Electronic structure calculations constitute a valuable tool to predict the properties of materials. In this study we propose an efficient scheme to study correlated electron systems with essentially only one free parameter, the screening length of the Coulomb potential. A general reformulation of the exchange energy of the correlated electron shell is combined with this method in order to analyze the calculations. The results are interpreted in terms of different polarization channels, due to different multipoles. The method is applied to various actinide compounds, in order to increase the understanding of the complicate behaviour of 5f electrons in these systems. We studied the non-magnetic phase of δ-Pu, where the spin polarization is taken over by a spin-orbit-like term that does not break the time reversal symmetry. We also find that a non-trivial high multipole of the magnetization density, the triakontadipole, constitutes the ordering parameter in the mysterious hidden order phase of the heavy-fermion superconductor URu2Si2. This type of multipolar ordering is also found to play an essential role in the hexagonal-based superconductors UPd2Al3,  UNi2Al3 and UPt3 and in the dioxide insulators UO2, NpO2 and PuO2. The triakontadipole moments are also present in all magnetic actinides we considered, except for Cm. These results led us to formulate a new set of rules for the ground state of a system, that are valid in presence of strong spin-orbit coupling interaction instead of those of Hund; the Katt's rules. Finally, we applied our method to a new class of high-Tc superconductors, the Fe-pnictides, where the Fe 3d electrons are moderately correlated. In these materials we obtain the stabilization of a low spin moment solution, in agreement with experiment, over a large moment solution, due to the gain in exchange energy in the formation of large multipoles of the spin magnetization density. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 705

Les composés cubiques à base de terres rares sont un terrain favorable à l'expression de degrés de liberté alternatifs, liés à la dégénérescence d'orbite et/ou aux instabilités cristallographiques. Du fait du caractère multiaxial de la symétrie cubique, une simple anisotropie à un ion associée à des couplages d'échange isotrope y conduirait à des états d'ordre magnétique de dégénérescence élevée. Celle-ci étant systématiquement levée, on est forcé de mettre en cause des degrés de liberté autres que celui de spin. Cet impératif est confirmé par l'observation dans ces systèmes de transitions magnétiques du premier ordre, de structures magnétiques exotiques (notamment multiaxiales), d'effets magnétoélastiques, d'une anisotropie ne relevant pas du seul champ cristallin etc., phénomènes tous impossibles à appréhender sur la base de l'échange isotrope et de l'anisotropie à un ion. Nous étudions l'influence de deux types de degrés de liberté, qui interviennent par une redistribution de la charge dans le cristal : - la "déformation" de la couche 4f , décrite par l'émergence de multipôles électriques. - le déplacement des ions terre rare, lorsque la structure cristalline le permet. Dans les états d'ordre magnétique, ces deux modes correspondent à l'émergence de paramètres d'ordre secondaires, composantes multipolaires 4f et distribution de déplacement, qui participent à la définition des états ordonnés. Ils en déterminent largement les propriétés et donnent lieu à des phénomènes spécifiques qui, via la charge, trahissent le magnétisme. A l'état paramagnétique, ils sont également actifs, modifiant l'anisotropie magnétique, les propriétés magnétoélastiques et de transport etc.. Ils peuvent même y induire des transitions de phase non-magnétiques, où seule intervient la distribution de charge (ordres quadrupolaires, effet Jahn-Teller).

Thesis (Ph.D.); Submitted to the Massachusetts Inst. of Tech., Cambridge, MA (US); 1 Oct 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-174" "DOE/ER/40150-2571" Zhengwei Chai. 10/01/2003. Report is also available in paper and microfiche from NTIS.

