Abstract
A scaling law on the wear of three-grid optics is proposed for the lifetime estimation of ion engines. The charge exchange ions erode the accel grid holes; therefore, the reduced retarding potential results in electron backstreaming, which is the end of life of the three-grid optics. The arithmetic formulas are induced by use of the space-charge-limited current density law and a newly introduced parameter called the modified effective acceleration length. The model is based on the following scenario of grid life: (1) Charge exchange ion erosion enlarges the accel grid hole diameter, (2) which shortens the modified effective acceleration length between the screen and accel grids and (3) reduces the retarding potential to keep the beam current constant under the space-charge limited flow. The characteristic of the proposed formulas is that the lifetime of the three-grid optics strongly depends on the beam current and the accel grid voltage. The correlation between the arithmetic formulas and the numerical simulations showed good qualitative agreement with one another in all regions of the normalized perveance per hole and achieved quantitative consistency in its high value.
