Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-27T13:51:20.216Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpretation of dispersion relations for bounded systems

Published online by Cambridge University Press:  13 March 2009

T. D. Rognlien  and
S. A. Self
T. D. Rognlien
Affiliation:
Institute for Plasma Research, Stanford University
S. A. Self
Affiliation:
Institute for Plasma Research, Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

A treatment is given of the problem of constructing normal modes for anarbitrarily bounded system from roots of the linear dispersion relation D( ω, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form (uniform along an axis z, say), each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant roots kαz(ω) of D = 0 satisfying the boundary conditions which are characterized by complex reflexion coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current on Q-machines.

Type
Research Article
Information
Journal of Plasma Physics , Volume 7 , Issue 1 , February 1972 , pp. 13 - 48
Copyright
Copyright © Cambridge University Press 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baldwin, P. E. & Rowlands, G. 1970 Phys. Fluids, 13, 2036.CrossRefGoogle Scholar
Batchelor, G. K. 1960 The Theory of Homogeneous Turbulence (Student's edn., chs. 1, 2). bCambridge University Press.Google Scholar
Bers, A. & Briggs, R. J. 1963 MIT Quarterly Progress Rep. 71.Google Scholar
Bers, A. & Briggs, R. J. 1964 MIT Quarterly Progress Rep. 74.Google Scholar
Bertotti, B. & Nocentini, A. 1970 Plasma Phys. 12, 39.CrossRefGoogle Scholar
Boot, H. A. H., Foster, H. & Self, S. A. 1958 Proc. I.E.E. 105 B (suppl. 10), 419.Google Scholar
Braginskii, S. I. 1965 Reviews in Plasma Physics, vol. 1 (ed. Leontovich, M. A.). New York: Consultants Bureau.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Callen, J. P. & McCune, J. E. 1968 Bull. Am. Phys. Soc. 13, 282.Google Scholar
Chen, F. F. 1965 Plasma Phys. 7,399.Google Scholar
Chen, F. F. 1965 Plasma Phys. 9,2534.Google Scholar
Cheng, C. C. & Harris, E. G. 1969 Phys. Fluids, 12, 1262.CrossRefGoogle Scholar
Derfler, H. 1961 Proc. 5th Int. Conf. on Phenomena in Ionized Gases, Amsterdam, vol. 2, p. 1423. North-Holland.Google Scholar
Derfler, H. 1967 a Proc. 8th mt. Conf. on Phenomena in Ionized Gases, p. 294. Springer, Vienna.Google Scholar
Derfler, H. 1967 b Phys. Lett. 24 A, 763.CrossRefGoogle Scholar
Derfler, H. 1970 Phys. Rev. A 1, 1467.CrossRefGoogle Scholar
Derfler, H. & Simonen, T. C. 1969 Phys. Fluids, 12, 269.CrossRefGoogle Scholar
Diament, P., Granatsten, V. L. & Schlesinger, S. P. 1966 J. Appl. Phys. 37, 1711.CrossRefGoogle Scholar
Dobrowolny, M., Engelmen, F. & Sestero, A. 1969 Z. Naturforsch, 24, 1235.CrossRefGoogle Scholar
Drummond, W. E. 1964 Phys. Fluids, 7, 816.CrossRefGoogle Scholar
Drummond, W. E. & Pines, P. 1962 Nucl. Fusion Suppl. Pt. 3, 1049.Google Scholar
Drummond, W. E. & Pines, P. 1964 Ann. Phys. (N.Y.) 28, 478.CrossRefGoogle Scholar
Duncan, A. J. & Forrest, J. R. 1971 Phys. Fluids, 14, 1973.CrossRefGoogle Scholar
Duncan, A. J., Forrest, J. R., Crawford, F. W. & Self, S. A. 1969 Phys. Fluids, 12, 2607.CrossRefGoogle Scholar
Duncan, A. J., Forrest, J. R., Crawford, F. W. & Self, S. A. 1969 Phys. Fluids, 14, 1959.CrossRefGoogle Scholar
Dysthe, K. B. 1966 Nuclear Fusion, 6, 215.CrossRefGoogle Scholar
Ewald, H. N., Crawford, F. W. & Self, S. A. 1969 Phys. Fluids, 12, 303.CrossRefGoogle Scholar
