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Nonlinear Development of the Beam‐Plasma Instability
1.W. E. Drummond and D. Pines, Nucl. Fusion Suppl. Pt. 3, 1049 (1962);
1.and A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, Nucl. Fusion Suppl. Pt. 2, 465 (1962)., Nucl. Fusion Suppl.
2.The identical problem has been treated previously by V. D. Shapiro, Zh. Eksp. Teor. Fiz. 44, 613 (1963)
2.[V. D. Shapiro, Sov. Phys. JETP 17, 416 (1963)]. However, he made the assumption that at the time of trapping the oscillation energy of the beam could be identified with a beam temperature.
3.This is similar to the treatment of ion acoustic waves by T. E. Stringer, J. Nucl. Energy Pt. C 6, 267 (1964).
4.T. M. O’Neil and J. H. Malmberg, Phys. Fluids 11, 1754 (1968).
5.This result from linear theory is still valid, because the background electrons still have linear orbits.
6.This effect is very similar to the decay of oscillations associated with the damping of large amplitude plasma waves. See T. M. O’Neil, Phys. Fluids 8, 2255 (1965).
7.The numerical results reported here should be considered rough estimates, but the parametric dependence is correctly indicated.
8.J. H. Malmberg and C. B. Wharton, Phys. Fluids 12, 2600 (1969).
8.See also J. R. Apel, Phys. Rev. Letters 19, 744 (1967).
9.K. V. Roberts and H. L. Berk, Phys. Rev. Letters 19, 297 (1967).
10.J. A. Davis and A. Bers, in Turbulence of Fluids and Plasmas (Polytechnic Institute of Brooklyn Press, Brooklyn, New York, 1969), p. 87.
11.J. M. Dawson and R. Shanny, Phys. Fluids 11, 1506 (1968).
12.R. L. Morse (private communication).
13.R. W. Gould (private communication).
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