Abstract
The three major sources of radiation loss from a plasma are described: bremsstrahlung (free-free), line (bound-bound), and recombination (free-bound) radiation are shown and the impact of these radiative mechanisms are discussed from the standpoint of impurities in low-Z fusion plasmas. A fourth potential radiation loss term in magnetically confined plasmas, synchrotron radiation, is also discussed. The optical thickness of the plasma is discussed to contrast the methods used to calculate radiation loss in a magnetically confined plasma vis-a-vis an inertially confined plasma are shown, with the coronal model for the former and the Saha equation and more complex models for the latter. The radiation in transient situations is discussed, including the non-LTE effects found in inertially confined plasma. The basic Lawson criterion is introduced in order to form an overall energy balance for the plasma. The equivalent rho-R condition for inertial confinement is introduced. Energy balance for reactors with other features including blanket multiplication and direct conversion is also addressed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramowitz, M.: Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1974)
Biedenharn, L.C.: A note on Sommerfeld’s bremsstrahlung formula. Phys. Rev. 102, 262–263 (1956). http://link.aps.org/doi/10.1103/PhysRev.102.262
Chung, H.K., Chen, M., Morgan, W., Ralchenko, Y., Lee, R.: FLYCHK: generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements. High Energy Dens. Phys. 1(1), 3–12 (2005). http://dx.doi.org/10.1016/j.hedp.2005.07.001; http://www.sciencedirect.com/science/article/pii/S1574181805000029
Colchin, R.: Target plasma trapping. Nucl. Fusion 11(4), 329 (1971). http://stacks.iop.org/0029-5515/11/i=4/a=002
Davis, J., Jacobs, V.L., Kepple, P.C., Blaha, M.: Radiative cooling of tokamak plasmas due to multiply-charged Fe impurity ions. J. Quant. Spectrosc. Radiat. Transf. 17, 139–147 (1977)
Dunn, G.H., Van Zyl, B.: Electron impact dissociation of \({\mathrm {H}}_{2}^{+}\). Phys. Rev. 154, 40–51 (1967). http://link.aps.org/doi/10.1103/PhysRev.154.40
Fowler, T.K.: Effect of energy degradation on the critical current in an OGRA-type device. Oak Ridge National Laboratory Technical Report, ORNL-3037 (1960)
Fraley, G.S., Linnebur, E.J., Mason, R.J., Morse, R.L.: Thermonuclear burn characteristics of compressed deuterium-tritium microspheres. Phys. Fluids 17(2), 474–489 (1974). http://dx.doi.org/10.1063/1.1694739; http://scitation.aip.org/content/aip/journal/pof1/17/2/10.1063/1.1694739
Ginzburg, V.L.: Important elementary processes in cosmic-ray astrophysics and X-ray astronomy. In: DeWitt, C., Schatzman, E., Veron, P. (eds.) High Energy Astrophysics, vol. 1. Gordon and Breach, New York (1967)
Griem, H.R.: Principles of Plasma Spectroscopy. Cambridge University Press, Cambridge (1997). Cambridge Books Online, http://dx.doi.org/10.1017/CBO9780511524578
Hopkins, G.R., Rawls, J.M.: Impurity radiation from medium density plasmas. Nucl. Technol. 36(2), 171–186 (1977)
International Atomic Energy Agency: ALLADIN database. https://www-amdis.iaea.org/ALADDIN/ (2016)
Janev, R.K., Langer, W.D., Post, D.E., Evans, K.: Electron impact collision processes. In: Elementary Processes in Hydrogen-Helium Plasmas: Cross Sections and Reaction Rate Coefficients, pp. 17–114. Springer, Berlin (1987). http://dx.doi.org/10.1007/978-3-642-71935-6_2
Karzas, W.J., Latter, R.: Electron radiative transitions in a coulomb field. Astrophys. J. Suppl 6, 167 (1961). https://doi.org/10.1086/190063
