Cos Theta Research Articles

Status and Challenges of the Interaction Region Magnets for HL-LHC

About one hundred magnets of six different types shall be installed in the High Luminosity LHC (HL-LHC) in the years 2026-2028 at CERN. The magnets design, construction and test are based on CERN collaborations with institutes and industrial partners in USA, Spain, Italy, Japan and China. Three types of correctors are based on Nb–Ti technology and feature conductor peak fields in the 2 to 4 T range: for all of them the protoype phase has been successfully completed. The production is well advanced for the superferric correctors, and is starting for the canted cos theta correctors and for the nested correctors. The separation and recombination Nb–Ti dipoles D1 and D2, with a 4.5-6 T bore field range, are both in the prototype phase after the completion of the short model program. The most challenging magnet, the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn quadrupole with conductor peak field above 11 T, is in the prototype phase at CERN and halfway through the production phase in the USA. In this paper we will give, for each type of magnet, an overview of the main achievements obtained so far and we will outline the technical points still needing validation from the prototype program.

A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms

We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal and dual might have a nonzero duality gap. Nevertheless, there are arbitrary small perturbations to the problem data which would make them strongly feasible thus zeroing the duality gap. In this paper, we conduct an asymptotic analysis of the optimal value as the perturbation for regularization is driven to zero. Specifically, we fix two positive definite matrices, I_p and I_d, say, (typically the identity matrices), and regularize the primal and dual problems by shifting their associated affine space by eta I_p and varepsilon I_d, respectively, to recover interior feasibility of both problems, where varepsilon and eta are positive numbers. Then we analyze the behavior of the optimal value of the regularized problem when the perturbation is reduced to zero keeping the ratio between eta and varepsilon constant. A key feature of our analysis is that no further assumptions such as compactness or constraint qualifications are ever made. It will be shown that the optimal value of the perturbed problem converges to a value between the primal and dual optimal values of the original problems. Furthermore, the limiting optimal value changes “monotonically” from the primal optimal value to the dual optimal value as a function of theta , if we parametrize (varepsilon , eta ) as (varepsilon , eta )=t(cos theta , sin theta ) and let trightarrow 0. Finally, the analysis leads us to the relatively surprising consequence that some representative infeasible interior-point algorithms for SDP generate sequences converging to a number between the primal and dual optimal values, even in the presence of a nonzero duality gap. Though this result is more of theoretical interest at this point, it might be of some value in the development of infeasible interior-point algorithms that can handle singular problems.

Observation of the temperature and barometric effects on the cosmic muon flux by the DANSS detector

The DANSS detector (Alekseev et al. in JINST 11:P11011, 2016) is located directly below a commercial reactor core at the Kalinin Nuclear Power Plant. Such a position provides an overburden about 50 m.w.e. in vertical direction. In terms of the cosmic rays it occupies an intermediate position between surface and underground detectors. The sensitive volume of the detector is a cubic meter of plastic scintillator with fine segmentation and combined PMT and SiPM readout, surrounded by multilayer passive and active shielding. The detector can reconstruct muon tracks passing through its sensitive volume. The main physics goal of the DANSS experiment implies the antineutrino spectra measurements at various distances from the source. This is achieved by means of a lifting platform so that the data is taken in three positions – 10.9, 11.9 and 12.9 meters from the reactor core. The muon data were collected for nearly four calendar years. The overburden parameters langle E_{thr}cos theta rangle and langle E_{thr} rangle , as well as the temperature and barometric correlation coefficients are evaluated separately for the three detector positions and, in each position, in three ranges of the zenith angle – for nearly vertical muons with cos theta >0.9, for nearly horizontal muons with cos theta <0.36, and for the whole upper hemisphere.

