Vacuum-Tube Networks

Llewellyn, F. B.; Peterson, Liss C.

doi:10.1109/jrproc.1944.230037

Cited by 85 publications

(7 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (53) gives precisely the same result as the Llewellyn [12] equations for initial current modulation alone. Equation (53) can be written in the form…”

Section: On Some Effects Of Velocity Distribution In Electron Streamsmentioning

confidence: 59%

On some effects of velocity distribution in electron streams

Yadavalli¹

1954

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract.Based on the Liouville theorem an integral equation is obtained for the solution of electron beam problems having a velocity spread. Assuming a rectangular velocity distribution (which is justified later) the integral equation is solved by Laplace Transforms to obtain the solution of the problems of small-signal velocity modulation in a drifting electron stream, and a drifting electron stream initially possessing full shot noise in each velocity class.It is shown that one obtains from the above integral equation the same results as those given by the Llewellyn equations for the case of a single valued velocity stream. The problem of finite but narrow velocity spread in the case of an accelerated electron stream is briefly considered.1. Introduction.To investigate the consequences of treating the electron stream as a plasma one can use either one of the two following methods: 1) treat the electron stream as being composed of a number of beams whose velocities are discrete, or 2) use the distribution function treatment. The first method has been used by many; quite recently Bohm and Gross [1] used the same to discuss many characteristics of the plasma. The second method has been used by Vlasov [2], Landau [3], and recently by Watkins [4] to discuss the behavior of a plasma, the effect of a velocity distribution on noise in electron streams, etc. We will use below the distribution function method.The plasma is completely described by a distribution function of /(r, v, t) such that -/(r, v,t)/e gives the average number of electrons in a small range of position and velocity at a time t in the phase space whose coordinates are position r and velocity v. The behavior of the distribution function is completely specified by the Boltzmann equation (i) where dv/dt is determined by the interparticle forces and any external impressed fields. The physical assumptions involved in the above are based on the following [5], The forces acting on a particle in a plasma can be divided into two parts. One is the shortrange force acting on a particle when a close collision is experienced by it during which there is a heavy momentum transfer, and this is taken care of by the term on the right hand side in (1). The other part is the long-range coulomb force, due to the other particles of the system. In the second type of collision, the momentum transfer is small. At any instant a single electron is engaged in a many body collision, and in (1) the effect of the same is taken into account as a smoothed out force. This latter force depends on the distribution function itself and gives rise to many of the plasma characteristics. ♦Received June 2, 1953.

show abstract

“…Equation (53) gives precisely the same result as the Llewellyn [12] equations for initial current modulation alone. Equation (53) can be written in the form…”

Section: On Some Effects Of Velocity Distribution In Electron Streamsmentioning

confidence: 59%

On some effects of velocity distribution in electron streams

Yadavalli¹

1954

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…The quantity relates the input to the output by the ratio (∆I/∆ξ in ) , where ξ in is the controlling input voltage. Amplification is then V out = V g g m Z o , where V g is the input and Z o is the load impedance 12 , 13 .…”

Section: Introductionmentioning

confidence: 99%

Characterization of carrier behavior in photonically excited 6H silicon carbide exhibiting fast, high voltage, bulk transconductance properties

Sampayan

Grivickas

Conway

et al. 2021

Sci Rep

View full text Add to dashboard Cite

Unabated, worldwide trends in CO2 production project growth to > 43-BMT per year over the next two decades. Efficient power electronics are crucial to fully realizing the CO2 mitigating benefits of a worldwide smart grid (~ 18% reduction for the United States alone). Even state-of-the-art SiC high voltage junction devices are inefficient because of slow transition times (~ 0.5-μs) and limited switching rates at high voltage (~ 20-kHz at ≥ 15-kV) resulting from the intrinsically limited charge carrier drift speed (< 2 × 107-cm-s−1). Slow transition times and limited switch rates waste energy through transition loss and hysteresis loss in external magnetic components. Bulk conduction devices, where carriers are generated and controlled nearly simultaneously throughout the device volume, minimize this loss. Such devices are possible using below bandgap excitation of semi-insulating (SI) SiC single crystals. We explored carrier dynamics with a 75-fs single wavelength pump/supercontinuum probe and a modified transient spectroscopy technique and also demonstrated a new class of efficient, high-speed, high-gain, bi-directional, optically-controlled transistor-like power device. At a performance level six times that of existing devices, for the first time we demonstrated prototype operation at multi-10s of kW and 20-kV, 125-kHz in a bulk conduction transistor-like device using direct photon-carrier excitation with below bandgap light.

show abstract

“…Section II describes the high frequency instability of an electron-rich sheath. Two concepts are involved, the negative rf conductance due to the electron inertia [2] and the sheath resonance due to plasma inductance and sheath capacitance [3]. The observation of the instability has been demonstrated experimentally [4].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2021

J. Technol. Space Plasmas

View full text Add to dashboard Cite

The properties of sheaths and associated potential structures and instabilities cover a broad field which even a review cannot cover everything. Thus, the focus will be on about a dozen examples, describe their observations and focus on the basic physical explanations for the effects, while further details are found in the references. Due to familiarity the review focuses mainly on the authors work but compared and referenced related work. The topics start with a high frequency oscillation near the electron plasma frequency. Low frequency instabilities also occur at the ion plasma frequency. The injection of ions into an electron-rich sheath widens the sheath and forms a double layer. Likewise, the injection of electrons into an ion rich sheath widens and establishes a double layer which occurs in free plasma injection into vacuum. The sheath widens and forms a double layer by ionization in an electron rich sheath. When particle fluxes in "fireballs" gets out of balance the double layer performs relaxation instabilities which has been studied extensively. Fireballs inside spherical electrodes create a new instability due to the transit time of trapped electrons. On cylindrical and spherical electrodes the electron rich sheath rotates in magnetized plasmas. Electrons rotate due to E × B 0 which excites electron drift waves with azimuthal eigenmodes. Conversely a permanent magnetic dipole has been used as a negative electrode. The impact of energetic ions produces secondary electron emission, forming a ring of plasma around the magnetic equator. Such "magnetrons" are subject to various instabilities. Finally, the current to a positively biased electrode in a uniformly magnetized plasma is unstable to relaxation oscillations, which shows an example of global effects. The sheath at the electrode raises the potential in the flux tube of the electrode thereby creating a radial sheath which moves unmagnetized ions radially. The ion motion creates a density perturbation which affects the electrode current. If the electrode draws large currents the current disruptions create large inductive voltages on the electrode, which again produce double layers. This phenomenon has been seen in reconnection currents. Many examples of sheath properties will be explained. Although the focus is on the physics some examples of applications will be suggested such as neutral gas heating and accelerating, sputtering of plasma magnetrons and rf oscillators.

show abstract

Vacuum-Tube Networks

Cited by 85 publications

References 10 publications

On some effects of velocity distribution in electron streams

On some effects of velocity distribution in electron streams

Characterization of carrier behavior in photonically excited 6H silicon carbide exhibiting fast, high voltage, bulk transconductance properties

Untitled

Contact Info

Product

Resources

About