Beam propagation of x rays in a laser-produced plasma and a modified relation of interferometry in measuring the electron density

In this paper, using a quantum mechanical technique and introducing the so-called V representation (where the representation transformation is made by using the potential Hamiltonian V), we studied x-ray propagation in a linear plasma medium both analytically and numerically. A modified relation between the phase of the probe and the reference light and the electron density of the plasma is derived, in which the contribution of the gradient of the electron density has been taken into account. It is shown that this relation has the advantage in measurements of the electron density of a plasma using the x-ray interferometry technique of lessening the errors originating from the electron density gradient. The validity of x-ray interferometry is discussed in both mathematical and physical terms.