The periodic rotary motions of a rigid body in a new domain of angular velocity

In the previous works, the limiting case for the motion of a rigid body about a fixed point in a Newtonian force field, which comes from a gravity center lies on Z-axis, is solved. The authors apply the small parameter technique which is achieved giving the body a sufficiently large angular velocity component ro about the fixed z-axis of the body. The periodic solutions of motion are obtained in neighborhood ro tends to infty. In our work, we aim to find periodic solutions to the problem of motion in the neighborhood of r0 tends to 0. So, we give a new assumption that: ro is sufficiently small. Under this assumption, we must achieve a large parameter and search for another technique for solving this problem. This technique is named; a large parameter technique instead of the small one well known previously. We see the advantage of the new technique which appears in saving high energy used to begin the motion and give the solution of the problem in another domain. The obtained solutions by the new technique depend on ro. We consider that the center of mass of this body does not necessarily coincide with the fixed point O. We reduce the six nonlinear differential equations of the body and their three first integrals to a quasilinear autonomous system of two degrees of freedom and one first integral. We solve the rational case when the frequencies of the generating system are rational except (,omega = ,1,,2,1/2,3,1/3, ldots ) under the condition gamma^{primeprime}_{0} = cos theta_{o} approx 0. We use the fourth-order Runge–Kutta method to find the periodic solutions in the closed interval of the time t and to compare the analytical method with the numerical one.

Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

We study the imprint of higher spin supermultiplets on cosmological correlators, namely the non-Gaussianity of the cosmic microwave background. Supersymmetry is used as a guide to introduce the contribution of fermionic higher spin particles, which have been neglected thus far in the literature. This necessarily introduces more than just a single additional fermionic superpartner, since the spectrum of massive, higher spin super- multiplets includes two propagating higher spin bosons and two propagating higher spin fermions, which all contribute to the three point function. As an example we consider the half-integer superspin Y = s + 1/2 supermultiplet, which includes particles of spin values j = s + 1, j = s + 1/2, j = s + 1/2 and j = s. We compute the curvature perturbation 3-point function for higher spin particle exchange and find that the known Ps(cos θ) angu- lar dependence is accompanied by superpartner contributions that scale as Ps+1(cos θ) and {sum}_m{P}_s^mleft(cos theta right) , with Ps and {P}_s^m defined as the Legendre and Associated Legendre polynomials respectively. We also compute the tensor-scalar-scalar 3-point function, and find a complicated angular dependence as an integral over products of Legendre and associated Legendre polynomials.

Baseline Design of a 16 T $\cos \theta$ Bending Dipole for the Future Circular Collider

The EuroCirCol project is part of the Future Circular Collider (FCC) study under the European Union leadership in the framework of a H2020 project. In particular, the Italian Institute for Nuclear Physics, in collaboration with CERN and other European laboratories, is developing the design of a cos theta Nb3 Sn dipole magnet which will be part of the Conceptual Design Report of the FCC studies in 2019. The magnet, with an aperture diameter of 50 mm and a bore field of 16 T, will be able to bend the beams at final energies and within collider size constraints. Here we present an update of the electromagnetic design of the Nb3 Sn cos theta dipole in double-aperture configuration, the 2-D mechanical analysis, and also the 3-D coil-ends study.

The 16 T Dipole Development Program for FCC and HE-LHC

A future circular collider (FCC) with a center-of-mass energy of 100 TeV and a circumference of around 100 km, or an energy upgrade of the LHC (HE-LHC) to 27 TeV require bending magnets providing 16 T in a 50-mm aperture. Several development programs for these magnets, based on Nb3Sn technology, are being pursued in Europe and in the U.S. In these programs, cos–theta, block-type, common-coil, and canted–cos–theta magnets are explored; first model magnets are under manufacture; limits on conductor stress levels are studied; and a conductor with enhanced characteristics is developed. This paper summarizes and discusses the status, plans, and preliminary results of these programs.

