Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.

Determination of Ten Kinds of Alpha-2 Agonists Residues in Animal Derived Food by UHPLC-Triple Quadrupole/Composite Linear Ion Trap Mass Spectrometry

[Objectives]The paper was to establish an ultra high performance liquid chromatography-quadrupole/linear ion trap complex mass spectrometry for the determination of 10 kinds ofα2-receptor agonists in animal derived food.[Methods]The samples were extracted with sodium carbonate buffer solution and ethyl acetate,and analyzed by mass spectrometry after solid phase extraction and high performance liquid chromatography separation.[Results]Ten kinds ofα2-receptor agonists showed a good linear relationship in the range of 1-100μg/mL,with the average recovery of over 69%and the relative standard deviation less than 8.32%.The detection limit of 10 kinds of α_(2)-receptor agonists was up to 1μg/kg.[Conclusions]The method has good selectivity and strong anti-interference ability,and can meet the requirements of 10 kinds ofα2-receptor agonists residues in animal derived food.

Development of short prototype of dual aperture quadrupole magnet for CEPC ring

Main quadrupole magnets are critical for the Circular Electron and Positron Collider(CEPC)and are specifically designed as dual aperture quadrupole(DAQ)magnets.However,the field crosstalk between the two apertures presents challenges.As the CEPC will work at four beam energies of Z,W,Higgs and ttbar mode,the DAQ magnets will operate at four field gradients spanning from 3.18 to 12.63 T/m.The first short quadrupole magnet prototype with the bore diameter of 76 mm and magnetic length of 1.0 m revealed the problems of large magnetic field harmonics and a magnetic center shift within the beam energy range.Accordingly,a compensation method was proposed in this work to solve the field crosstalk effect.By adjusting the gap height at the middle of the two apertures,the field harmonics and magnetic center shift are significantly reduced.After optimization,the short prototype was modified using a new scheme.The field simulations are validated from the magnetic measurement results.Further,the multipole field meets the requirements of the four beam energies.The detailed magnetic field optimization,field harmonics adjustment,and measurement results are presented herein.

Research on the influence of quadrupole deformation and continuum effects on the exotic properties of 15,17,19B with the complex momentum representation method

The properties of exotic nuclei are the focus of the present research.Two-neutron halo structures of neutron-rich17,19B were experimentally confirmed.We studied the formation mechanism of halo phenomena in17,19B using the complex momentum representation method applied to deformation and continuum coupling.By examining the evolution of the weakly bound and resonant levels near the Fermi surface,s–d orbital reversals and certain prolate deformations were observed.In addition,by analyzing the evolution of the occupation probabilities and density distributions occupied by valence neutrons,we found that the ground state of15B did not exhibit a halo and the ground states of17B and19B exhibited halos at 0.6≤β2≤0.7 and0.3≤β2≤0.7,respectively.The low-l components in the valence levels that are weakly bound or embedded in the continuous spectrum lead to halo formation.

Formalism of rotating-wave approximation in high-spin system with quadrupole interaction

We investigate the rotating wave approximation applied in the high-spin quantum system driven by a linearly polarized alternating magnetic field in the presence of quadrupole interactions.The conventional way to apply the rotating wave approximation in a driven high-spin system is to assume the dynamics being restricted in the reduced Hilbert space.However,when the driving strength is relatively strong or the driving is off resonant,the leakage from the target resonance subspace cannot be neglected for a multi-level quantum system.We propose the correct formalism to apply the rotating wave approximation in the full Hilbert space by taking this leakage into account.By estimating the operator fidelity of the time propagator,our formalism applied in the full Hilbert space unambiguously manifests great advantages over the conventional method applied in the reduced Hilbert space.

Correction to:Development of short prototype of dual aperture quadrupole magnet for CEPC ring

While typesetting the article,in the Figs.13 and 17 there were several errors introduced.The correct Figs.13 and 17 are copied below:The original article has been corrected.

