Trapped particle bounds on stimulated scatter in the large kλd regime

Physics of Plasmas

Volumn 10, Issue 5 I, 2003, Pages 1468-1482

  Rose, Harvey A ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BRILLOUIN SCATTERING; ELECTRON TRAPS; FREQUENCIES; NONLINEAR SYSTEMS; PLASMA WAVES; SPECKLE;

BACKSCATTER STIMULATED RAMAN SCATTER (BSRS);

RAMAN SCATTERING;

EID: 0038633517     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1566029     Document Type: Article

References (51)

1. J. Lindl, Phys. Plasmas 2, 3933 (1995).
2. M. N. Rosenbluth, Phys. Rev. Lett. 29, 565 (1972).
3. B. B. Afeyan, A. E. Chou, J. P. Matte, R. P. J. Town, and W. L. Kruer, Phys. Rev. Lett. 80, 2322 (1998); S. Brunner and E. Valeo, Phys. Plasmas 9, 923 (2002), and references contained therein.
4. B. B. Afeyan, A. E. Chou, J. P. Matte, R. P. J. Town, and W. L. Kruer, Phys. Rev. Lett. 80, 2322 (1998); S. Brunner and E. Valeo, Phys. Plasmas 9, 923 (2002), and references contained therein.
5. The first observation of SEAS in a single hot spot geometry was reported by D. S. Montgomery, R. J. Focia, H. A. Rose, D. A. Russell, J. A. Cobble, J. C. Fernández, and R. P. Johnson, Phys. Rev. Lett. 87, 155001 (2001). After this work was published, the observation of what was then at the time viewed as an "interesting" spectral feature, was subsequently reinterpreted as SEAS in a random phase plate conditioned laser beam environment, see Fig. 8 in J. A. Cobble, J. C. Fernández, N. A. Kurnit, D. S. Montgomery, R. P. Johnson, N. Renard-Le Galloudec and M. R. Lopez, Phys. Plasmas 7, 323 (2000).
6. The first observation of SEAS in a single hot spot geometry was reported by D. S. Montgomery, R. J. Focia, H. A. Rose, D. A. Russell, J. A. Cobble, J. C. Fernández, and R. P. Johnson, Phys. Rev. Lett. 87, 155001 (2001). After this work was published, the observation of what was then at the time viewed as an "interesting" spectral feature, was subsequently reinterpreted as SEAS in a random phase plate conditioned laser beam environment, see Fig. 8 in J. A. Cobble, J. C. Fernández, N. A. Kurnit, D. S. Montgomery, R. P. Johnson, N. Renard-Le Galloudec and M. R. Lopez, Phys. Plasmas 7, 323 (2000).
7. B. D. Fried, M. Gell-Mann, J. D. Jackson, and H. W. Wyld, J. Nucl. Energy, Part C 1, 190 (1960).
8. To simplify notation, in later occurrences, the modulus operator about the product e φ will be suppressed.
9. H. A. Rose and D. A. Russell, Phys. Plasmas 8, 4784 (2001).
10. See Sec. III.B.4 of Ref. 7.
11. See Sec. III.B.5 of Ref. 7.
12. J. P. Holloway and J. J. Dorning, Phys. Rev. A 44, 3856 (1991).
13. V. E. Zakharov and V. I. Karpman, Sov. Phys. JETP 16, 351 (1963).
14. For the driven problem damping means resonance width.
15. e of order unity and the validity of Ξ's perturbative evaluation in this strong regime has not been established.
16. 0 is Maxwellian.
17. B. I. Cohen and A. N. Kaufman, Phys. Fluids 21, 404 (1978).
18. For example, it may be obtained from Eq. (7.10) in W. L. Kruer, The Physics of Laser Plasma Interactions, 1st ed., edited by D. Pines (Addison-Wesley, New York, 1988), Chap. 7, p. 76, by using the envelope representations for the light and plasma waves. The equation for the laser envelope field is omitted for simplicity since it is not needed to obtain the gain rate upper bound. Collisional absorption is ignored.
19. A qualitatively similar model has been studied by H. X. Vu, D. F. DuBois, and B. Bezzerides, Phys. Plasmas 9, 1745 (2002).
20. For numerical results, the exact, finite density, light wave dispersion relation is used.
21. 0, the Langmuir branch of BGK modes is more responsive than the electron acoustic branch, so that for the purpose of optimizing the gain rate, it is BSRS which wins.
22. If the imaginary part is retained, then short wavelength fluctuations are unstable, which violates the smoothly varying envelope ansatz.
