Theory of ion beam generation for ripple anode surface

Theoretical analysis of ion beam formation provided for the space charge-limit cold particle emission from slightly ripple anode. It can be applyed also for electron guns. The steady-state solution is obtained for a quasi-planar diode with the ripple anode by a sinusoidal profile. It is type of XA= θA/K·Sin Ky, where θA ⩽ 0.1 (∼6°) -angle small parameter, λ= 2π/K -ripple wavelength, λ ⩽ 0.5α, α - diode gap. The weak ripple emitter in the diode provides visible space variations of a current density of accelerated ion beam δJ/Jo ∼ 20% for θA ∼ 0.1 (|XA/d| ⩽ 0.01). Meanwhile the ion beam divergence is small ̄εi < 0.5°. The results agree with experimental dates. The theory model of the ripple emission charge flow may be used in computer codes. A sharp roughness (θA ∼ 1) of the emitter may provide a non-stationary charge-limit emission with time-space fluctuations and high effective temperature Tef>> TS (TS# -emitter temperature). It is very complicated physics problem. For towards progress it will be needed systematic experimental dates concerning of a non-uniformity charge-limit emission.