Radio Frequency Quadrupole for Bunching Electron Beam: Electromagnetic Field, Particle Velocity Range, and Accuracy at 10 GHz

The Radio Frequency Quadrupole (RFQ) accelerator invented by Kapchinskii and Tepliakov can focus, bunch, and accelerate charged-particle beams simultaneously. Typically, it operates at frequencies up to 500 MHz, for low particle velocities ( β ). The first attempt to design cylindrical RFQ for electrons in the GHz region was done using 3 GHz at Frascati in 1990. In this paper, an analytical approximation of the electromagnetic field is given, and linearized in the beam region for a rectangular Electron Radio Frequency Quadrupole (ERFQ). The differences between the proton-RFQ and the electron-RFQ are discussed. Then, it will be shown that contrary to the quadrupoles for protons or heavy-ions, the ERFQ is suited for electron velocities in the range 0.5 - 0.7 c, and possible applications are given. Finally, it is illustrated, with numerical field computations that this approach gives sufficient accuracy at 10 GHz.

Determination of Oleuropein in Cosmetics by Ultra Performance Liquid Chromatography-Triple Quadrupole Tandem Mass Spectrometry

An ultrahigh performance liquid chromatography-triple quadrupole tandem mass spectrometry(UPLC-MS/MS)was established to quickly and accurately determine the content of oleuropein in cosmetics.The samples were extracted with methanol-aqueous solution,and the mobile phase with methanol-formic acid solution(0.1 mol/L)=40∶60 was separated by Agilent ZORBAX Eclipse Plus C18(2.1 mm×50 mm×1.8μm-Micron)column temperature 30℃,flow rate 0.3 mL/min.The MS end was detected by electrospray negative mode ionization(ESI-)and multiple reaction monitoring(MRM)mode.The results show a good linear relationship in the range of 0.002~5 mg/L,with a correlation coefficient R2 of 0.999,5.Method recovery range from 84.2%~107.6%and the relative standard deviation RSD is 5.8%.The detection time is 5 min,the detection limit is 0.000,6 mg/L,and the limit of quantification is 0.002 mg/L.This method has the advantages of convenient operation,low quantification limit,high precision and good repeatability,and is suitable for measuring the content of oleuropein in many kinds of cosmetics.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

Simultaneous determination of amino acids in different teas using supercritical fluid chromatography coupled with single quadrupole mass spectrometry

Tea is a widely consumed beverage and has many important physiological properties and potential health benefits. In this study, a novel method based on supercritical fluid chromatography coupled with mass spectrometry (SFC-MS) was developed to simultaneously determine 11 amino acids in different types of tea (green teas, Oolong tea, black tea and Pu-erh tea). The separation conditions for the analysis of the selected amino acids including the column type, temperature and backpressure as well as the type of additive, were carefully optimized. The best separation of the 11 amino acids was obtained by adding water (5%, v/v) and trifluoroacetic acid (0.4%, v/v) to the organic modifier (methanol). Finally, the developed SFC-MS method was fully validated and successfully applied to the determination of these amino acids in six different tea samples. Good linearity (r ≥ 0.993), precision (RSDs≤ 2.99%), accuracy (91.95%-107.09%) as well as good sample stability were observed. The limits of detection ranged from 1.42 to 14.69 ng/mL, while the limits of quantification were between 4.53 and 47.0 ng/mL. The results indicate that the contents of the 11 amino acids in the six different tea samples are greatly influenced by the degree of fermentation. The proposed SFC-MS method shows a great potential for further investigation of tea varieties.

Quadrupole-Linear Ion Trap Tandem Mass Spectrometry System for Clinical Biomarker Analysis

