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Synergies between Accelerators, Lasers and Plasma
Published in Andrei Seryi, Unifying Physics of Accelerators, Lasers and Plasma, 2015
The simplest form of an electron source is the thermal cathode gun (Fig. 4.3). According to the “three-halves power” law (or the Child-Langmuir law), the space charge effects of the non-relativistic accelerated electron beam often limit the current in electron guns. I=P⋅U3/2 where I is the current, U is the cathode to anode voltage and the coefficient P is called perveance.
Cyclotron Resonance Effects on a Rectilinear Electron Beam for the Generation of High-Power Microwaves
Published in R A Cairns, A D R Phelps, P Osborne, Generation and Application of High Power Microwaves, 2020
It can be seen in Eq. (5) that the growth rate, the quantity Im{⍵} = Im{Δ⍵}, has its largest value at exact resonance, i.e. when Δ⍵0 = 0. At such conditions the real frequency shift Re{Δ⍵} vanishes, while the growth rate is proportional to the square root of the coupling factor (and therefore of the beam current). These features are different than in cyclotron-resonance interactions based on the ordinary Doppler effect (including the gyrotron limit, in which the Doppler shift vanishes), for which the maximum growth rate (still at exact resonance) is associated with a non-zero real frequency shift and is proportional to the cubic root of the coupling factor. Since the coupling factor, in the appropriate dimensionless units, is below unity, this means that the interaction with the ordinary Doppler shift is stronger than with the anomalous one, in a ratio proportional to the sixth root of the dimensionless current. Thus, in high-power implementations, the large value of the current would make this difference rather insignificant. Furthermore, due to space-charge (perveance) limitations, a large current can be achieved only with a relativistic electron beam. It turns out that the growth rate of the anomalous Doppler cyclotron interaction scales with the inverse square root of 70, while the scaling for the ordinary one (as well as for the potential competitor, represented by the Cherenkov interaction) is much more unfavourable. This indicates the suitability of relativistic electron beams for this interaction, which thus makes it attractive for high-power applications. Furthermore, for such beams, the condition υ0 > ⍵/κ imposes less stringent conditions on the structure that are anyhow required to be present in order to support the slow waves.
Microwave Power Tubes
Published in Jerry C. Whitaker, Power Vacuum Tubes, 2017
The constant k is a function of the geometry of the cathode–anode structure, and is termed perveance. Because the modulating anode is physically positioned between the RF structure (body) and the cathode, even if the full beam voltage is maintained between cathode and body, the actual beam current into the tube may be reduced at will by biasing the modulating anode to any voltage between cathode and body. Figure 6.22 shows the relationship between beam current and voltage described in the previous equation.
Laser-heated cathode electron beam source for electron beam technologies
Published in Welding International, 2022
Yu. I. Semenov, O. N. Alyakrinskiy, D. Yu. Bolkhovityanov, T. A. Devyataykina, M. Yu. Kosachev, P. V. Logachev, E. A. Cooper, V. K. Ovchar, V. V. Repkov, A. A. Starostenko, A. S. Tsyganov
The electron gun operates according to the diode scheme. Therefore at specified accelerating voltage, cathode–focusing electrode and cathode–anode distances, the gun current is controlled effectively by regulating the heating power in the region where the density of the emission current is limited by the cathode temperature, and with further increase in temperature, the density of the emission current is limited by the space charge in the cathode region and there is a decrease in effectiveness of control of the gun current by regulating the heating power. This problem can be solved by using interchangeable focusing electrodes for a particular range of working current, optimizing the cathode–focusing electrode and cathode–anode distances or regulating the accelerating voltage of the gun, i.e. optimizing the perveance of the electron gun for the specified range of working current of the electron beam source.