courier Corporation.Google Scholar
Helander, P., Eriksson, L.-G. & Andersson, F. 2002 Runaway acceleration during magnetic reconnection in tokamaks. Plasma Phys. Control. Fusion 44, B247–B262.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
Hesslow, L., Embréus, O., Stahl, A., Dubois, T. C., Papp, G., Newton, S. L. & Fülöp, T. 2017 Effect of partially screened nuclei on fast-electron dynamics. Phys. Rev. Lett. 118, 255001.Google Scholar
Hesslow, L., Embréus, O., Wilkie, G. J., Papp, G. & Fülöp, T. 2018 Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation. Plasma Phys. Control. Fusion 60, 074010.Google Scholar
Hirvijoki, E., Pusztai, I., Decker, J., Embréus, O., Stahl, A. & Fülöp, T. 2015 Radiation reaction induced non-monotonic features in runaway electron distributions. J. Plasma Phys. 81 (5), 475810502.Google Scholar
Hollmann, E. M., Parks, P. B., Commaux, N., Eidietis, N. W., Moyer, R. A., Shiraki, D., Austin, M. E., Lasnier, C. J., Paz-Soldan, C. & Rudakov, D. L. 2015 Measurement of runaway electron energy distribution function during high-z gas injection into runaway electron plateaus in DIII-D. Phys. Plasmas 22 (5), 056108.Google Scholar
Hunt, A. W., Cassidy, D. B., Selim, F. A., Haakenaasen, R., Cowan, T. E., Howell, R. H., Lynn, K. G. & Golovchenko, J. A. 1999 Spatial sampling of crystal electrons by in-flight annihilation of fast positrons. Nature 402, 157.Google Scholar
Jayakumar, R., Fleischmann, H. & Zweben, S. 1993 Collisional avalanche exponentiation of runaway electrons in electrified plasmas. Phys. Lett. A 172, 447–451.Google Scholar
Landau, L. & Lifshitz, E. 1983 Quantum Electrodynamics. Pergamon.Google Scholar
Landreman, M., Stahl, A. & Fülöp, T. 2014 Numerical calculation of the runaway electron distribution function and associated synchrotron emission. Comput. Phys. Commun. 185 (3), 847–855.Google Scholar
Lehtinen, N. G., Bell, T. F. & Inan, U. S. 1999 Monte Carlo simulation of runaway MeV electron breakdown with application to red sprites and terrestrial gamma ray flashes. J. Geophys. Res. 104 (A11), 24699.Google Scholar
Liu, C. & Wang, H. 2009 Reconnection electric field and hardness of X-Ray emission of solar flares. Astrophys. J. 696, L27–L31.Google Scholar
Liu, J., Qin, H., Fisch, N. J., Teng, Q. & Wang, X. 2014 What is the fate of runaway positrons in tokamaks?. Phys. Plasmas 21 (6), 064503. doi:10.1063/1.4882435.Google Scholar
Murphy, R. J., Share, G. H., Skibo, J. G. & Kozlovsky, B. 2005 The physics of positron annihilation in the solar atmosphere. Astrophys. J. Suppl. Ser. 161 (2), 495.Google Scholar
Pautasso, G., Bernert, M., Dibon, M., Duval, B., Dux, R., Fable, E., Fuchs, J., Conway, G., Giannone, L., Gude, A. et al. 2016 Disruption mitigation by injection of small quantities of noble gas in ASDEX Upgrade. Plasma Phys. Control. Fusion 59 (1), 014046.Google Scholar
Paz-Soldan, C., Cooper, C. M., Aleynikov, P., Pace, D. C., Eidietis, N. W., Brennan, D. P., Granetz, R. S., Hollmann, E. M., Liu, C., Lvovskiy, A. et al. 2017 Spatiotemporal evolution of runaway electron momentum distributions in tokamaks. Phys. Rev. Lett. 118, 255002.Google Scholar
Prantzos, N., Boehm, C., Bykov, A. M., Diehl, R., Ferrière, K., Guessoum, N., Jean, P., Knoedlseder, J., Marcowith, A., Moskalenko, I. V. et al. 2011 The 511 keV emission from positron annihilation in the galaxy. Rev. Mod. Phys. 83, 1001–1056.Google Scholar
Priest, E. & Forbes, T. 2002 The magnetic nature of solar flares. Astron. Astrophys. Rev. 10 (4), 313–377.Google Scholar
Raichle, M. E. 1985 Positron emission tomography: progress in brain imaging. Nature 317, 574.Google Scholar
Rosenbluth, M. & Putvinski, S. 1997 Theory for avalanche of runaway electrons in tokamaks. Nucl. Fusion 37, 1355–1362.Google Scholar
Sarri, G. 2015 Laser-driven generation of high-quality ultra-relativistic positron beams. J. Plasma Phys. 81 (2), 415810202.Google Scholar
Sokolov, Y. 1979 ‘Multiplication’ of accelerated electrons in a tokamak. JETP Lett. 29, 218–221.Google Scholar
Solodov, A. & Betti, R. 2008 Stopping power and range of energetic electrons in dense plasmas of fast-ignition fusion targets. Phys. Plasmas 15 (4), 042707.Google Scholar
Stahl, A., Embréus, O., Papp, G., Landreman, M. & Fülöp, T. 2016 Kinetic modelling of runaway electrons in dynamic scenarios. Nucl. Fusion 56 (11), 112009.Google Scholar
Stahl, A., Hirvijoki, E., Decker, J., Embréus, O. & Fülöp, T. 2015 Effective critical electric field for runaway electron generation. Phys. Rev. Lett. 114, 115002.Google Scholar
Surko, C. M. & Greaves, R. G. 2004 Emerging science and technology of antimatter plasmas and trap-based beams. Phys. Plasmas 11 (5), 2333–2348.Google Scholar
Tsuchiya, H., Enoto, T., Yamada, S., Yuasa, T., Nakazawa, K., Kitaguchi, T., Kawaharada, M., Kokubun, M., Kato, H., Okano, M. et al. 2011 Long-duration $\unicode[STIX]{x1D6FE}$ ray emissions from 2007 and 2008 winter thunderstorms. J. Geophys. Res. 116 (D9), d09113.Google Scholar
Vodopiyanov, I., Dwyer, J. R., Cramer, E. S., Lucia, R. & Rassoul, H. K. 2015 The effect of direct electron–positron pair production on relativistic feedback rates. J. Geophys. Res. 120 (1), 800–806.Google Scholar
Wilks, S. C., Langdon, A. B., Cowan, T. E., Roth, M., Singh, M., Hatchett, S., Key, M. H., Pennington, D., MacKinnon, A. & Snavely, R. A. 2001 Energetic proton generation in ultra-intense laser–solid interactions. Phys. Plasmas 8 (2), 542–549.Google Scholar
Wilson, C. T. R. 1925 The acceleration of $\unicode[STIX]{x1D6FD}$ -particles in strong electric fields such as those of thunderclouds. Math. Proc. Cambridge Philos. Soc. 22, 534.Google Scholar