The accurate and efficient measurement of small molecule disease markers for clinical diagnosis is of great importance.In this study,a quadrupole-linear ion trap(Q-LIT)tandem mass spectrometer was designed and built in our laboratory.Target precursor ions were first selected in the quadrupole,and then injected,trapped,and fragmented simultaneously in the linear ion trap(LIT)to reduce the space charge effect,enrich the target product ions,and promote sensitivity.The targeted analytes were measured with selected reaction monitoring using a positive scan mode with electrospray ionization(ESI).Ions with a mass-to-charge ratio(m/z)ranging from 195 to 2022 were demonstrated.When scanning at 1218amu.s^(-1),unit resolution and an accuracy of higher than m/z 0.28 was obtained for m/z up to 2000.The dimensionless Mathieu parameter(q)value used in this study was 0.40 for collision-induced dissociation(CID),which was activated by resonance excitation.And an overall CID efficiency of 64%was achieved(activation time,50 ms).Guanidinoacetic acid(GAA)and creatine(CRE)were used as model compounds for small molecule clinical biomarkers.The limits of quantification were 1.0 and 0.2 nmol.L^(-1)for GAA and CRE,respectively.A total of 77 actual samples were successfully analyzed by the home-built ESI-Q-LIT tandem mass spectrometry system.The developed method can reduce matrix interference,minimize space charge effects,and avoid the chromatographic separation of complex samples to simplify the pretreatment process.This novel Q-LIT system is expected to be a good candidate for the determination of biomarkers in clinical diagnosis and therapeutics.

Dimension-Enhanced Ultra-High Performance Liquid Chromatography/Ion Mobility-Quadrupole Time-of-Flight Mass Spectrometry Combined with Intelligent Peak Annotation for the Rapid Characterization of the Multiple Components from Seeds of Descurainia sophia

The complex composition of herbal metabolites necessitates the development of powerful analytical techniques aimed to identify the bioactive components.The seeds of Descurainia sophia(SDS)are utilized in China as a cough and asthma relieving agent.Herein,a dimension-enhanced integral approach,by combining ultra-high performance liquid chromatography/ion mobility-quadrupole time-of-flight mass spectrometry(UHPLC/IMQTOF-MS)and intelligent peak annotation,was developed to rapidly characterize the multicomponents from SDS.Good chromatographic separation was achieved within 38 min on a UPLC CSH C18(2.1×100 mm,1.7μm)column which was eluted by 0.1%formic acid in water(water phase)and acetonitrile(organic phase).Collision-induced dissociation-MS^(2)data were acquired by the data-independent high-definition MS^(E)(HDMS^(E))in both the negative and positive electrospray ionization modes.A major components knockout strategy was applied to improve the characterization of those minor ingredients by enhancing the injection volume.Moreover,a self-built chemistry library was established,which could be matched by the UNIFI software enabling automatic peak annotation of the obtained HDMS^(E)data.As a result of applying the intelligent peak annotation workflows and further confirmation process,a total of 53 compounds were identified or tentatively characterized from the SDS,including 29 flavonoids,one uridine derivative,four glucosides,one lignin,one phenolic compound,and 17 others.Notably,four-dimensional information related to the structure(e.g.,retention time,collision cross section,MS^(1)and MS^(2)data)was obtained for each component by the developed integral approach,and the results would greatly benefit the quality control of SDS.

Trapped Bose–Einstein condensates with quadrupole–quadrupole interactions

We numerically investigate the ground-state properties of a trapped Bose–Einstein condensate with quadrupole–quadrupole interaction.We quantitatively characterize the deformations of the condensate induced by the quadrupolar interaction.We also map out the stability diagram of the condensates and explore the trap geometry dependence of the stability.

Production of Rubidium Bose-Einstein Condensate in an Optically Plugged Magnetic Quadrupole Trap

We experimentally produce the rubidium Bose-Einstein condensate in an optically plugged magnetic quadrupole trap. A far blue-detuned focused laser beam with a wavelength of 532nm is plugged in the center of the magnetic quadrupole trap to increase the number of trapped atoms and to suppress the heating. An rf evaporative cooling in the magneto-optical hybrid trap is applied to decrease the atom temperature into degeneracy. The atom number of the condensate is 1.2（0.4）× 10^5 and the temperature is below lOOnK. We also study characteristic behaviors of the condensate, such as phase space density, condensate fraction and anisotropic expansion.

Dependence of Decamethylcyclopentasiloxane (DMCPS) Dissociation on Ionized Energy by Using Quadrupole Mass Spectrum

Dependence of decamethylcyclopentasiloxane （DMCPS） organosilicon dissociation on ionized energy in the energy range of 25 eV to 70 eV is investigated by using a quadrupole mass spectrometry. At the ionized energy below 55 eV, the dissociation of DMCPS is dominant. As the ionized energy is above 55 eV, the DMCPS dissociation achieves the maximum cross section, while the fragments from the DMCPS dissociation can further dissociate, which leads to a different ingredient of fragments. At the lower ionized energy of 25 eV, the main fragments are SiOC2H＋, SiCH＋, Si＋, O＋ and CH＋ ions, which shows an important effect on the SiCOH low-k film deposition.

