Resistive wall impedance and tune shift for a chamber with a finite thickness

Since the resistive wall impedance for a beam pipe of a nonround cross section depends on the coordinates of a witness particle, the witness particle receives an incoherent tune shift. When the expression for the impedance of an infinitely thick chamber is applied to the calculation of this tune shift, it becomes infinite. We have derived the resistive wall impedance for a chamber with a finite thickness and calculated the tune shift. There is no ambiguity in this expression for the tune shift, because it is automatically finite.