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ILL Experimental Apparatus and Linear Properties
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according to Eq Active wave phase beam current beam-plasma instability beam-plasma systems bounce length calculated characteristic parameters circuit computed damping coefficient destroying the trapping detrapping detuning parameter dielectric dielectric constant Dimonte dispersion relation eigenfunction electric field experimental FIGURE Fluids injected beam power injection velocity interaction impedance J. H. Malmberg lab frame launched Lett linear Lost beam power main wave nonlinear region normalized to injected numerical solutions particle phase particle velocity phase mixing phase space phase velocity Phys plasma physics positions in Fig power vs distance radius resonant particle result saturated wave saturation power sheath helix shown in Fig sidebands single wave model slow wave structure small cold beam solid line space charge space dynamics spatial T. M. O'Neil theory tion trapped particle oscillations trapping oscillations travelling wave tube values various positions wave amplitude wave phase shifts wave potential Wave power normalized wavenumber