Abstract
The standard theoretical formulas for resistive wall impedance are usually derived in a model which assumes an infinitely long pipe. In practice, one often has to deal with resistive inserts with a conductivity different from the rest of the pipe. To address this case, we calculate the resistive wall impedance when the wall conductivity varies along the axis of the pipe. We show that at not very high frequencies the impedance of an insert per unit length is given by the same formulas as for an infinitely long pipe.
Highlights
The standard theoretical formulas for resistive wall impedance are derived in a model of an infinitely long pipe
One often has to deal with resistive inserts with a conductivity different from the rest of the pipe
In this paper we calculate the resistive wall impedance when the wall conductivity varies along the axis of the pipe in the regime when condition (2) is satisfied
Summary
The standard theoretical formulas for resistive wall impedance (see, e.g., [1]) are derived in a model of an infinitely long pipe. One often has to deal with resistive inserts with a conductivity different from the rest of the pipe. In this paper we calculate the resistive wall impedance when the wall conductivity varies along the axis of the pipe in the regime when condition (2) is satisfied. In a recent paper [3], the problems of the impedance of an insert with a different conductivity have been studied for a more general case, without the assumption (2), for a cylindrical geometry only. In the last section of this paper we discuss the relation of our results to that of Ref. [3]
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