23. When diffraction of the laser light is included, then in regions of space where there is constructive interference, speckles, or intensity hot spots, the laser intensity may attain values large compared to its average, 〈I〉 and upper bound estimates based on a model with uniform intensity at that average value may be wildly off the mark. For example, the absolute instability threshold may be locally exceeded in a collection of hot spots, but not exceeded in the corresponding uniform case. More importantly, the distinction between models with and without diffraction is most dramatic when 〈I〉 exceed its critical value. See the discussion in Sec. IV.
24. This has been seen in particle simulations, H. X. Vu, D. F. DuBois, and B. Bezzerides, Phys. Rev. Lett. 86, 4306 (2001).
25. This is not quite correct since the envelope value of k was chosen to maximize K in the linear regime, and since the Landau damping is large, this optimal k is in fact slightly smaller than that which would give a linear resonance. As a result, at the right-hand boundary (z/μm = 1200) where φ = 0, Re(ε) = 0.010, and therefore the frequency shift is proportional to Re(ε) as shown in Fig. 4, minus 0.010.
26. The related phenomenon of wave breaking gives a similar estimate, for example, see T. P. Coffey, Phys. Fluids 14, 1402 (1971); W. L. Kruer, in The Physics of Laser Plasma Interactions, 1st ed., edited by D. Pines (Addison-Wesley, New York, 1988), Chap. 9, p. 104.
27. The related phenomenon of wave breaking gives a similar estimate, for example, see T. P. Coffey, Phys. Fluids 14, 1402 (1971); W. L. Kruer, in The Physics of Laser Plasma Interactions, 1st ed., edited by D. Pines (Addison-Wesley, New York, 1988), Chap. 9, p. 104.
28. SRS(δω)φ(-δω).
29. In a multi-speckle environment, the inter-speckle distribution function, which serves as the "background" for any given speckle, will differ from that at infinity.
30. It has recently been shown that there are no such traveling wave solutions, L.-J. Chen, D. Thouless, and J.-M. Tang, Bull. Am. Phys. Soc. 47, 291 (2002), but if the previous estimate for the loss of trapped electrons is valid, then large enough amplitude waves will appear as traveling wave solutions for many bounce periods.
31. Since the simulation region is 1200 μm long, the MFAM takes about 1100 μm to come up from thermal fluctuations, while the MCM only takes about 1000 μm.
32. For perfect consistency of notation, the ordinale of Fig. 9 should be encased by parentheses with the subscript "max," but in the interest of a lighter notation this is not done. The figure caption is unambiguous.
33. In the sense that it yields the maximum gain rate.
34. Recall that if it exceeds 0.53, resonance is not possible.
35. D as large as 0.55.
36. J. C. Fernândez, J. A. Cobble, D. S. Montgomery, M. D. Wilke, and B. B. Afeyan, Phys. Plasmas 7, 3743 (2000).
37. H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994).
38. A. J. Schmitt and B. B. Afeyan, Phys. Plasmas 5, 503 (1998); also R. L. Berger and E. A. Williams (private communication).
39. A. J. Schmitt and B. B. Afeyan, Phys. Plasmas 5, 503 (1998); also R. L. Berger and E. A. Williams (private communication).
40. M. Buchanan and J. Dorning, Phys. Rev. E 52, 3015 (1995).
41. H. X. Vu, J. M. Wallace, and B. Bezzerides, Phys. Plasmas 1, 3542 (1994).
42. E. A. Williams, R. L. Berger, R. P. Drake, A. M. Rubenchik, B. S. Bauer, D. D. Meyerhofer, A. C. Gaeris, and T. W. Johnston, Phys. Plasmas 2, 129 (1995).
43. However, just as in the electron plasma wave discussion just before Sec. II A, whether or not these modes can be realized in the context of stimulated scatter may depend on the evolution of the background ion distribution function away from Maxwellian.
44. D≫0.55.
45. 2.
46. 2.
47. 0, and it is more convenient to characterize its response by its frequency, or phase velocity v, rather than k, unlike the SRS case.
48. D. S. Montgomery (private communication).
49. For perfect consistency of notation, the ordinate of Fig. 18 should be encased by parentheses with the subscript "max," but in the interest of a lighter notation this is not done. The figure caption is unambiguous.
50. H=0.7.
51. D for this case is 0.52, on the verge of LOR.