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A high-resolution spectroscopic diagnostic for the measurement of spatial profiles of impurity ion toroidal rotation velocities on the ADITYA-U tokamak has been upgraded to cover the complete plasma minor radius. Earlier, the coverage of diagnostics toward the plasma edge was restricted due to the placement of collection optics on the tangential port outside the vacuum vessel. The coverage of the full plasma minor radius, from 0 to 24 cm, has been achieved using the newly designed and developed collection optics that have seven lines of sight to view the tokamak plasma mounted inside a customized re-entrant view port which is installed in the shadow of the limiter inside the vacuum vessel. The upgraded diagnostic also includes a faster charged coupled device detector with a smaller pixel size for the detection of a small wavelength shift. The complete spatial profile has been measured using the Doppler shifted passive change exchange spectral line at 529.0 nm from the C5+ ion. In this article, we present the collection optics’ design, installation, calibration, and results obtained using the upgraded diagnostic.

A high resolution spectroscopic diagnostic for the measurement of the spatial profile of toroidal rotation velocity (vt) and temperature (Ti) of carbon ions has been developed and implemented on the Aditya-U tokamak. The diagnostic consists of a high resolution 1 m (f/8.7) spectrometer having an 1800 grooves/mm grating coupled with a charged couple device. The setup allows measurements from 5 toroidal lines-of-sights passing through different minor radii in the horizontal mid-plane of the Aditya-U tokamak. The carbon line emissions at 529 nm in visible and 229.6 and 227.09 nm in the ultra violet spectral range are recorded using the setup. Initial results show that typical Aditya-U plasmas have a maximum carbon ion temperature (Ti) of ∼120 eV and a rotation velocity (vt) of ∼-14 km/s in the counter plasma-current direction.

A tangential soft x-ray crystal spectrometer has been designed to measure the x-ray spectrum of He-like argon for the Aditya-U tokamak plasma. The system enables to measure electron temperature using the intensity ratio of the resonance line to the satellite line. For this purpose, an x-ray spectral line at 3.9494 A from He-like argon, Ar16+, is considered. The spectrometer consists of a cylindrically bent silicon (111) crystal and a CCD detector to measure the resonance spectral line and its satellite lines in the wavelength region of 3.94-4.0 A, viewing the plasma tangentially at an angle of 26° with respect to the toroidal direction in the magnetic axis. Considering Aditya-U tokamak plasma parameters and its geometrical constraints, plasma to crystal and crystal to detector distances have been kept at 1.47 m and 0.5 m, respectively, to detect a sufficient signal. The engineering design has been optimized after adequately addressing the issues related to port geometry and machine accessibility. Details on the design of the crystal spectrometer are presented in this paper.

Impurity ion toroidal rotation profile has been observed in the ohmic discharges of Aditya-U tokamak from the Doppler-shifted passive charge exchange line emission of C5+ at 529 nm. . The line has been monitored using a space resolved visible spectroscopy diagnostic consisting of 1 m multi-track spectrometer coupled with a charge coupled device (CCD) detector. In typical discharges with central chord-averaged electron density 2.5 x 1019 m-3, the maximum toroidal rotation velocity at the plasma core is found to be -20 km/s in the counter-current direction. Reversal of plasma toroidal rotation is observed for high electron density discharges with central chord-averaged density of ~ 5 x 1019 m-3. During the rotation reversal, direction of toroidal rotation changes to co-current direction in the core. Interestingly, in the discharges with central chord-averaged electron density of 2.5 x 1019 m-3 where neon gas is injected at the plasma current flat-top, the toroidal rotation reversal has been observed after the gas puff.

Spectral distribution theory, based on average-fluctuation separation and trace propagation, is applied in the analysis of some properties of a system of m (identical) nucleons in shell model j-orbits with random interactions preserving angular momentum J-symmetry. Employing the bivariate Gaussian form with Edgeworth corrections for fixed E (energy) and M (Jz eigenvalue) density of states ρ(E,M), analytical results, in the form of expansions to order [J(J+1)]2, are derived for energy centroids Ec(m,J) and spectral variances σ2(m,J). They are used to study distribution of spectral widths, J=0 preponderance in energy centroids, lower order cross correlations in states with different J's and so on. Also, an expansion is obtained for occupation probabilities over spaces with fixed M. All the results obtained with spectral distribution theory compare well with those obtained recently using quite different methods. In addition, using trace propagation methods, a regular feature, that they are nearly constant, of spectral variances generated by random interactions is demonstrated using several examples. These open a new window to study regular structures generated by random interactions.

We study the returns of stock prices and show that in the context of data from Bombay stock exchange there are groups of stocks that remain moderately correlated for up to 3 days. We use the delay correlations to identify these groups of stocks. In contrast to the results of same-time correlation matrix analysis, the groups in this case do not appear to come from any industry segments. We present our results using the closing prices of 326 significant stocks of Bombay stock exchange for the period 1995 to 2005.

We study the spectral correlation properties of the polarized fluorescence spectra of normal and cancerous human breast tissues, corresponding to patients belonging to diverse age groups and socioeconomic backgrounds. The emission range in the visible wavelength regime of 500 to 700 nm is analyzed, with the excitation wavelength at 488 nm, where flavin is one of the active fluorophores. The correlation matrices for parallel and perpendicularly polarized fluorescence spectra reveal correlated domains, differing significantly in normal and cancerous tissues. These domains can be ascribed to different fluorophores and absorbers in the tissue medium. The spectral fluctuations in the perpendicular component of the cancerous tissue clearly reveal randomization not present in the normal channel. Random matrix-based predictions for the spectral correlations match quite well with the observed behavior. The eigenvectors of the correlation matrices corresponding to large eigenvalues clearly separate out different tissue types and identify the dominant wavelengths, which are active in cancerous tissues.