Effects of Magnetic Field on Stability and Power of Vacuum Electronic Amplifiers

The theory and modeling of the effects of magnetic focusing field on the stability, gain, and power of the large class of VE amplifiers based on RF structures with a series of interaction gaps used in traveling-wave tubes, klystrons, and other VE devices is presented. The RF structure and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i>-beam lumped circuit parameter matrices are computed for different magnetic focusing conditions, and then the self-excitation thresholds are obtained from the determinant equations. A new formulation for the RF structure gain is derived and used for the found self-excitation thresholds. An analytical solution of the beam envelope equation not limited by the small-amplitude oscillations is obtained and employed to define the magnetic focusing conditions providing various beam envelope radii and oscillation amplitudes. It is shown for the example <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>a</i></sub>-band serpentine structure that the optimum magnetic focusing, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i>-beam radius, as well as axial position of the oscillating beam envelope allow significantly greater gain and power. The methods and analysis described here are essential for the computation, research, and design of advanced RF amplifiers.