The field in a presence of two confocal shells

Let us consider some examples of the different location of field sources. 

We suppose that field sources are located outside both shells and, first of all, derive formulae for a field caused by one harmonic of the primary field only  

For simplicity of transformations let iw/xC = 1. The process of forming the secondary field due to the m-harmonic can be presented in the following way. The field is partly reflected by the shell with the reflection coefficient Wie. 

The other part of the primary field passes the first shell without a change of its structure and it is equal to  

Arriving at the internal shell it is partly reflected (coefficient of reflection W2e) -W2ePlUm a)ct)m l3) (3.35) 

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