This thesis presents results of investigations on fields and multipole expansion coefficients in axially symmetric (referred to as 3D)and two dimensional (2D)ion trapmass analysers. 3D mass analysers have a three-electrode geometry with two (electrically shorted) endcap electrodes and one central ring electrode. rf-only or rf/dc potential applied across the electrodes creates a linear trapping field in the central cavity of the mass analyser.2Dmass analysers have four longitudinal electrodes in which the opposite pairs of electrodes are electrically shorted. Here, rf-only or rf/dc potential applied across the pair of electrodes creates a linear trapping field and fragment ions of the analyte gas are trapped along the central axis of the mass analyser. Both these mass analysers have apertures machined on the electrodes (holes in case of 3D traps and slits in case of 2D traps) to permit entry of electrons for ionizing the analyte gas and for collection of destabilized fragment ions. This thesis is concerned with how these apertures influence the fields and multipole expansion coefficients within the traps. This thesis is divided into five chapters. Chapter 1 provides the background information which is required for the thesis. It begins with a description of the geometry of the 3D and the 2D mass analysers used in the present work.These include the quadrupole ion trap (QIT) and cylindrical ion trap (CIT) for 3D structures and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for 2D structures. This is followed by a brief description of the numerical method, the boundary element method (BEM), used in the thesis. Also presented here are the Green’s function for 3D and 2D geometries. In the final section, the scope of the thesis is presented. Chapter 2 presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E= EnoAperture + EdueToAperture where EnoAperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing; and where EdueToAperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis of the trap can in this way be well approximated for any aperture that is not too large. To derive EdueToAperture, classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes. EnoAperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact (though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the quadrupole ion trap (QIT), the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT)and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics studies than have been hitherto attempted. In Chapter 3we complement and complete the work presented in Chapter 2 by considering off-axis fields in the axially symmetric (3D) and the two dimensional (2D) ion traps whose electrodes have apertures. Our approximation has two parts. The first, EnoAperture, is the field obtained numerically for the trap under study with no apertures. We have used the boundary element method (BEM) for obtaining this field. The second part, EdueToAperture, is an analytical expression for the field contribution of the aperture. In EdueToAperture, aperture size is a free parameter. A key element in our approximation is the electrostatic field near an infinite thin plate with an aperture, and with different constant valued far field intensities on either side. Compact expressions for this field can be found using separation of variables, wherein the choice of coordinate system is crucial. This field is, in turn, used four times within our trap specific approximation. The off-axis field expressions for the 3D geometries were tested on the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT), and the corresponding expressions for the 2D geometries were tested on the linear ion trap (LIT) and rectilinear ion trap (RIT). For each geometry, we have considered apertures which are 10%, 30% and 50% of the trap dimension. We have found that our analytical correction term EdueToAperture, though based on a classical small-aperture approximation, gives good results even for relatively large apertures. Chapter 4 presents approximate analytical expressions for estimating the variation in multipole expansion coefficients with the size of apertures in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers. Following the approach adopted in Chapter 2 and Chapter 3 which focused on the role of apertures to fields within traps, here too, the analytical expression is a sum of two terms, An,noAperture, the multipole expansion coefficient for a trap with no apertures and An,dueToAperture, the multipole expansion coefficient contributed by the aperture. An,noAperture has been obtained numerically and An,dueToAperture is obtained from the nth derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A2 to A24, estimated by our analytical expressions were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap size. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be in the range of 10% to 15%. The leading multipole expansion coefficient, A2, however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and LIT only at larger aperture sizes. Chapter 5 presents a few concluding remarks.

Recent experimental achievements in active noise control (ANC) for cooling fans have used near-field error sensors whose locations are determined according to a theoretical condition of minimized sound power. A theoretical point source model, based on the condition previously stated, reveals the location of near-field pressure nulls that may be used to optimize error sensor placement. The actual locations of these near-field pressure nulls for both an axial cooling fan and a monopole loudspeaker were measured over a two-dimensional grid with a linear array of microphones. The achieved global attenuation for each case is measured over a hemisphere located in the acoustic far field of the ANC system. The experimental results are compared to the theoretical pressure null locations in order to determine the efficacy of the point source model. The results closely matched the point source model with a loudspeaker as the primary source, and the sound power reduction was greatly reduced when error sensors were placed in non-ideal locations. A weakness of the current near-field modeling process is that a point monopole source is used to characterize the acoustic noise from an axial cooling fan, which may have multipole characteristics. A more complete characterization of fan noise may be obtained using a procedure based on the work of Martin and Roure [J. Sound Vib. 201 (5), 577--593 (1997)]. Pressure values are obtained over a hemisphere in the far field of a primary source and the contributions from point source distributions up to the second order, centered at the primary source, may be calculated using a multipole expansion. The source information is then used in the aforementioned theoretical near-field calculation of pressure. The error sensors are positioned using the complete fan characterization. The global far-field attenuation for the multipole expansion model of fan noise is compared to that of previous experiments. Results show that the multipole expansion model yields a more accurate representation the near field, but is not successful in achieving greater sound power reductions in the far field.