On the Hidden Beauty of Trigonometric Functions

In the unit circle with radius R = E0 = mc2 = 1 we have defined the trigonometric function cos(Theta) = v/c. The known trigonometric functions revealed the hidden relationships between sensible energy, latent energy, sensible momentum and latent momentum of the moving object, and the absorbed momentum from outside and the available momentum in the outside of the moving object. We present the trigonometric concept inspired by the old Babylonian clay tablet IM 55357 and based on the knowledge of the School of Athens (the fresco of Raphael) and the work of many generations of the Masters of trigonometry. The concept of the Divided Line of Plato can be now quantitatively tested. For the experimental analysis of this concept we propose to study in details the very well known beta decay of RaE to determine the sensible and latent energy (heat) of those beta particles and the sensible and latent energy of the remaining nucleus. The longitudinal momentum and the transverse (latent) momentum can be studied on the effects of the slow neutrons. The longitudinal momentum and the transverse momentum of photons can be manipulated in a convenient medium in order to prepare slow photons. The photoormi effect might improve the efficiency of the light-to-electricity conversion and the efficiency of the light-to-heat conversion.

Wigner functions for the pair angle and orbital angular momentum

The problem of constructing physically and mathematically well-defined Wigner functions for the canonical pair angle and angular momentum is solved. While a key element for the construction of Wigner functions for the planar phase space (q,p) in R^2 is the Heisenberg-Weyl group, the corresponding group for the cylindrical phase space (theta,p) in S^1 x R is the Euclidean group E(2) of the plane and its unitary representations. Here the angle theta is replaced by the pair (cos theta, sin theta) which corresponds uniquely to the points on the unit circle. The main structural properties of the Wigner functions for the planar and the cylindrical phase spaces are strikingly similar. A crucial role plays the sinc function which provides the interpolation for the discontinuous quantized angular momenta in terms of the continuous classical ones, in accordance with the famous Whittaker cardinal function, well-known from interpolation and sampling theories. The quantum mechanical marginal distributions for angle (continuous) and angular momentum (discontinuous) are as usual uniquely obtained by appropriate integrations of the (theta,p) Wigner function. Among the examples discussed is an elementary system of simple "cat" states.

Experimental Study of the Mechanical Characteristics of SIS300 Cos&amp;#x2013;Theta Dipolar Coils

The synchrotron SIS300 is a core component of the FAIR facility, which is under development at GSI. The high intensities of proton and heavy ion beams require the synchrotron to be ramped in a few seconds. In particular, the bending dipole magnets have to be pulsed from the injection magnetic field of 1.5 T up to the maximum field of 4.5 T at the rate of 1 T/s. The fast field ramp together with the particular characteristic to be geometrically curved (the sagitta is 114 mm) make these dipoles critical from design and construction point of views. Aside from the thermal ac losses, the mechanical fatigue is one of the main issues of these 7.8-m long magnets having cos–theta shaped coils with a 100-mm bore. Just the large number of magnetic cycles (107) oriented the mechanical design to the involvement of stiff structures working at a relatively low stress level with respect to the elastic limits. To this aim, the coils are mechanically supported by 3-mm thick laminated stainless steel collars, assembled through keys, and 1-mm thick iron yoke laminations kept together through large stainless steel C-shaped clamps. The mechanical behavior of these challenging dipoles has been studied in detail through several 2 and 3-D finite-element (FE) analyses. In order to assess the soundness of the mechanical analysis, a series of mechanical studies were performed on stacking samples and single poles under compression, comparing FE computations with the results of the mechanical tests. Finally, the collaring of short models was performed and the measured deformations were compared with expectations.

THE DETECTION OF THE LARGE-SCALE ALIGNMENT OF MASSIVE GALAXIES AT z ∼ 0.6

We report on the detection of the alignment between galaxies and large-scale structure at z~0.6 based on the CMASS galaxy sample from the Baryon Oscillation Spectroscopy Survey data release 9. We use two statistics to quantify the alignment signal: 1) the alignment two-point correlation function which probes the dependence of galaxy clustering at a given separation in redshift space on the projected angle (theta_p) between the orientation of galaxies and the line connecting to other galaxies, and 2) the cos(2theta)-statistic which estimates the average of cos(2theta_p) for all correlated pairs at given separation. We find significant alignment signal out to about 70 Mpc/h in both statistics. Applications of the same statistics to dark matter halos of mass above 10^12 M_sun/h in a large cosmological simulation show similar scale-dependent alignment signals to the observation, but with higher amplitudes at all scales probed. We show that this discrepancy may be partially explained by a misalignment angle between central galaxies and their host halos, though detailed modeling is needed in order to better understand the link between the orientations of galaxies and host halos. In addition, we find systematic trends of the alignment statistics with the stellar mass of the CMASS galaxies, in the sense that more massive galaxies are more strongly aligned with the large-scale structure.