Kieffer, L.J., Dunn, G.H.: Dissociative ionization of H2 and D2. Phys. Rev. 158, 61–65 (1967). http://link.aps.org/doi/10.1103/PhysRev.158.61
Kieffer, L.J., Dunn, G.H.: Dissociative ionization of H2 and D2. Phys. Rev. 164, 270–270 (1967). http://link.aps.org/doi/10.1103/PhysRev.164.270.5
Kramers, H.A.: Xciii. On the theory of X-ray absorption and of the continuous x-ray spectrum. Philos. Mag. Ser. 6 46(275), 836–871 (1923). https://doi.org/10.1080/14786442308565244
Kraus, D., Chapman, D.A., Kritcher, A.L., Baggott, R.A., Bachmann, B., Collins, G.W., Glenzer, S.H., Hawreliak, J.A., Kalantar, D.H., Landen, O.L., Ma, T., Le Pape, S., Nilsen, J., Swift, D.C., Neumayer, P., Falcone, R.W., Gericke, D.O., Döppner, T.: X-ray scattering measurements on imploding CH spheres at the National Ignition Facility. Phys. Rev. E 94, 011202 (2016). http://link.aps.org/doi/10.1103/PhysRevE.94.011202
Kukushkin, A.B., Minashin, P.V., Polevoi, A.R.: Impact of magnetic field inhomogeneity on electron cyclotron radiative loss in tokamak reactors. Plasma Phys. Rep. 38(3), 187–196 (2012). DOI 10.1134/S1063780X12030038. http://dx.doi.org/10.1134/S1063780X12030038
Lawson, J.D.: Some criteria for a power producing thermonuclear reactor. Technical report, Atomic Energy Research Establishment, Harwell, Berkshire (1955). https://www.euro-fusion.org/wpcms/wp-content/uploads/2012/10/dec05-aere-gpr1807.pdf
Lotz, W.: Electron-impact ionization cross-sections and ionization rate coefficients for atoms and ions from hydrogen to calcium. Z. Phys. 216(3), 241–247 (1968). http://dx.doi.org/10.1007/BF01392963
More, R.M.: Atoms in dense plasmas. In: Briand, J.P. (ed.) Atoms in Unusual Situations, pp. 155–215. Springer US, Boston (1986). http://dx.doi.org/10.1007/978-1-4757-9337-6_7
Morozov, D.K., Baronova, E.O., Senichenkov, I.Y.: Impurity radiation from a tokamak plasma. Plasma Phys. Rep. 33(11), 906–922 (2007). http://dx.doi.org/10.1134/S1063780X07110037
Planck, M.: Zur quantenstatistik des bohrschen atommodells (On the quantum statistics of Bohr’s atom model). Ann. Phys. 380, 673–684 (1924)
Post, D., Jensen, R., Tarter, C., Grasberger, W., Lokke, W.: Steady-state radiative cooling rates for low-density, high-temperature plasmas. At. Data Nucl. Data Tables 20(5), 397–439 (1977). http://dx.doi.org/10.1016/0092-640X(77)90026-2; http://www.sciencedirect.com/science/article/pii/0092640X77900262
Saha, M.N.: LIII. Ionization in the solar chromosphere. Philos. Mag. Ser. 6 40(238), 472–488 (1920). http://dx.doi.org/10.1080/14786441008636148
Scott, H., Hansen, S.: Advances in NLTE modeling for integrated simulations. High Energy Dens. Phys. 6(1), 39–47 (2010). http://dx.doi.org/10.1016/j.hedp.2009.07.003; http://www.sciencedirect.com/science/article/pii/S1574181809000834
Seaton, M.J.: Radiative recombination of hydrogenic ions. Mon. Not. R. Astron. Soc. 119(2), 81–89 (1959). https://doi.org/10.1093/mnras/119.2.81; http://mnras.oxfordjournals.org/content/119/2/81.abstract
Sommerfeld, A.J.F.: Atombau und Spektrallinien, vol. 2. Ungar, New York (1953)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Morse, E. (2018). Energy Gain and Loss Mechanisms in Plasmas and Reactors. In: Nuclear Fusion. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-98171-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-98171-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98170-3
Online ISBN: 978-3-319-98171-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)