Finite-field calculation of electric quadrupole moments of^2P3/2,^2D3/2,5/2,and^2F5/2,7/2 states for Yb^+ion

Electric quadrupole moments of low-lying excited states of Yb^+are calculated by relativistic coupled-cluster theory with perturbations from external fields.The field-dependent energy differentiation provides accurate values of the electric quadrupole moments of^2P3/2,^2D3/2,5/2,and^2F5/2,7/2 states which agree well with experimental values.The important role of the electronic correlation to the electric quadrupole moments is investigated.Our calculations indicate the early dispute of the electric quadrupole moment of the Yb^+(2F7/2)state for which the measured and theoretical values have a large discrepancy.These electric quadrupole moment values can help us to determine the electric quadrupole shifts in start-of-the-art experiments of the Yb+ion.

Chaos feature of test particle in the gravitational field with a quadrupole

In this paper we investigate the dynamics of a test particle in the gravitational field with a quadrupole. By constructing Poincare sections for different values of the parameters and initial conditions, we find a chaotic evolution.From these Poincare sections, we further confirm that the chaotic evolution of the test particle originates from the quadrupole.

Corrections to atomic ground state energy due to interaction between atomic electric quadrupole and optical field

We study the ground state energy of an atom interacting with an oscillating optical field with electric dipole and quadrupole coupling.Under the rotating wave approximation,we derive the effective atomic Hamiltonians of the dipole/quadrupole coupling term within the perturbation theory up to the second order.Based on the effective Hamiltonians,we analyze the atomic ground-state energy corrections of these two processes in detail.As an application,we find that for alkali-like atoms,the energy correction from the quadrupole coupling is negligible small in comparison with that from the dipole coupling,which justifies the so-called dipole approximation used in literatures.Some special cases where the quadrupole interaction may have considerable energy corrections are also discussed.Our results would be beneficial for the study of atom–light interaction beyond dipole approximation.

Theoretical study of the hyperfine interaction constants, Landé g-factors, and electric quadrupole moments for the low-lying states of the 61Niq+(q=11,12,14,and 15) ions

Highly charged nickel ions have been suggested as candidates for the ultra-precise optical clock, meanwhile the relevant experiment has been carried out. In the framework of the multiconfiguration Dirac–Hartree–Fock(MCDHF)method, we calculated the hyperfine interaction constants, the Landég-factors, and the electric quadrupole moments for the low-lying states in the 61Ni11+,61Ni12+,61Ni14+, and61Ni15+ ions. These states are clock states of the selected clock transitions in highly charged nickel ions(see Fig. 1). Based on discussing the effects of the electron correlations, the Breit interaction, and quantum electrodynamics(QED) effect on these physical quantities, reasonable uncertainties were obtained for our calculated results. In addition, the electric quadrupole frequency shifts and the Zeeman frequency shifts of the clock transitions concerned were analyzed.

Fabrication and cold test of prototype of spatially periodic radio frequency quadrupole focusing linac

A 325 MHz aluminum prototype of a spatially periodic RF quadrupole focusing linac was developed at the Institute of Modern Physics,Chinese Academy of Sciences,as a promising candidate for the front end of a high-current linac.It consists of an alternating series of crossbar H-type drift tubes and RF quadrupole sections.Owing to its special geometry,cavity fabrication is a major hurdle for its engineering development and application.In this paper,we report the detailed mechanical design of this structure and describe its fabrication process,including machining,assembly,and inspection.The field distribution was measured by the bead-pull technique.The results show that the field errors of both the accelerating and focusing fields are within an acceptable range.A tuning scheme for this new structure is proposed and verified.The cold test process and results are presented in detail.The development of this prototype provides valuable guidance for the application of the spatially periodic RF quadrupole structure.