A simple and direct development of the theory of the plasma inverse problem is given, and it is shown that the time record of the reflected wave arising from a δ function electric field normally incident on a stratified plasma determines uniquely the plasma density through an integral equation.
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Irvin Kay, “On the Determination of the Free Electron Distribution of an Ionized Gas,” Research Report No. EM‐141, NYU Div. of EM Research (1959).
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G. N. Balanis, “Plasma Inverse Scattering Theory,” PhD. Thesis in EE Dept. of California Institution of Tech. (June, 1972).
17.
The electron density is assumed to be a nonnegative, bounded, continuous, and with continuous derivative function of z throughout this paper.
18.
It can be easily seen from (14)‐(19) that as
19.
is the Heaviside step function,.
20.
It is of interest to note that we could also obtain from the characteristic fields by solving for in Eqs. (39) and (43); however, such a procedure is rather cumbersome.
21.
It is evident that this essential property of the characteristic fields is a consequence of the invariance of the plasma wave equation under a time reversal.
22.
S. G. Mikhlin, Linear Equations of Mathematical Physics (Holt and Rinehart, New York, 1967), p. 27.
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© 1972 The American Institute of Physics.
1972
The American Institute of Physics
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