Resonant Impedance of Transmission Lines

Nergaard, L.S.; Salzberg, B.

doi:10.1109/jrproc.1939.228755

Cited by 9 publications

(2 citation statements)

References 2 publications

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“…They showed that single-humped distributions are always stable (Berz 1956, Appendix by W. Newcomb in Bernstein 1958, Auer 1958, Penrose 1960, Noerdlinger 1960, Jackson 1960. Then, they considered double humped distributions modeling two contrastreaming beams (Haeff 1949, Nergaard 1948, Pierce & Hebenstreit 1949 and determined particular conditions under which such distributions are unstable (Twiss 1952, Buneman 1958, Auer 1958, Kahn 1959, Buneman 1959, Penrose 1960, Noerdlinger 1960, Jackson 1960. They found qualitatively that the plasma becomes unstable when the stream velocity becomes sensibly larger than the thermal velocity.…”

Section: A Brief Historicmentioning

confidence: 99%

Dynamical stability of infinite homogeneous self-gravitating systems and plasmas: application of the Nyquist method

Chavanis

2012

Eur. Phys. J. B

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Abstract. We complete classical investigations concerning the dynamical stability of an infinite homogeneous gaseous medium described by the Euler-Poisson system or an infinite homogeneous stellar system described by the Vlasov-Poisson system (Jeans problem). To determine the stability of an infinite homogeneous stellar system with respect to a perturbation of wavenumber k, we apply the Nyquist method. We first consider the case of single-humped distributions and show that, for infinite homogeneous systems, the onset of instability is the same in a stellar system and in the corresponding barotropic gas, contrary to the case of inhomogeneous systems. We show that this result is true for any symmetric single-humped velocity distribution, not only for the Maxwellian. If we specialize on isothermal and polytropic distributions, analytical expressions for the growth rate, damping rate and pulsation period of the perturbation can be given. Then, we consider the Vlasov stability of symmetric and asymmetric double-humped distributions (two-stream stellar systems) and determine the stability diagrams depending on the degree of asymmetry. We compare these results with the Euler stability of two self-gravitating gaseous streams. Finally, we determine the corresponding stability diagrams in the case of plasmas and compare the results with self-gravitating systems.

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Section: A Brief Historicmentioning

confidence: 99%

Dynamical stability of infinite homogeneous self-gravitating systems and plasmas: application of the Nyquist method

Chavanis

2012

Eur. Phys. J. B

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“…For correct evaluation of the loss, it important not to neglect the imaginary part of the characteristic impedance [17], and so we use the use the complex form:…”

Section: Design Principlementioning

confidence: 99%