Random volume scattering

The disturbances produccd by a sligh tly inhomogeneo us r andom mcdium o n a pass ing wave can be classified in to co ntr ibutions depe nding on a n inCl'easing llu mber of successive scatterings. The indi vidu al co nt ribu t ions a ppear in an expansion of t he Ro lu t io n of a n in tegr al equation. The first te rm, the Born approximation , o illy accou nts for a sing le scattering. Convenient expressions for t hi s approx imation res ult from a sad dl e poi li t t reatment for s hor t distances, and from a Fraun hofer approximation for la rge r di stances . The evalu a\ ion of t he higher-order co ntr ibu t ions, describi ng plura l-scattering effects, leads to mathematical d iffi cul t ies which a re evaded by co nsidering t he scat terill g; mecha ni s m as a M a rkov ia n p rocess . The correspond ing t heory can be developed with t he a id of an integro-dir-ferent ial diffusion eq uation ; t he latte r r efers to t he join t probabili ty de nsity of t he lateral and angula r deviations suffered by t he trajecto ry of t he passi ng w'tve . The equat ion in quest ion can be solved w ith t he a id of four-d imensiona l operat iona l calc ulu s ; i t red uces to t he simp le d iffere nt ial eq uat ion of Fok ker-Pla nck und cr s pecial co nd itio ns . The appl ication of t he general equat ion to t ro pospheri c point-to-point rad io comm uni cation is work ed out. It is sh own t hat t he fa r-d istance fi eld, associated in t his case with multip le scattering, docs dec rease proportio na ll y to t he second or t hird powe r of t he in verse di stance.