H-Formulation

The full vectorial wave equation for H is given by:

BPM - Equation 1

By substituting BPM - Equation b into Equation 1 we get:

BPM - Equation 2

The term BPM - Equation a is null.

We can separate Equation 2 into one for longitudinal terms and another one for transversal terms:

BPM - Equation 3

for longitudinal terms, and

BPM - Equation 4

By substituting

BPM - Equation 5

into the first right hand term of Equation 4, we get:

BPM - Equation 6

By substituting Equation 5 into the second right hand term of Equation 4, we get:

BPM - Equation 7

The third term of Equation 4 can be rewritten as:

BPM - Equation 8

By substituting Equation 5 into the second right hand term of Equation 4, we get:

BPM - Equation 9

where

BPM - Equation 10