## Wave enhancement due to a static electric field |

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accelerating electrode applied field average particle momentum axial distance beam current beam electrons beam plasma system beam voltage calculated charge electric field cold beam plasma conservation of momentum corresponds damping density detuning parameter dielectric function dispersion relation dotted curve effect experimental Figure 15 finite beam strength helix input RF drive J. H. Malmberg large amplitude wave linear region maximum measured Normalized secular growth normalized static field phase space plots phase velocity Phys Pierce parameters Plasma Physics Poisson's equation position of saturation power plot power vs axial pulsed result RF drive level RF input drive runaway secular growth rate slow wave structure small cold beam space charge electric space charge force static electric field static field applied static field strength transmitter trapping oscillations Traveling Wave Tube tube wave amplitude wave equation wave launched wave momentum wave phase wave potential wave power enhancement wavenumber