Analytical Theory of Energy Relaxation Upon Propagation of a High-Energy Electron Beam in Gas

Abstract

This study is devoted to the development of an analytical theory for calculating the spatial distribution of the energy release upon propagation of a high-energy (1–100 keV) electron beam in a gas (based on the example of air). Based on the analysis of data on the cross sections of elastic and inelastic interactions between electrons and molecules of gases that are in the air composition, it was suggested that inelastic interaction causes energy relaxation, whereas elastic interaction leads to momentum relaxation. The model cross section of inelastic collisions of electrons with molecules is used for solving the Boltzmann kinetic equation for electrons; this cross section provides adequate description of the experimentally found energy dependence of the mass stopping power of electrons. The results for the dependence of the mean electron energy on the number of inelastic collisions are in good agreement with the results of calculation based on expansion of the distribution function in the number of collisions and solution by the Monte Carlo method. The calculations we performed show that the consideration of elastic collisions increases the spatial density of the energy release due to narrowing of the region where the main part of the energy of fast electrons is released, in comparison with calculations where only inelastic deceleration is taken into account.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Fraishtadt, V.L., Kuranov, A.L., and Sheikin, E.G., Tech. Phys., 1998, vol. 43, no. 11, p. 1309.

    Article  Google Scholar 

  2. 2.

    Sheikin, E.G. and Kuranov, A.L., MHD control in hypersonic aircraft, AIAA Pap. 2005-1335, 2005.

    Google Scholar 

  3. 3.

    Bityurin, V. and Bocharov, A.N., High Temp., 2010, vol. 48, no. 6, p. 874.

    Article  Google Scholar 

  4. 4.

    Park, C., Bogdanoff, D.W., and Mehta, U.B., J. Propul. Power, 2003, vol. 9, no. 4, p. 529.

    Article  Google Scholar 

  5. 5.

    Palm, P., Plonjes, E., Adamovich, I.V., and Rich, J.W., E-beam sustained low power budget air plasma, AIAA Pap. 2002-0637, 2002.

    Google Scholar 

  6. 6.

    Sheikin, E.G., Nucl. Instrum. Methods Phys. Res., Sect. B, 2014, vol. 319, p. 1.

    ADS  Article  Google Scholar 

  7. 7.

    Sheikin, E.G., Phys. Scr., 2010, 81045702.

    Google Scholar 

  8. 8.

    Sheikin, E.G. and Sukhomlinov, V.S., Calculation of space distribution of energy deposited by E-beam for flow control applications, AIAA Pap. 2006-1369, 2006.

    Google Scholar 

  9. 9.

    Marchuk, G.I., Metody rascheta yadernykh reaktorov (Methods for Calculating Nuclear Reactors), Moscow: Gosatomizdat, 1961.

    Google Scholar 

  10. 10.

    Kol’chuzhkin, A.M. and Uchaikin, V.V., Vvedenie v teoriyu prokhozhdeniya chastits cherez veshchestvo (Introduction to the Theory of the Passage of Particles through a Substance), Moscow: Atomizdat, 1978.

    Google Scholar 

  11. 11.

    Stopping powers for electrons and positrons, ICRU Rep. no. 37, Bethesda, MD: Int. Commission on Radiation Units and Measurements, 1984.

  12. 12.

    Mayol, R.R. and Salvat, F., Atom. Data Nucl. Data Tables, 1997, vol. 65, no. 21, p. 55.

    ADS  Article  Google Scholar 

  13. 13.

    Akkerman, A.F., Modelirovanie traektorii zaryazhennykh chastits v veshchestve (Simulation of the Trajectory of Charged Particles in Matter), Moscow: Energoatomizdat, 1991.

    Google Scholar 

  14. 14.

    Korn, G. and Korn, T., Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas, New York: McGraw-Hill, 1968.

    Google Scholar 

  15. 15.

    Macheret, S.O., Shnieder, M.N., and Miles, R.B., External supersonic flow and scramjet intel control by MHD with electron beam ionization, AIAA Pap. 2001-0492, 2001.

    Google Scholar 

  16. 16.

    Dapor, M., Nucl. Instrum. Methods Phys. Res., Sect. B, 2011, vol. 269, p. 1668.

    ADS  Article  Google Scholar 

  17. 17.

    Bateman, H. and Erdélyi, A., Tables of Integral Transforms, New-York: McGraw-Hill, 1954, vol. 1.

    Google Scholar 

  18. 18.

    Abramowits, M. and Stegun, I.A, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, 1964.

    Google Scholar 

  19. 19.

    Cercignani, C., Theory and Application of the Boltzmann Equation, Edinburgh: Scottish Academic Press, 1975.

    Google Scholar 

  20. 20.

    Cercignani, C., Mathematical Methods in Kinetic Theory, New York, Plenum, 1969.

    Google Scholar 

  21. 21.

    Von Grün, A.E., Z. Naturforsch., A: Phys. Sci., 1957, vol. 12, no. 2, p. 89.

    ADS  Article  Google Scholar 

  22. 22.

    Fröman, N. and Fröman, P.O., JWKB Approximation, Contributions to the Theory, Amsterdam: North-Holland, 1965.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to V. S. Sukhomlinov.

Additional information

Original Russian Text © V.S. Sukhomlinov, A.S. Mustafaev, 2018, published in Teplofizika Vysokikh Temperatur, 2018, Vol. 56, No. 1, pp. 14–23.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sukhomlinov, V.S., Mustafaev, A.S. Analytical Theory of Energy Relaxation Upon Propagation of a High-Energy Electron Beam in Gas. High Temp 56, 10–19 (2018). https://doi.org/10.1134/S0018151X18010182

Download citation