Asymptotic and hybrid methods in electromagnetics by F. Molinet, I. Andronov, D. Bouche

By F. Molinet, I. Andronov, D. Bouche

Asymptotic equipment offer enormous actual perception and realizing of diffraction mechanisms and are very helpful within the layout of electromagnetic units corresponding to radar pursuits and antennas. even though, problems can come up whilst attempting to resolve difficulties utilizing multipole and asymoptotic tools jointly, akin to in radar move part items. This new publication deals an answer to this challenge by way of combining those techniques into hybrid tools, for this reason growing excessive call for for either figuring out and studying the best way to observe asymptotic and hybrid ways to remedy diffraction difficulties. The e-book offers the very most recent and such a lot accomplished learn in this subject.

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Sample text

60). 14). Away from this discontinuity line, the surface is assumed to be smooth with the radii of curvature large in terms of the wavelength. 38) and an additional term Ed , due to the presence of the edge, called the diffracted field: ES (r) = ER (r) + Ed (r). 70) We suppose that Ed has the general form: N 1 d (ik)−n end (r) + o(k −N ). 15 s=0 s = s0 s Astigmatic pencil of diffracted rays the corresponding model or canonical problem. This form of the solution is not valid close to the edge and to the shadow boundaries of the reflected field where the field of rays is singular.

In the case of the Dirichlet or Neumann boundary conditions ξp are constants and in the last case ξp are functions of s. When the parameter ξ = ξp is found the function p(s) is a simple integral s ξp (t) dt. 85) is not defined from the principal order equation. 86) one finds that together with boundary and radiation conditions this is the Sturm–Liouville problem for U1 with the parameter ξ taken on the spectrum. In order that this problem be solvable, the right-hand side should be compatible and the compatibility condition appears to be an equation for the amplitude A0 .

74) √ √ where a is a constant since |J (σ )| behaves like σ when σ tends to zero. For n = 0 this limit must be the same as for a straight wedge. 71) is not valid in the vicinity of the edge, neither for the model problem (straight wedge) nor for the original problem (curved wedge). 74) when σ tends to zero in order that both outer expansions match to the corresponding inner expansions. If e0d (σ ) is the zeroth-order term of the asymptotic expansion for a straight wedge, we have therefore: √ δ 0 = a lim (e0d (σ ) σ ) σ →0 and since: 1 e0d (σ ) = √ e0i (Q) · De σ (De is dyadic diffraction coefficient given in Chapter 3) we obtain by taking into account that |J (σ )| is proportional to (ρ + σ )σ : e0d (σ ) = e0i (Q) · De ρ , σ (ρ + σ ) where ρ is the radius of curvature of the diffracted wave front in the plane of diffraction (t, sd ).

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