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In nano-capillaries of large aspect ratio, the attractive image charge forceis strong enough to affect the trajectory of ions passing through capillariesand consequently to diminish the fraction of transmitted beam ions. Wecalculated the theoretically transmitted fraction, using an approached butCPU-friendly expression of the image charge force valid in the case of a staticion and an infinite cylindrical dielectric interface. When comparing thetheoretically transmitted fraction to available experimental data fornano-capillaries with an inner diameter of less than 200 nm, we found asurprisingly large disagreement, i.e., the theoretically transmitted fractionswere easily an order of magnitude lower than the experimental ones. Noting thatthe image charge force depends on the velocity of the ion via the frequencydependent relative permittivity of the insulator, we investigated whether thedisagreement could be lifted using a velocity depend image charge force. Wegive the exact expressions of the dynamical image charge force for a plane andcylindrical dielectric interface as a function of the ion velocity. We thenre-evaluated the theoretically transmitted fractions in the case of SiO$_2$ andPET dielectric interfaces. Our findings are discussed in the light of theavailable experimental data.

What is wrong with the image charge force of keV ions in insulating nano-capillaries