Quantifying the coherent outflows of galaxies around voids in the SDSS DR7

We report the detection, with a high level of confidence, of coherent outflows around voids found in the seventh data release of the Sloan Digital Sky Survey (SDSS DR7). In particular, we developed a robust <|cos theta|> statistical test to quantify the strength of redshift-space distortions (RSD) associated with extended coherent velocity fields. We consistently find that the vector that joins void centers with galaxies that lie in shells around them is more likely to be perpendicular to the line-of-sight than parallel to it. This effect is clear evidence for the existence of outflows in the vicinity of voids. We show that the RSD exist for a wide range of void radius and shell thickness, but they are more evident in the largest voids in our sample. For instance, we find that the <|cos theta|> for galaxies located in shells within 2 h^-1 Mpc from the edge of voids larger than 15 h^-1 Mpc deviates 3.81sigma from uniformity. The measurements presented in this work provide useful information to constrain cosmological parameters, in particular Omega_m and Sigma_8.

Local content of bipartite qubit correlations

One of the last open problems concerning two qubits in a pure state is to find the exact local content of their correlation, in the sense of Elitzur, Popescu and Rohrlich (EPR2) [Phys. Lett. A 162, 25 (1992)]. We propose a new EPR2 decomposition that allows us to prove, for a wide range of states psi(theta)=cos(theta)|00>+sin(theta)|11>, that their local content is pL(theta)=cos(2theta). We also share reflections on how to possibly extend our result to all two-qubit pure states.

Directed Nanoparticle Motion on an Interfacial Free Energy Gradient

Using total internal reflection fluorescence microscopy (TIRFM), we have observed the directed motion of 20 nm probe particles on specific regions of surfaces that exhibited strong gradients of hydrophobicity. Patterned surfaces were prepared by selective photodegradation (using a contact photomask) of a hydrophobically modified fused silica surface. The lateral distribution of hydrophobicity was characterized in situ using the selective affinity of amphiphilic probes (i.e., hydrophobic interaction microscopy). Probe particles were observed to move unidirectionally from regions of lower to higher to hydrophobicity over distances of approximately 1 microm when the hydrophobicity gradient was greater than d(cos theta)/dx = 0.05 +/- 0.02 microm(-1), where theta is the water contact angle on the bare surface. Only adsorption events were observed on energetically homogeneous surface regions.

Quantitative Investigation of the Photodegradation of Polyethylene Terephthalate Film by Friction Force Microscopy, Contact-Angle Goniometry, and X-ray Photoelectron Spectroscopy

Studies of the UV-induced photodegradation of poly(ethylene terephthalate) (PET) have been carried out using contact-angle goniometry, X-ray photoelectron spectroscopy (XPS), and friction force microscopy (FFM). The advancing contact angle of water, theta, decreased following exposure of free-standing PET films to UV light. Measurements of surface friction by FFM showed that the coefficient of friction mu increased as the degradation proceeded, reaching a limiting value after ca 200 min, in agreement with the contact angle data. Using a modified form of the Cassie equation, a quantitative analysis of the extent of modification could be carried out. There was a very close correlation between the coefficient of friction determined by FFM and the value of cos theta. XPS provided more detailed information on surface bonding that also correlated closely with the FFM data. Although FFM provides quantitative data on surface modification with nanometer-scale spatial resolution, it does not provide detailed structural information such as is provided by XPS. The oxygen content at the surface was found to increase as photo-generated radicals within the PET reacted with atmospheric oxygen. Increases in both ester and carbonyl contributions within XPS data accompanied this increase. It was concluded that the photodegradation process follows mainly Norrish type I reaction pathways, following previous work by Fechine et al and Grosstete et al.

