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A special class of Pierce diodes, that consists of a pair of grounded coaxial cylindrical electrodes, with electrons streaming radially between them, is studied. The full set of roots of the dispersion relation of the Pierce instability is obtained by solving the dispersion relation numerically. The nonlinear behaviour of the system is then investigated using particle simulation. It is shown that the behaviour of cylindrical systems depends on two nondimensional parameters. Linear and nonlinear properties are different for convergent and divergent configurations. Several remarkable differences between cylindrical and planar Pierce diodes are reported.

Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes