Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien Filter

For the measurement of the electric dipole moment of protons and deuterons, a novel waveguide RF Wien filter has been designed and will soon be integrated at the COoler SYnchrotron at J\"ulich. The device operates at the harmonic frequencies of the spin motion. It is based on a waveguide structure that is capable of fulfilling the Wien filter condition ($\vec{E} \perp \vec{B}$) \textit{by design}. The full-wave calculations demonstrated that the waveguide RF Wien filter is able to generate high-quality RF electric and magnetic fields. In reality, mechanical tolerances and misalignments decrease the simulated field quality, and it is therefore important to consider them in the simulations. In particular, for the electric dipole moment measurement, it is important to quantify the field errors systematically. Since Monte-Carlo simulations are computationally very expensive, we discuss here an efficient surrogate modeling scheme based on the Polynomial Chaos Expansion method to compute the field quality in the presence of tolerances and misalignments and subsequently to perform the sensitivity analysis at zero additional computational cost.Comment: 12 pages, 19 figure

Magnesium Coprecipitation with Calcite at Low Supersaturation: Implications for Mg-Enriched Water in Calcareous Soils

The concentrations of magnesium (Mg) and calcium (Ca) in natural aqueous environments are controlled by sorption and dissolution–precipitation reactions. Ca binding in calcareous soils depends on the degree of solution saturation with respect to CaCO$_{3}$. Mg may be bound in precipitating calcite. Here, we investigated Mg incorporation into calcite via the recrystallization of vaterite, which simulates a very low supersaturation in a wide range of Mg to Ca ratios and pH conditions. Increasing the Mg to Ca ratios (0.2 to 10) decreased the partition coefficient of Mg in calcite from 0.03 to 0.005. An approximate thermodynamic mixing parameter (Guggenheim a0 = 3.3 ± 0.2), that is valid for dilute systems was derived from the experiments at the lowest initial Mg to Ca ratio (i.e., 0.2). At elevated Mg to Ca ratios, aragonite was preferentially formed, indicating kinetic controls on Mg partitioning into Mg-calcite. Scanning electron microscopy (SEM-EDX) analyses indicated that Mg is not incorporated into aragonite. The thermodynamic mixing model suggests that at elevated Mg to Ca ratio (i.e., ≥1) Mg-calcite becomes unstable relative to pure aragonite. Finally, our results suggest that the abiotic incorporation of Mg into calcite is only effective for the removal of Mg from aqueous environments like calcareous soil solution, if the initial Mg to Ca ratio is already low

Electromagnetic Simulation and Design of a Novel Waveguide RF Wien Filter for Electric Dipole Moment Measurements of Protons and Deuterons

The conventional Wien filter is a device with orthogonal static magnetic and electric fields, often used for velocity separation of charged particles. Here we describe the electromagnetic design calculations for a novel waveguide RF Wien filter that will be employed to solely manipulate the spins of protons or deuterons at frequencies of about 0.1 to 2 MHz at the COoler SYnchrotron COSY at J\"ulich. The device will be used in a future experiment that aims at measuring the proton and deuteron electric dipole moments, which are expected to be very small. Their determination, however, would have a huge impact on our understanding of the universe.Comment: 10 pages, 10 figures, 4 table

A thermodynamic adsorption/entrapment model for selenium(IV) coprecipitation with calcite

Selenium is an environmentally relevant trace element, while the radioisotope 79Se is of particular concern in the context of nuclear waste disposal safety. Oxidized selenium species are relatively soluble and show only weak adsorption at common mineral surfaces. However, a possible sorption mechanism for selenium in the geosphere is the structural incorporation of selenium(IV) (selenite, SeO3 2) into calcite (CaCO3). In this study we investigate the interactions between selenite and calcite by a series of experimental and computational methods with the aim to quantify selenite incorporation into calcite at standard conditions. We further seek to describe the thermodynamics of selenite-doped calcite, and selenite coprecipitation with calcite. The structure of the incorporated species is investigated using Se K-edge EXAFS (isotropic and polarization dependent) and results are compared to density functional theory (DFT) calculations. These investigations confirm structural incorporation of selenite into calcite by the substitution of carbonate for selenite, leading to the formation of a Ca(SeO3)X(CO3)(1-X)solid solution.Coprecipitation experiments at low supersaturation indicate a linear increase of the selenite to carbonate ratio in the solid with the increase of the selenite to carbonate ratio in the contact solution. This relationship can be described under the assumption of an ideal mixing between calcite and a virtual CaSeO3 endmember, whose standard Gibbs free energy (G0(CaSeO3_exp) = 953 ± 6 kJ/mol, log10(KSP(CaSeO3_exp)) = 6.7 ± 1.0) is defined by linear extrapolation of the excess free energy from the dilute Henry’s law domain to X(CaSeO3) = 1. In contrast to this experimental result, DFT and force field calculations predict the virtual bulk CaSeO3 endmember to be significantly less stable and more soluble: G0(CaSeO3 bulk) = 912 ± 10 kJ/mol and log10(KSP(CaSeO3_bulk)) = 0.5 ± 1.7. To explain this discrepancy we introduce a thermodynamic adsorption/entrapment concept. This concept is based on the idea that the experimental value of 953 ± 6 kJ/mol reflects the Gibbs free energy of CaSeO3 within the surface layer, while the value obtained from atomistic calculations reflects bulk thermodynamic properties. In coprecipitation experiments performed at steady-state conditions the difference between these values is compensated by the supersaturation. Thus, if the Gibbs free energies of the bulk CaCO3 and CaSeO3 endmembers are substituted with the Gibbs free energies of the surface endmembers, the coprecipitation experiment can still be treated within the formalism of equilibrium thermodynamics. This concept leads to a number of important consequences, which can be tested both experimentally and theoretically.We show that selenite adsorption at the calcite surface and selenite coprecipitation with calcite under supersaturated conditions can be described with the same partition coefficient. This implies that the coprecipitation can be viewed as a sequence of adsorption and entrapment events. On the other hand, our aragonite recrystallization experiments show that at near equilibrium conditions the calcite growth is inhibited in the presence of selenite. Consistent with these observations, our DFT calculations show that the substitution of carbonate for selenite is energetically more favorable at the surface than inside the bulk. The whole set of the experimental and atomistic simulation results leads to the conclusion that the calcite–CaSeO3 solid solution can only grow continuously if the aqueous solution is supersaturated with respect to the bulk solid solution. Under these conditions selenite coprecipitates with calcite at a partition coefficient of D = 0.02 ± 0.01. If the solution is undersaturated with respect to the bulk solid solution, only surface ion-exchange occurs. Elevated selenite concentrations in bulk calcite therefore reflect non-equilibrium conditions

Adsorption of dissolved aluminum on sapphire-c and kaolinite: Implications for points of zero charge of clay minerals

We have studied the impact of dissolved aluminum on interfacial properties of two aluminum bearing minerals, corundum and kaolinite. The effect of intentionally adding dissolved aluminum on electrokinetic potential of basal plane surfaces of sapphire was studied by streaming potential measurements as a function of pH and was complemented by a second harmonic generation (SHG) study at pH 6. The electrokinetic data show a similar trend as the SHG data, suggesting that the SHG electric field correlates to zeta-potential. A comparable study was carried out on kaolinite particles. In this case electrophoretic mobility was measured as a function of pH. In both systems the addition of dissolved aluminum caused significant changes in the charging behavior. The isoelectric point consistently shifted to higher pH values, the extent of the shift depending on the amount of aluminum present or added. The experimental results imply that published isoelectric points of clay minerals may have been affected by this phenomenon. The presence of dissolved aluminum in experimental studies may be caused by particular pre-treatment methods (such as washing in acids and subsequent adsorption of dissolved aluminum) or even simply by starting a series of measurements from extreme pH (causing dissolution), and subsequently varying the pH in the very same batch. This results in interactions of dissolved aluminum with the target surface. A possible interpretation of the experimental results could be that at low aluminum concentrations adatoms of aluminum (we will refer to adsorbed mineral constituents as adatoms) can form at the sapphire basal plane, which can be rather easily removed. Simultaneously, once the surface has been exposed to sufficiently high aluminum concentration, a visible change of the surface is seen by AFM which is attributed to a surface precipitate that cannot be removed under the conditions employed in the current study. In conclusion, whenever pre-treatment or the starting point of an experiment favor the dissolution of aluminum, dissolved Al may remain in the experimental system and interact with the target surfaces. The systems are then no longer pristine and points of zero charge or sorption data are those of aluminum-bearing systems

Extent of the microbial biosphere in the oceanic crust

We estimate the depth of the 120°C isotherm by constructing crustal thermal gradients based on theoretical and observed conductive heat flux as a function of lithospheric age. We chose the 120°C isotherm because it is close to the upper limit for prokaryotic life, and therefore, the isotherm approximates the maximum depth at which life can persist in the ocean crust. The depth of the potential microbial biosphere increases with lithospheric age from approximately 0.5 to 1 km for 1 Ma lithosphere to as much as 5 km at a subduction age of 180 Ma. We use global models of oceanic plate creation to estimate the volume of crust occupied by the biosphere today and throughout geologic time. Presently, the volume of the ocean crust that is capable of containing life is similar to the volume of the oceans (∼1018 m3). Depending on the model used for the growth of continental crust, the volume of rock available to house the subsurface biosphere may have remained constant or doubled since the Archean. Although the thermal models presented here provide estimates for the potential depth and volume of rock in which microbes may live, the biomass in this volume is not well constrained. Using a previously published model, the prokaryotic biomass in the igneous ocean crust is estimated to exceed that in all aquatic and soil environments and is similar to that in the continental subsurface and in marine sediment. Most of the crustal biomass beneath the sediments is likely contained within the extrusive layer, and this has probably been the case since microbes first colonized the oceanic crust in the Archean.Keywords: Microbial biosphere, Ocean crust, Thermal structur

Phase Measurement for Driven Spin Oscillations in a Storage Ring

This paper reports the first simultaneous measurement of the horizontal and vertical components of the polarization vector in a storage ring under the influence of a radio frequency (rf) solenoid. The experiments were performed at the Cooler Synchrotron COSY in J\"ulich using a vector polarized, bunched $0.97\,\textrm{GeV/c}$ deuteron beam. Using the new spin feedback system, we set the initial phase difference between the solenoid field and the precession of the polarization vector to a predefined value. The feedback system was then switched off, allowing the phase difference to change over time, and the solenoid was switched on to rotate the polarization vector. We observed an oscillation of the vertical polarization component and the phase difference. The oscillations can be described using an analytical model. The results of this experiment also apply to other rf devices with horizontal magnetic fields, such as Wien filters. The precise manipulation of particle spins in storage rings is a prerequisite for measuring the electric dipole moment (EDM) of charged particles

Spin tune mapping as a novel tool to probe the spin dynamics in storage rings

Precision experiments, such as the search for electric dipole moments of charged particles using storage rings, demand for an understanding of the spin dynamics with unprecedented accuracy. The ultimate aim is to measure the electric dipole moments with a sensitivity up to 15 orders in magnitude better than the magnetic dipole moment of the stored particles. This formidable task requires an understanding of the background to the signal of the electric dipole from rotations of the spins in the spurious magnetic fields of a storage ring. One of the observables, especially sensitive to the imperfection magnetic fields in the ring is the angular orientation of stable spin axis. Up to now, the stable spin axis has never been determined experimentally, and in addition, the JEDI collaboration for the first time succeeded to quantify the background signals that stem from false rotations of the magnetic dipole moments in the horizontal and longitudinal imperfection magnetic fields of the storage ring. To this end, we developed a new method based on the spin tune response of a machine to artificially applied longitudinal magnetic fields. This novel technique, called \textit{spin tune mapping}, emerges as a very powerful tool to probe the spin dynamics in storage rings. The technique was experimentally tested in 2014 at the cooler synchrotron COSY, and for the first time, the angular orientation of the stable spin axis at two different locations in the ring has been determined to an unprecedented accuracy of better than $2.8\mu$rad.Comment: 32 pages, 15 figures, 7 table