Electromagnetic Efficiency of Block Design in Superconducting Dipoles

Semi-analytical scaling laws have been derived for the electromagnetic design of superconducting dipoles based on sector coils approximation. Here we discuss the different features of block coils designs used in the past, focusing on the field quality issues, and on the efficiency of the electromagnetic design (i.e. short sample field versus the quantity of superconductor) with respect to the standard cos theta design.

FT-IR Methodology for Quality Control of Arabinogalactan Protein (AGP) Extracted from Green Tea (Camellia sinensis)

A rapid methodology of quality control was developed for arabinogalactan proteins (AGP) extracted and purified from green tea. Using the vectorial angle method and IR spectrum analysis, the 1200-800 cm(-1) region in second-derivative IR spectra was determined as the key fingerprinting region of green tea AGP, with the 1090-900 cm(-1) region reflecting their conservative and common characteristics. In fact, the key monosaccharides, galactose (Gal) and arabinose (Ara), were shown to have intense peaks at about 1075 and 1045 cm(-1), respectively, and uronic acids at about 1018 cm(-1) in second-derivative IR spectra. The variable region was identified to be at about 1134-1094 and 900-819 cm(-1) and was probably due to compositional and structural differences between AGPs. The constructed methodology was tested on green tea AGP extracted by three treatments and purified to apparent homogeneity as water-extracted Camellia sinensis AGP (CSW-AGP), pectinase-extracted C. sinensis AGP (CSP-AGP), and trypsin-extracted C. sinensis AGP (CST-AGP) with an Ara/Gal ratio of 1.37, 1.57, and 1.82, respectively. Regarding in vitro antioxidant activity, the AGPs (CSW-AGP and CST-AGP) with higher similarity (closer cos theta values calculated for second-derivative IR spectra) exhibited a similar ability of chelating ferrous ions and had a similar capability for scavenging hydroxyl radicals. In conclusion, the combination of second-derivative IR spectrum analysis and the vectorial angle method has allowed a successful characterization of green tea AGPs and was shown to be suitable for their compositional and activity discrimination and rapid quality evaluation.

Aspects of structure and bonding in copper-amino acid complexes revealed by single-crystal EPR/ENDOR spectroscopy and density functional calculations.

This work deduces from a series of well-defined copper-doped amino acid crystals, relationships between structural features of the copper complexes, and ligand-bound proton hyperfine parameters. These were established by combining results from electron paramagnetic resonance (EPR)/electron-nuclear double resonance (ENDOR) studies, crystallography, and were further assessed by quantum mechanical (QM) calculations. A detailed evaluation of previous studies on Cu(2+) doped into alpha-glycine, triglycine sulfate, alpha-glycylglycine, and L-alanine crystals reveal correlations between geometric features of the copper sites and proton hyperfine couplings from amino-bound and carbon-bound hydrogens. Experimental variations in proton isotropic hyperfine coupling values (a(iso)) could be fit to cosine-square dependences on dihedral angles, namely, for C(alpha)-bound hydrogens, a(iso) = -1.09 + 8.21 cos(2) theta MHz, and for amino hydrogens, a(iso) = -6.16 + 4.15 cos(2) phi MHz. For the C(alpha) hydrogens, this dependency suggests a hyperconjugative-like mechanism for transfer of spin density into the hydrogen 1s orbital. In the course of this work, it was also necessary to reanalyze the ENDOR measurements from Cu(2+)-doped alpha-glycine because the initial study determined the (14)N coupling parameters without holding its nuclear quadrupole tensor traceless. This new treatment of the data was needed to correctly align the (14)N hyperfine tensor principal directions in the molecular complex. To provide a theoretical basis for the coupling variations, QM calculations performed at the DFT level were used to compute the proton hyperfine tensors in the four crystal complexes as well as in a geometry-optimized Cu(2+)(glycine)(2) model. These theoretical calculations confirmed systematic changes in couplings with dihedral angles but greatly overestimated the experimental geometric sensitivity to the amino hydrogen isotropic coupling.

