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Warm-fluid description of intense beam equilibrium and electrostatic stability properties

### Abstract

A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij–Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with and about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be *identical* to the eigenfunction derived in a full kinetic treatment. However, in contrast to the kinetic treatment, the warm-fluid model predicts stable oscillations. None of the instabilities that are present in a kinetic description are obtained in the fluid model. A careful comparison of the mode oscillation frequencies associated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which may have general applicability.

© 1998 American Institute of Physics

Received Mon Mar 30 00:00:00 UTC 1998
Accepted Thu Apr 16 00:00:00 UTC 1998

/content/aip/journal/pop/5/8/10.1063/1.873027

1.

1.R. C. Davidson, Physics of Nonneutral Plasmas (Addison–Wesley, Reading, MA, 1990), and references therein.

2.

2.M. Reiser, Theory and Design of Charged Particle Beams (Wiley, New York, 1994).

3.

3.H. Wiedemann, Particle Accelerator Physics (Springer, New York, 1993), Vols. I and II.

4.

4.J. D. Lawson, The Physics of Charged-Particle Beams (Oxford Science, New York, 1988).

5.

5.E. P. Lee and J. Hovingh, Fusion Technol. 15, 369 (1989).

6.

6.R. A. Jameson, in Advanced Accelerator Concepts, Port Jefferson, NY, 1992, edited by J. S. Wurtele [AIP Conf. Proc. 279, 969 (1993)].

7.

7.R. W. Muller, in Nuclear Fusion by Inertial Confinement: A Comprehensive Treatise, edited by G. Velarde, Y. Ronen and J. M. Martinez-Val (CRC, Boca Raton, FL, 1993), Chap. 17, pp. 437–453.

8.

8.See, for example, Proceedings of the 1995 International Symposium on Heavy Ion Inertial Fusion, edited by J. J. Barnard, T. J. Fessenden and E. P. Lee [J. Fusion Eng. Design32, 1-620 (1996)], and references therein.

9.

9.A. Friedman, R. O. Bangerter, and W. B. Hermannsfeldt, in Proceedings of the IAEA Technical Committee Meeting on Drivers for Inertial Confinement Fusion, Paris, France, 1994 (Commisariat a l’Energie Atomique, Saclay, France, 1995), p. 243.

10.

10.I. Kapchinskij and V. Vladimirskij, in Proceedings of the International Conference on High Energy Accelerators and Instrumentation (CERN Scientific Information Service, Geneva, 1959), p. 274.

11.

11.R. L. Gluckstern, in Proceedings of the 1970 Proton Linear Accelerator Conference, Batavia, IL, 1971, edited by M. R. Tracy (National Accelerator Laboratory, Batavia, IL, 1971), p. 811.

12.

12.R. L. Gluckstern, W.-H. Cheng, and H. Yee, Phys. Rev. Lett. 75, 2835 (1995).

13.

13.R. L. Gluckstern, W.-H. Cheng, S. S. Kurennoy, and H. Ye, Phys. Rev. E 54, 6788 (1996).

14.

14.T.-S. Wang and L. Smith, IEEE Trans. Nucl. Sci. NS-28, 2399 (1981).

15.

15.T.-S. Wang and L. Smith, Part. Accel. 12, 247 (1982).

16.

16.H. S. Uhm and R. C. Davidson, Phys. Fluids 23, 1586 (1980).

17.

17.H. S. Uhm and R. C. Davidson, Part. Accel. 11, 65 (1980).

18.

18.I. Hofmann, L. J. Laslett, L. Smith, and I. Haber, Part. Accel. 13, 145 (1983).

19.

19.I. Hofmann, “Stability of anisotropic beams with space charge,” Phys. Rev. E (in press).

20.

20.G. P. Saraph and M. Reiser, Part. Accel. 49, 15 (1995).

21.

21.C. Chen, R. Pakter, and R. C. Davidson, Phys. Rev. Lett. 79, 225 (1997).

22.

22.C. Chen and R. C. Davidson, Phys. Rev. Lett. 72, 2195 (1994).

23.

23.C. Chen and R. C. Davidson, Phys. Rev. E 49, 5679 (1994).

24.

24.E. P. Lee and R. K. Cooper, Part. Accel. 7, 83 (1976).

25.

25.I. Hofmann, Adv. Electron. Electron Phys. Suppl. 13C, 49 (1983).

26.

26.I. Hofmann and J. Struckmeier, Part. Accel. 21, 69 (1987).

27.

27.M. Reiser, J. Appl. Phys. 70, 1919 (1991).

28.

28.J. Struckmeier and I. Hofmann, Part. Accel. 39, 219 (1992).

29.

29.R. C. Davidson and S. M. Lund, in Thomas H. Stix Symposium on Advances in Plasma Physics, Princeton, NJ, 1992, edited by N. J. Fisch [AIP Conf. Proc. 314, 1 (1994)].

