Experimental Evidence of Landau Damping in Electron Beams

Caulton, M.; Hershenov, B.; Paschke, F.

doi:10.1063/1.1777170

Cited by 19 publications

(4 citation statements)

References 5 publications

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“…11 ' 12 A spatially periodic interference pattern results along the beam, with minima at every half-plasma wavelength, if both waves are excited with equal amplitude. 13 Such patterns are clearly indicated from the experimental results of Beam 14 , and Caulton et al 10 The fundamental plasma wavelength varies with both beam current and drift potential. Therefore, as the delay is varied by altering the drift space potential the amplitude of the output signal (gain) will vary.…”

Section: December 1964mentioning

confidence: 82%

“…Such a phenomenon is referred to as Landau damping 15 and has been analysed by Dawson 16 and Berghammer 13 and experimentally verified by Caulton et al 10 Berghammer has shown that the decay of the velocity modulation is attributable to a spatial Landau damping of the 'fast' space-charge wave.…”

Section: December 1964mentioning

confidence: 93%

“…The amplifier power gain then becomes (10) The amplifier gain is thus fixed by the ratio of the input impedance to output load. This relationship is valid as long as the cut-off frequency of the transistor is not exceeded.…”

Section: High-gain Wideband Digital Delaymentioning

confidence: 99%

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Wideband, high-gain, variable time-delay techniques for array antennae

Payne

1964

Radio Electron. Eng. UK

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The purpose of this paper is to present two improved techniques for obtaining a wideband, high-gain, non-dispersive, variable time-delay device to steer array antennae. The first time-delay technique utilizes two wideband helix structures separated by a cylindrical drift tube to obtain a variable delay of 20 ns or more with a gain of 20 to 30 dB. An electron beam passes through the two helices and drift region. Signal energy coupled on to the beam at the input helix is decoupled at the output helix. A variable delay is obtained by controlling the beam velocity through the drift region by varying the drift tube potential. Gain variation is minimized by maintaining constant beam velocity through the helices. The gain of the device is proportional to output helix length.The second method for obtaining a variable time-delay is realized by switching different time-delay elements into the signal path. Such a technique is controlled digitally and is referred to as a digital delay line. In this technique each switch is replaced by a wideband amplifier. It is the bandwidth of these amplifiers that determines the system bandwidth (200 to 800 Mc/s). Each bit is capable of producing 12 dB gain. The amplifiers can be easily gated on or off.

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Section: December 1964mentioning

confidence: 82%

Section: December 1964mentioning

confidence: 93%

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Wideband, high-gain, variable time-delay techniques for array antennae

Payne

1964

Radio Electron. Eng. UK

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“…In some of the electron beam experimcntal work on this problem (Caulton et al 1962, Mihran 1962, it has been assumed, with good reason, that velocity spreads of the order of 10% of the beam velocity were present and the parameter (w,,/wO)2 was of the order of 10-3 . Accordingly, for numerical solution we have chosen these numbers and the velocity distribution:…”

Section: Problem Of the Experimental Confirmation Of Landau Damping 407mentioning

confidence: 99%

The Problem of the Experimental Confirmation of Landau Damping†

Kent

1967

International Journal of Electronics

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The experimental confirmation of Landau damping in a one-dimensional ptusma or electron beam requires the measurement of the velocity dist.ribution. the wave amplitude as a function of time or space, and the numerical solution of t.he Volterra integral equation. through which these data ure theoretically related. It is shown that the errors inherent in the two measurements arc, under the best of circumstances, of such magnitude that it is not possible to adduce a damping law. The analysis is devoted for the most part to the spatial damping on an electron beam, and a t-ypical nurnerieal example is given. § 1. INTRODUCTlON FOR the past two decades the problem of Landau damping (Landau 1946) of plane waves in a plasma has been the subject of many technical papers. With few exceptions, the discussion of this problem has been theoretical, and there is a great paucity of experimental confirmation. Perhaps the most important single result of the theory is the conclusion that Landau damping occurs under certain conditions so that thc propagation of longitudinal waves in a warm plasma approximation is approached. The more detailed results of the theory, including the exact rate of damping, are not easily accessible to experimental observation, particularly if the initial distribution in velocity space is not Maxwellian. This paper considers the problem of experimental confirmation of the Landau theory for a non-Maxwellian initial distribution. Parts of the problem arc (i) the experimental determination of the velocity distribution, (ii) the computation of the electric field from these experimental data, (iii) the inference of a damping law from measurements of the electric field, and (iv) the significance of a comparison between theory and experiment.As subsequently established, the theory of signal evanescence on a polychromatic electron beam (Berghammer 1962) is formally equivalent to the theory of the propagation of a longitudinal plane wave in a warm plasma. Although there are physical differences in so far as different phenomena have been omitted from the theory in the two cases, these are t Communicated by the Author. If)

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Microwave and RF Vacuum Electronic Power Sources

Carter

2018

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Experimental Evidence of Landau Damping in Electron Beams

Cited by 19 publications

References 5 publications

Wideband, high-gain, variable time-delay techniques for array antennae

Wideband, high-gain, variable time-delay techniques for array antennae

The Problem of the Experimental Confirmation of Landau Damping†

Microwave and RF Vacuum Electronic Power Sources

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