Laser-plasma electron-density measurement using x-ray interferometry

In this paper, the propagation of x-rays in laser-produced plasma is studied both analytically and numerically. The coupling relation between phase and amplitude of x-rays is derived, the solutions with higher-order corrections are given where the higher-order electron-density gradients have been taken into account. An important parameter eta was introduced, which is related to the errors of the electron-density measurement using x-ray interferometry. It is justified that so long as eta<1, the x-ray interferometry can be used for the measurement of electron density and for greater value of eta, higher-order modifications are needed.