30.

30.N. Brown and M. Reiser, Phys. Plasmas 2, 965 (1995).

31.

31.R. C. Davidson and C. Chen, “Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov–Maxwell equations,” Part. Accel. (in press).

32.

32.R. C. Davidson, W. W. Lee, and P. Stoltz, Phys. Plasmas 5, 279 (1998).

33.

33.J. Struckmeier and J. Klabunde, Part. Accel. 15, 47 (1984).

34.

34.A. Friedman and D. P. Grote, Phys. Fluids B 4, 2203 (1992).

35.

35.I. Haber, D. A. Callahan, A. Friedman, D. P. Grote, and A. B. Langdon, J. Fusion Eng. Design 32, 159 (1996).

36.

36.I. Haber, D. A. Callahan, A. Friedman, D. P. Grote, S. M. Lund, and T.-F. Wang, “Transverse-longitudinal temperature equilibration in a bounded nonneutral plasma,” Nucl. Instrum. Methods Phys. Res. (in press).

37.

37.W. W. Lee, Q. Qian, and R. C. Davidson, Phys. Lett. A 230, 347 (1997).

38.

38.Q. Qian, W. W. Lee, and R. C. Davidson, Phys. Plasmas 4, 1915 (1997).

39.

39.S. M. Lund, J. J. Barnard, G. D. Craig, A. Friedman, D. P. Grote, H. S. Hopkins, T. C. Sangster, W. M. Sharp, S. Eylon, T. J. Fessenden, E. Henestroza, S. Yu, and I. Haber, “Numerical simulation of intense-beam experiments at LLNL and LBNL,” Nucl. Instrum. Methods Phys. Res. (in press).

40.

40.M. G. Tiefenback, “Space-Charge Limits on the Transport of Ion Beams in a Long Alternating Gradient System, Ph.D. thesis, University of California, Berkeley, 1986 (Lawrence Berkeley Laboratory Publication, LBL-22465, 1986).

41.

41.W. M. Fawley, T. Garvey, S. Eylon, E. Henestroza, A. Faltens, T. J. Fessenden, K. Hahn, L. Smith, and D. P. Grote, Phys. Plasmas 4, 880 (1997).

42.

42.S. Yu, S. Eylon, E. Henestroza, and D. Grote, in Space Charge Dominated Beams and Applications of High Brightness Beams, Bloomington, IN, 1995, edited by S. Y. Lee [AIP Conf. Proc. 377, 134 (1996)].

43.

43.S. S. Yu, S. Eylon, E. Henestroza, C. Peters, L. Reginato, A. Tauschwitz, D. Grote, and F. Deadrick, J. Fus. Eng. Design 32, 309 (1996).

44.

44.M. Reiser, C. R. Chang, D. Kehne, K. Low, T. Shea, H. Rudd, and I. Haber, Phys. Rev. Lett. 61, 2933 (1988).

45.

45.F. J. Sacherer, IEEE Trans. Nucl. Sci. NS-18, 1105 (1971).

46.

46.See, e.g., Chaps. 2, 4, 9 and 10 of Ref. 1.

47.

47.Reference 1 presents a general derivation of the macroscopic fluid-Maxwell equations from the Vlasov–Maxwell equations on pages 22–26. Several aspects of cold-fluid equilibrium and stability properties of nonneutral beam-plasma systems are described on pages 240–276 of Ref. 1.

48.

48.R. C. Davidson, Handbook of Plasma Physics-Basic Plasma Physics, edited by M. N. Rosenbluth and R. Z. Sagdeev (North-Holland, Amsterdam, 1984), Vol. 2, pp. 729–819.

49.

49.I. Hofmann, IEEE Trans. Nucl. Sci. NS-26, 3083 (1979).

50.

50.G. A. Krafft, J. W.-K. Mark, and T.-S. Wang, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 43, 1390 (1983).

51.

51.R. C. Davidson, B. H. Hui, and C. A. Kapetanakos, Phys. Fluids 18, 1040 (1975).

52.

52.R. C. Davidson and B. H. Hui, Ann. Phys. (N.Y.) 94, 209 (1975).

53.

53.M. Reiser, Phys. Fluids 20, 477 (1977).

54.

54.R. C. Davidson, P. Stoltz, and C. Chen, Phys. Plasmas 4, 3710 (1997).

55.

55.The authors wish to thank Ed Lee for bringing to our attention energy arguments analogous to those employed in magnetohydrodynamics [see, for example, G. Schmidt, Physics of High Temperature Plasmas (Academic, New York, 1979)] can be used in the present warm-fluid model to bound perturbations for rigidly-rotating fluid equilibria with radial profiles satisfying certain derivative conditions. This can be used to show that the macroscopic profiles for a KV beam equilibrium satisfy a sufficient condition for fluid stability.

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