The Dreicer field (or Dreicer electric field) is the critical electric field above which electrons in a collisional plasma can be accelerated to become runaway electrons. It was named after Harry Dreicer who derived the expression in 1959[1] and expanded on the concept (i.e. runaway generation) in 1960.[2] The Dreicer field is an important parameter in the study of tokamaks to suppress runaway generation in nuclear fusion.[3][4][5]

The Dreicer field is given by[6][7]

where is the electron density, is the elementary charge, is the Coulomb logarithm, is the vacuum permittivity, is the electron mass and is the electron thermal speed. It was derived by considering the balance between the electric field and the collisional forces acting on a single electron within the plasma.[6][8]

Recent experiments have shown that the electric field required to accelerate electrons is significantly larger than the theoretically calculated Dreicer field.[9][10][11] New models have been proposed to explain the discrepancy.[8][12]

References

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  1. ^ Dreicer, H. (1959-07-15). "Electron and Ion Runaway in a Fully Ionized Gas. I". Physical Review. 115 (2): 238–249. Bibcode:1959PhRv..115..238D. doi:10.1103/PhysRev.115.238.
  2. ^ Dreicer, H. (1960-01-15). "Electron and Ion Runaway in a Fully Ionized Gas. II". Physical Review. 117 (2): 329–342. Bibcode:1960PhRv..117..329D. doi:10.1103/PhysRev.117.329. ISSN 0031-899X.
  3. ^ Plyusnin, V. V.; Riccardo, V; Jaspers, R; Alper, B; Kiptily, V. G.; Mlynar, J; Popovichev, S; Luna, E. de La; Andersson, F (2006). "Study of runaway electron generation during major disruptions in JET". Nuclear Fusion. 46 (2): 277–284. Bibcode:2006NucFu..46..277P. doi:10.1088/0029-5515/46/2/011. ISSN 0029-5515. S2CID 121189586.
  4. ^ Smith, H. M.; Verwichte, E. (2008-07-01). "Hot tail runaway electron generation in tokamak disruptions". Physics of Plasmas. 15 (7): 072502. Bibcode:2008PhPl...15g2502S. doi:10.1063/1.2949692. ISSN 1070-664X.
  5. ^ TEXTOR Team; Lehnen, M.; Bozhenkov, S. A.; Abdullaev, S. S.; Jakubowski, M. W. (2008-06-24). "Suppression of Runaway Electrons by Resonant Magnetic Perturbations in TEXTOR Disruptions". Physical Review Letters. 100 (25): 255003. Bibcode:2008PhRvL.100y5003L. doi:10.1103/PhysRevLett.100.255003. hdl:11858/00-001M-0000-0027-0160-8. PMID 18643669.
  6. ^ a b Wesson, John; Campbell, D. J. (2004). Tokamaks (3rd ed.). Oxford: Clarendon Press. ISBN 0198509227. OCLC 52324306.
  7. ^ Connor, J.W.; Hastie, R.J. (1975-06-01). "Relativistic limitations on runaway electrons". Nuclear Fusion. 15 (3): 415–424. Bibcode:1975NucFu..15..415C. doi:10.1088/0029-5515/15/3/007. ISSN 0029-5515. S2CID 120694150.
  8. ^ a b Stahl, A.; Hirvijoki, E.; Decker, J.; Embréus, O.; Fülöp, T. (2015-03-17). "Effective Critical Electric Field for Runaway-Electron Generation". Physical Review Letters. 114 (11): 115002. arXiv:1412.4608. Bibcode:2015PhRvL.114k5002S. doi:10.1103/physrevlett.114.115002. ISSN 0031-9007. PMID 25839283. S2CID 15889985.
  9. ^ Martín-Solís, J. R.; Sánchez, R.; Esposito, B. (2010-10-25). "Experimental Observation of Increased Threshold Electric Field for Runaway Generation due to Synchrotron Radiation Losses in the FTU Tokamak". Physical Review Letters. 105 (18): 185002. Bibcode:2010PhRvL.105r5002M. doi:10.1103/PhysRevLett.105.185002. PMID 21231111.
  10. ^ Paz-Soldan, C.; Eidietis, N. W.; Granetz, R.; Hollmann, E. M.; Moyer, R. A.; Wesley, J. C.; Zhang, J.; Austin, M. E.; Crocker, N. A. (2014-02-01). "Growth and decay of runaway electrons above the critical electric field under quiescent conditions". Physics of Plasmas. 21 (2): 022514. Bibcode:2014PhPl...21b2514P. doi:10.1063/1.4866912. ISSN 1070-664X. OSTI 1354820.
  11. ^ Granetz, R. S.; Esposito, B.; Kim, J. H.; Koslowski, R.; Lehnen, M.; Martin-Solis, J. R.; Paz-Soldan, C.; Rhee, T.; Wesley, J. C. (2014-07-01). "An ITPA joint experiment to study runaway electron generation and suppression". Physics of Plasmas. 21 (7): 072506. Bibcode:2014PhPl...21g2506G. doi:10.1063/1.4886802. ISSN 1070-664X.
  12. ^ Konovalov, S. V.; Aleynikov, P.; Ismailov, R. E. (2016). "Dreicer mechanism of runaway electron generation in presence of high-Z impurities" (PDF). 43rd EPS Conference on Plasma Physics. European Physical Society.