Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Stationary state of an electron-ion ring

  • 14 Accesses


The stationary state of an electron-ion ring is investigated on the basis of the kinetic equation. The trajectories of the particles are found for given distributions of the charges on the assumption that the cross-sectional dimensions of the beam are much smaller than its radius. An analysis of the results shows that the formation of an electron-ion ring is characterized by the appearance of a stationary state in which the charge components of the ring are displaced relative to each other, the displacement decreasing the further the beam is away from the walls of the chamber and vanishing for complete charge neutralization.

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

Literature cited

  1. 1.

    O. I. Yarkovoi, Zh. Tekh. Fiz., No. 11, 1285 (1962).

  2. 2.

    I. N. Ivanov, M. L. Iovnovich, A. B. Kuznetsov, Yu. L. Obukhov, K. A. Reshetnikova, N. B. Rubin, V. P. Sarantsev, and O. I. Yarkovoi, Preprint of the Joint Institute for Nuclear Research, R9-4132, Dubna (1968).

  3. 3.

    R. C. Davidson and S. M. Mahajan, Part. Accel.,4, 53 (1972).

  4. 4.

    H. C. Davidson and J. D. Lawson, Part. Accel.,4, 1 (1972).

  5. 5.

    J. D. Laslett, ERAN-30. Lawrence Radiation Laboratory (1972).

  6. 6.

    A. N. Didenko, V. P. Grigor'ev, and Yu. P. Usov, High-Power Electron Beams and Their Application [in Russian], Atomizdat, Moscow (1977).

  7. 7.

    J. D, Laslett, Proc. Symposium ERA, Lawrence Radiation Laboratory (1968), p. 401.

Download references

Author information

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 29–35, November, 1979.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Grigor'ev, V.P., Veingardt, V.F. Stationary state of an electron-ion ring. Soviet Physics Journal 22, 1148–1152 (1979). https://doi.org/10.1007/BF00894961

Download citation


  • Stationary State
  • Kinetic Equation
  • Charge Neutralization
  • Charge Component
  • Complete Charge