Corrections for the systematic errors associated with the measurements of electron cyclotron emission from DITE Tokamak using a Michelson interferometer are considered under the following headings. (a) Finite optical depth an isotropic reflection model is developed leading to a line-integral expression for the emission intensity which depends on the optical depth and the wall reflection coefficient. (b) Finite density and refraction: the error due to the distortion of the instrument antenna pattern is calculated from results of ray-tracing computations. (c) Relativistic resonance layer width: an expression is derived for the corresponding spatial error for emission perpendicular to the magnetic field. (d) Magnetic field corrections: an expression for the spatial error due to the poloidal and diamagnetic field contributions is given and its effect on the observed Shafranov shift is investigated. (e) Frequency response: the general principles of quasi-optics are applied to the Michelson interferometer demonstrating that a small-aperture blackbody oven may be used to calibrate the system. (f) Spatial resolution of the viewing optics: the equivalence of lens optics and waveguide antenna is shown both theoretically and experimentally and expressions are given for the resolution perpendicular to the viewing axis. (g) Frequency resolution: it is shown that the resolution of a Michelson interferometer can be better than that suggested by application of the Rayleigh criterion. These corrections are applied to experimental emission spectra and the derived electron temperature profiles compared with laser scattering measurements in a discharge where the plasma equilibrium is changing. The Shafranov shift of the corresponding temperature surfaces is shown to be in good agreement with that expected for the magnetic flux surfaces. Using the wall reflection model, the electron density profile is derived from the emission profile of the third harmonic cyclotron frequency.
Illinois 601 15. USC M S . received 14th M a y 1970Ahtract. Starting from bare-ion pseudopotentials, net crystal potentials are evalutiied in direct space by (a) the usual linear screening technique and (b) the Thomas-Fermi method. For the metals considered (Na and AI), the potentials are quite similar, crossing outside the cores and never differing by more than 0.02 a.u. in the case of Na nor by more than 0.2 a.u. in the case of Al. The similarity of the results based on (a) and (b) suggest the use of the pseudopotential concept in conjunction with the rather general method (b) under conditions when (a) is questionable, that is whenever the zeroth order uniform electron gas solution is a poor physical approximation to the actual system under study (specific examples being molecules, insulating solids and interfaces).Methods (a) and (bj both yield shallower wells than those most often used as input information in band structure calculations and obtained by superposing atomic data.
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