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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The electron density N(z) is assumed to be a nonnegative, bounded, continuous, and with continuous derivative function of z throughout this paper.
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It can be easily seen from (14)‐(19) that |C1|,|C2|→0 as k→±∞.
19.
H(ξ) is the Heaviside step function,
.
20.
It is of interest to note that we could also obtain kp2(z) from the characteristic fields by solving for kp2(z) 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.
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