Nonlinear space‐charge wave propagation on thin annular electron beams

A warm fluid description of a relativistic thin annular electron beam is used to investigate large amplitude space‐charge waves for currents up to the space‐charge limit. The beam is centered within a conducting cylindrical boundary and is guided by a strong magnetic field in vacuum. Exact steady‐state periodic and solitary wave solutions are found numerically up to the breaking amplitude and are characterized by nonlinear wave velocities which vary significantly from linear phase velocities for currents ≳0.7I L . A time‐dependent pseudospectral code was developed and used to understand the dynamics of nonlinear wave interactions. The general character of these waves is to propagate as a stable superposition of solitary waves whose interactions are nearly elastic and preserve the coherence and form of the waves. The advantages of thin annular beams and the detrimental effects of warm beams are discussed. Recommendations are given concerning the amplitude, frequency, wavelength, and beam temperature of nonlinear waves for potential use in collective acceleration experiments.