S U M M A R YThe phase relationships contained in the magnetotelluric (MT) impedance tensor are shown to be a second-rank tensor. This tensor expresses how the phase relationships change with polarization in the general case where the conductivity structure is 3-D. Where galvanic effects produced by heterogeneities in near-surface conductivity distort the regional MT response the phase tensor preserves the regional phase information. Calculation of the phase tensor requires no assumption about the dimensionality of the underlying conductivity distribution and is applicable where both the heterogeneity and regional structure are 3-D.For 1-D regional conductivity structures, the phase tensor is characterized by a single coordinate invariant phase equal to the 1-D impedance tensor phase. If the regional conductivity structure is 2-D, the phase tensor is symmetric with one of its principal axes aligned parallel to the strike axis of the regional structure. In the 2-D case, the principal values (coordinate invariants) of the phase tensor are the transverse electric and magnetic polarization phases. The orientation of the phase tensor's principal axes can be determined directly from the impedance tensor components in both 2-D and 3-D situations. In the 3-D case, the phase tensor is nonsymmetric and has a third coordinate invariant that is a distortion-free measure of the asymmetry of the regional MT response. The phase tensor can be depicted graphically as an ellipse, the major and minor axes representing the principal axes of the tensor. 3-D model studies show that the orientations of the phase tensor principal axes reflect lateral variations (gradients) in the underlying regional conductivity structure. Maps of the phase tensor ellipses provide a method of visualizing this variation.
Matter with a high energy density (>10(5) joules per cm(3)) is prevalent throughout the Universe, being present in all types of stars and towards the centre of the giant planets; it is also relevant for inertial confinement fusion. Its thermodynamic and transport properties are challenging to measure, requiring the creation of sufficiently long-lived samples at homogeneous temperatures and densities. With the advent of the Linac Coherent Light Source (LCLS) X-ray laser, high-intensity radiation (>10(17) watts per cm(2), previously the domain of optical lasers) can be produced at X-ray wavelengths. The interaction of single atoms with such intense X-rays has recently been investigated. An understanding of the contrasting case of intense X-ray interaction with dense systems is important from a fundamental viewpoint and for applications. Here we report the experimental creation of a solid-density plasma at temperatures in excess of 10(6) kelvin on inertial-confinement timescales using an X-ray free-electron laser. We discuss the pertinent physics of the intense X-ray-matter interactions, and illustrate the importance of electron-ion collisions. Detailed simulations of the interaction process conducted with a radiative-collisional code show good qualitative agreement with the experimental results. We obtain insights into the evolution of the charge state distribution of the system, the electron density and temperature, and the timescales of collisional processes. Our results should inform future high-intensity X-ray experiments involving dense samples, such as X-ray diffractive imaging of biological systems, material science investigations, and the study of matter in extreme conditions.
We have used the Linac Coherent Light Source to generate solid-density aluminum plasmas at temperatures of up to 180 eV. By varying the photon energy of the x rays that both create and probe the plasma, and observing the K-α fluorescence, we can directly measure the position of the K edge of the highly charged ions within the system. The results are found to disagree with the predictions of the extensively used Stewart-Pyatt model, but are consistent with the earlier model of Ecker and Kröll, which predicts significantly greater depression of the ionization potential.
The newly commissioned Orion laser system has been used to study dense plasmas created by a combination of short pulse laser heating and compression by laser driven shocks. Thus the plasma density was systematically varied between 1 and 10 g/cc by using aluminum samples buried in plastic foils or diamond sheets. The aluminum was heated to electron temperatures between 500 and 700 eV allowing the plasma conditions to be diagnosed by K-shell emission spectroscopy. The K-shell spectra show the effect of the ionization potential depression as a function of density. The data are compared to simulated spectra which account for the change in the ionization potential by the commonly used Stewart and Pyatt prescription and an alternative due to Ecker and Kröll suggested by recent x-ray free-electron laser experiments. The experimental data are in closer agreement with simulations using the model of Stewart and Pyatt.
S U M M A R YGalvanic distortion has long been recognized as an obstacle in the interpretation of magnetotelluric (MT) data. One fundamental problem for distortion removal is that the equations that describe the effects of galvanic distortion on the impedance tensor are underdetermined. We have previously shown that an explicit solution for four of the parameters of the regional (undistorted) impedance tensor can be resolved without any assumptions. These determinable parameters are the components of a tensor (the phase tensor) representing the phase information contained in the impedance. The coordinate invariants of the phase tensor provide a simple and objective guide to the dimensionality of the regional impedance tensor at each measured frequency. Where the regional structure is 2-D, one of the principal axes of the phase tensor will be aligned parallel to the strike of the regional conductivity. The distortion tensor and the parameters of the regional impedance tensor that represent the amplitude information cannot be determined without assumptions. Where the phase tensor shows the regional impedance tensor to be 1-D, the distortion tensor and the regional impedance can be determined to within a single multiplicative constant. Where a 2-D regional structure is indicated, two assumptions are necessary to determine the regional impedance tensor but the solution is not unique, and any choice of assumptions could be made with equal validity. For 3-D structures, the phase tensor provides the direction of greatest inductive response, which is the closest equivalent of a strike direction. In this case four constraints are required for a solution. In practice, a MT sounding may contain sections that display different characteristic dimension and the distortion tensor can be determined from the section of the sounding with the lowest characteristic dimension. The greatest amount of information is determined from a 1-D section. The use of the information contained in the phase tensor overcomes some of the shortcomings of traditional distortion analysis. Illustrating the tensors using an elliptical representation aids the interpretation of the tensor data involved in this analysis.
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