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We can use the solution that we had in 9 because the RgE~M is a linear combination of RgN n and has a scattering coefficient of T~N) for scattering by a cylinder. The quantity RgE~E is a linear combination of RgMn and has a scattering coefficient of T~M). The expressions of T~M) and T~N) are as in (9.3.54) and (9.3.55) of 9. Thus the response Green's function of the magnetic field of the cylinder is z = --; _, = _ T) '""' (-It+ (N)-TM _ d GR(7,r).It--2d~ k 2 fzTn H n (kpz ,kzz ,p,z+"2) n,Z pZ m_n(k pl , kzz, p')e- in ' . It z iT) '""' (-It+ (M)-TE _ d - 2d~ k2 fzTn H n (k pz ,kzz ,p,z+"2) n,Z pi n-n(k pz , k zz , p')e- in ' . It (12.3.39) We also define the surface current modal solutions as the current on the surface of the cylinder. These can be obtained from the modal solutions of the magnetic field and using the Wronskian on p. 44 of Volume 1. The surface current modal solutions are -TE _ (-TE _ (M)-TE _) J sn (kp,kz,z) -px RgH n (kp,kz,p,z)+Tn H n (kp,kz,p,z) p=a

(kpa)

[-z:; cos (kzz) - ~ i Sin(kzZ)]

{cos kzz} em,/,

The constants are de ned with the Private modi er so that they can be used within the business object but not outside of it The CN_ pre x denotes that it is a column name This makes it easier to nd the column names using Intellisense and ensures that the names don t collide with the business object s property names You can either type all of these for each business object or use the same techniques de ned for the stored procedure generator to generate these constants

(12.3.40)

HAl) (kpa)

(12.3.41)

Summary

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Consider N cylinders placed between the two parallel plates and centered at PI' P2, ... , PN' Let there be magnetic surface current density M su at (pi, Z' = dj2) and M s = M sb at (pi, Zl = -dj2) (Fig. 12.3.3). The multiple scattering can be formulated in terms of Foldy-Lax multiple scattering equations similar to that of 9, Section 3. In the following, we use the upper sign for equations and results with source M su at (pi, Zl = dj2) and lower sign for equations and results with source Msb at (pl,.Z' = -dj2). Within the Foldy-Lax formulation, the final exciting field of cylinder p is

NOTE: To aid in defining the correct constants or resource strings, you can view the list of column names in each table using Server Explorer

-(p)

d j 2)

(12.3.42)

-(p) - "T(N) TM(p)-TM(k k - - dj ) H s - L.J m w lm Hm pI, zl,P pp,z 2 m,l " (M) +L.JTm w TE(p)-TE( kpl, k zl,P-Pp,z dj 2) Hm lm m,l

(12.3.43)

System elds are in every table Instead of adding constants for them to each business object, add the constants to the base business object class:

Figure 12.3.3 N cylinders are placed between two parallel plates with r .gnetic surface (pl,Z' = d/2) and M s = M sb at (P',Z' = -d/ J. Magnetic ring

(12.3.44)

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The scattered field will be incident on cylinder q. Since the mode functions are linear combinations of cylindrical wave functions of M n and N n . The translation formula for the magnetic modal fields are the same as the vector cylindrical wave functions of (9.3.71) and (9.3.72) from 9.

-TM d H m (k pl ,kz l,P-Pp,z "2) -

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