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The coupling impedance of beam tubes is a long-standing important topic for particle accelerators that many authors have addressed. The present study was initiated in view of a specific problem, but its novel approach is broadly applicable to the longitudinal and transverse coupling impedances of coated beam tubes or multilayer tubes. The matrix method presented here derives the wall impedance by treating the radial wave propagation of the beam-excited electromagnetic fields in full analogy to longitudinal transmission lines. Starting from the Maxwell equations, the radially transverse magnetic field components are described for monopole and dipole modes by a 2×2 matrix. Assuming isotropic material properties within one layer, the transverse field components at the inner boundary of a layer uniquely are determined by matrix transfer of the field components at its outer boundary. By imposing power-flow constraints on the matrix, wave impedance mapping and field matching between layers is enforced and replaced by matrix multiplication. The longitudinal and transverse coupling impedances are derived from the wall impedance at the innermost boundary, and the different procedures for its determination are discussed. The matrix method is demonstrated via selected yet representative examples of the well-documented cases of a stainless-steel tube, and of a graphite collimator

Matrix solution for the wall impedance of infinitely long multilayer circular beam tubes