Calculation of Charge Density Distribution of Multilayers From Transit Time Data
Calculation of Charge Density Distribution of Multilayers From Transit Time Data
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If (x^-x, ) Figure A CJoCO - 7 - we assume that co (x) is continuous and has continuous derivatives (as it would in an actual ionosphere), C'(«> ) is singtilar at all values of co conresponding to maxiiaa and minima of o> (x)» Since there is a family of distributions co (x) characterized by the same width E(ai ) and therefore yielding ths same transit time 21(a)), we cannot hope to calculate co (x). All we can calculate is ?(co ). This is more useful, however, than it might seem at first glance.... From the behavior of 4(a) ) near the singu- larities of its derivative we can calculate all the minimvun and maximum values of a) (but not their location), as well as the second derivatives of o) (x) at the extrema* We now proceed to calculate o) (C) or 4(a) ), In terms of o) (C) the transit time is (10) ^2*^1 ^12 ■ I / [^ - »o(«) / "T'^' ■^' where as (£) is a monotonically increasing function. At this point it is converient o to introduce a number of transformations. Let (11) E 2 2 "2 (12) V(4) - 0^ - 0)^(4), (13) V^ - V(0) - 0)2 - 0)^(0) -0^-0)^ Furthermore, instead of dealing with the transit time tl-, let us subtract it from the time of travel over a distance (xg-x^) of a pulse of the same frequenqy, a), in a homogeneous medium of plasma frequency o^.
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To quickly assess the difficulty of the text, read a short excerpt:
If (x^-x, ) Figure A CJoCO - 7 - we assume that co (x) is continuous and has continuous derivatives (as it would in an actual ionosphere), C'(«> ) is singtilar at all values of co conresponding to maxiiaa and minima of o> (x)» Since there is a family of distributions co (x) characterized by the same width E(ai ) and therefore yielding ths same transit time 21(a)), we cannot hope to calculate co (x). All we can calculate is ?(co ). This is more useful, however, than it might seem at first glance.... From the behavior of 4(a) ) near the singu- larities of its derivative we can calculate all the minimvun and maximum values of a) (but not their location), as well as the second derivatives of o) (x) at the extrema* We now proceed to calculate o) (C) or 4(a) ), In terms of o) (C) the transit time is (10) ^2*^1 ^12 ■ I / [^ - »o(«) / "T'^' ■^' where as (£) is a monotonically increasing function. At this point it is converient o to introduce a number of transformations. Let (11) E 2 2 "2 (12) V(4) - 0^ - 0)^(4), (13) V^ - V(0) - 0)2 - 0)^(0) -0^-0)^ Furthermore, instead of dealing with the transit time tl-, let us subtract it from the time of travel over a distance (xg-x^) of a pulse of the same frequenqy, a), in a homogeneous medium of plasma frequency o^.
What to read after Calculation of Charge Density Distribution of Multilayers From Transit Time Data?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Karp to read onlineMoreLess
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