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3343026580
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note
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If self-focusing is significant, some local measure of hot spot or filament width is required.
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22
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0031380560
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These estimates may be affected by self focusing, as in the case of SBS discussed in V. T. Tikhonchuk, S. Hüller, and P. Mounaix, Phys. Plasmas 4, 4369 (1997).
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Mounaix, P.3
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26
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3342990246
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note
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Since this model is in terms of the wave spatial envelopes, local in this context means over a wavelength of the EPW.
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31
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3342966281
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note
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Since the model is nonlinear, it is possible that solutions with period other than that of the source are possible, including nonperiodic solutions. However, those with period are the same as the source preferentially participate in stimulated scatter.
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32
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0007119676
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J. L. Schwarzmeier, H. R. Lewis, B. Abraham-Shrauner, and K. R. Symon, Phys. Fluids 22, 1747 (1979).
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33
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note
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Also, if the potential does not have a unique minimum, there will be more than one class of trapped orbits, some with the same energy.
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35
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3342908997
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note
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This and other technical results related to elliptic functions were facilitated by Mathematica, Copyright 1988-1999 Wolfram Research, Inc., Version number 4.0.0.0.
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36
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0038706448
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0039130750
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This is also the case when ν is the coefficient of the actual electron collision operator, S. P. Auerbach, Phys. Fluids 20, 1836 (1977).
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Auerbach, S.P.1
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0037691983
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edited by D. Pines Addison-Wesley, New York, Chap. 9
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W. L. Kruer, in The Physics of Laser Plasma Interactions, 1st edition, edited by D. Pines (Addison-Wesley, New York, 1988), Chap. 9, p. 104.
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Kruer, W.L.1
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44
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3342876071
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note
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This can be turned around: for given ν, what is the value of φ for which there is a loss of resonance? This is the curve which goes through the maxima of the curves in Fig. 2.
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45
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3342902142
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note
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Dewar (Ref. 10) has used such an approximation for a different class of BGK modes.
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47
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0000031833
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A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, Suppl. Nucl. Fusion, Part 2, 465 (1962).
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0010532141
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T. P. Armstrong, R. C. Harding, G. Knorr, and D. Montgomery, in Methods in Computational Physics, edited by B. Alder (Academic, New York, 1970), Vol. 9, p. 70.
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0345806392
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S. A. Orszag and R. H. Kraichnan, Phys. Fluids 10, 1720 (1967); F. C. Grant and M. R. Feix, ibid. 10, 1356 (1967).
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We are certainly aware that there is a large literature on the relative merits of Eulerian versus particle versus hybrid methods for solving what are basically hyperbolic partial differential equations. Since numerics is a side issue for us, we choose not to enter this often partisan debate. Eulerian methods which use the hyperbolic character of the Vlasov equation to predict the value of f after a time of evolution, dt, require interpolation of the initial condition to points off the numerical grid, introducing numerical dissipation. In the method used here, the numerical dissipation is controlled by D. Whatever the manner in which numerical dissipation is introduced, one must take care that it does not compete with the physical dissipation, measured by ν, especially in the compulation of equilibrium properties.
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This has been verified for N = 2 and 4.
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