Fainberg, Ya. B., Kurilko, V. I. & Shapiro, V. D. 1961 Zh. Techn. Fiz. 31, 633.Google Scholar
(Also Sov. Phys. Tech. Phys. 6, 459.)Google Scholar
Feix, M. 1963 Nuovo Cim. 27, 1130.CrossRefGoogle Scholar
Gaster, M. 1968 Phys. Fluids, 11, 723.CrossRefGoogle Scholar
Ginzton, E. L. 1957 Microwave Measurements. McGraw-Hill.Google Scholar
Von, Goeler S. 1964 Phys. Fluids, 7, 463.Google Scholar
Gould, R. W. 1964 Phys. Rev. 136 A, 991.CrossRefGoogle Scholar
Granatstein, V. L. & Schlesinger, S. P. 1965 J. Appl. Phys. 36, 3503.CrossRefGoogle Scholar
Hall, L. S. & Heckerotte, W. 1968 Phys. Rev. 166, 120.CrossRefGoogle Scholar
Hendel, H. W., Chu, T. K. & Politzer, P. A. 1968 Phys. Fluids, 11, 2426.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Klan, F. 1969 Institut für Plasmaphysik, Garching, Rep. 3/92.Google Scholar
Malmberg, J. H. & Wharton, C. B. 1969 Phys. Fluids, 12, 2600.CrossRefGoogle Scholar
Marcuvitz, N. ed. 1951 Microwave Handbook, MIT. Radiation Lab. Ser., vol. 10. McGraw- Hill.Google Scholar
Montgomery, D. & Gorman, D. 1962 Phys. Fluids, 5, 947.CrossRefGoogle Scholar
Motley, R. W. & Ellis, R. F. 1970 Phys. Fluids, 14, 886.CrossRefGoogle Scholar
Müller, G. L. J., Corbin, J. C. & Palmer, R. S. 1970 Feedback and Dynamic Control of Plasmas. A.I.P. Conf. Proc. 1, p. 129. New York: Am. Inst. Phys.Google Scholar
Nishida, Y., Hatta, Y. & Sato, M. 1965 Appl. Phys. Lett. 7, 251.CrossRefGoogle Scholar
Nocentini, A. 1970 Proc. 4th Europ. Conf. on Controlled Fusion and Plasma Physics, CNEN Rome, p. 147.Google Scholar
Pierce, J. R. 1951 Bell System Tech. J. 30, 626.CrossRefGoogle Scholar
Polovin, R. V. 1961 Zh. Techn. Fiz. 31, 1120.Google Scholar
(Also 1962 Soy. Phys. Tech. Phys. 6, 889.)Google Scholar
Rolland, P. 1965 Phys. Rev. 140 B, 776.CrossRefGoogle Scholar
Rowberg, R. W. & Wong, A. Y. 1970 Phys. Fluids, 13, 661.CrossRefGoogle Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory (ed. O'Neil, T. M. and Book, D. L.). New York: Benjamin.Google Scholar
Schlitt, L. G. & Hendel, H. W. 1970 Bull. Am. Phys. Soc. (2) 15, 1439.Google Scholar
Self, S. A. 1969 a J. Appl. Phys. 40, 5217.CrossRefGoogle Scholar
Self, S. A. 1969 b J. Appl. Phys. 40, 5232.CrossRefGoogle Scholar
Self, S. A. 1970 J. Plasma Phys. 4, 693.CrossRefGoogle Scholar
Self, S. A., Crawford, F. W. & Ewald, H. N. 1969 Phys. Fluids, 12, 316.CrossRefGoogle Scholar
Self, S. A., Shoucri, M. & Crawford, F. W. 1971 J. Appl. Phys. 42, 704.CrossRefGoogle Scholar
Sturrock, P. A. 1958 Phys. Rev. 112, 1488.CrossRefGoogle Scholar
Sudan, R. N. 1965 Phys. Fluids, 8, 1899.CrossRefGoogle Scholar
Trivelpiece, A. W. 1967 Slow-Wave Propagation in Plasma Waveguides. San Francisco:San Fransisco Press.Google Scholar
Trivelpiece, A. W. & Gould, R. W. 1959 J. Appl. Phys. 30, 1784.CrossRefGoogle Scholar
Tsai, S-T., Ellis, R. F. & Perkins, F. W. 1971 (To be published.)Google Scholar
Tsai, S-T., Perkins, F. W. & Stix, T. H. 1970 Phys. Fluids, 13, 2108.CrossRefGoogle Scholar
Twiss, R. Q. 1951 a Phys. Rev. 84, 448.CrossRefGoogle Scholar
Twiss, R. Q. 1951 b Proc. Phys. Soc. (Lond.) B 64, 654.CrossRefGoogle Scholar
Twiss, R. Q. 1952 Phys. Rev. 88, 1392.CrossRefGoogle Scholar
Watanabe, M. & Hartman, C. W. 1970 Electronics Res. Lab. Plasma Research QPR 1, p. 99. University of California, Berkeley.Google Scholar
Wong, A. Y. & Hai, F. 1969 Phys. Rev. Lett. 23, 163.CrossRefGoogle Scholar