Axial Asymmetry of the Charge- and Spin-Density Distributions in Π States. Molecular Quadrupole Moments and Hyperfine Coupling Constants of CH, NH, OH, CF, LiO, NO, and FO

The axial asymmetry of the charge- and spin-density distributions in Pi states is studied via second-rank traceless tensors P(ii) (ii = xx, yy, zz), namely, quadrupole moments (Theta(ii)), electric field gradients (q(ii)), and magnetic dipolar (T(ii)) hyperfine coupling constants (hfcc's). In linear molecules, it holds that P(xx) does not = P(yy) does not = P(zz) for Pi, but P(xx) = P(yy) does not = P(zz) for Sigma, Delta, Phi,..., states. Thus, traceless P(ii) in Pi states have two independent parameters, P(parallel) = P(zz) is proportional to [r(m)(3 cos2 theta - 1] and deltaP(perpendicular) = |P(xx) - P(yy)| is proportional to [r(m) sin2 theta], with m = 2(Theta(ii)) or -3(q(ii), T(ii)). All linear states have P(parallel) does not = 0, but only Pi states exhibit deltaP(perpendicular) does not = 0, as shown by hfcc's like c = (3/2)T(zz), and d = |T(xx) - T(yy)|, as well as q0 = (-q(zz)) and |q(2)/2| = |q(xx) - q(yy)|. Little is known about Theta(zz) and deltaTheta(perpendicular) = |Theta(xx) - Theta(yy)| in Pi states since most experimental values (gas-phase) are rotational averages, and several theoretical studies have reported Theta(zz) but assumed deltaTheta(perpendicular) = 0. The diatomics studied here have X2Pi(1/2)(pi1) ground states, like CH and NO, or are of type X2Pi(3/2)(pi3), like OH, CF, LiO, and FO. The A3Pi(sigma pi3) state of NH is also included. Our P(parallel) and deltaP(perpendicular) values--calculated at the experimental R(e)'s with the B3LYP/aug-cc-pVQZ method--reproduce well the available literature data. The properties of the CF and FO radicals are not well-known so that our {c, d} and {q0, q2} values should help future experimental studies of their hyperfine spectra. Excluding OH, the complete quadrupole sets {Theta(zz), deltaTheta(perpendicular)} are new for all species discussed here. For comparison purposes, Theta(zz) of a low-lying Sigma state is also calculated for each X2Pi radical.

Characteristics of surface-enhanced Raman scattering and surface-enhanced fluorescence using a single and a double layer gold nanostructure

This paper reports the characteristics of surface-enhanced Raman scattering (SERS) and surface-enhanced fluorescence (SEF) using a unique SERS-active substrate comprised of a single layer and a double layer of two-dimensional (2D) gold nanostructure. Colloidal gold nanoparticles were immobilized on a glass substrate and a multi-purpose experimental setup was adopted to obtain surface plasmon resonance (SPR), SERS and SEF on a single platform. Inhomogeneous intensity distribution was observed in correlated images of SPR and SERS. Several laser lines were used as excitation sources for further SERS measurements. Higher SERS intensities were observed with longer wavelength excitations at the same spatial position. Fluorescence measurements were carried out using 514 nm line and SEF images were obtained using the same sample. Fluorescence emissions were found to be enhanced in the presence of 2D gold nanostructure. A series of SERS spectra were recorded by conducting ensemble SERS measurements at a periodic interval of 2 microm, crossing bare substrates, the single layer and the double layer of gold nanostructure. The double layer provides higher enhancement in SERS than that of the single layer. Polarization-selective SERS measurements obtained at the single layer and double layer showed a clear difference in their dispersions. SERS intensities of the analytes adsorbed at the single layer were fitted well with cos(4)theta dependence; however, for the double layer, the relationship was quite uncertain.