Quadrupole Electric Field Research Articles

Self-consistent theory of spatial distribution of an assembly of charged drops in an electrodynamic balance

Levitation of several charged drops in the air by applying oscillating quadrupole electric fields in an electrodynamic (ED) balance offers opportunities for improving our understanding of the role played by inter-particle forces on pattern formation. In these systems, stable structures arise as a balance between the time-averaged quadrupole force, the drag force and the collective force of mutual repulsion acting on individual drops. In order to characterize these structures, we formulate a general theory for the spatial arrangement of the levitated charged drops via a many-body Mathieu-Poisson equation. Although this system is not amenable to an exact analytical treatment, we develop an approximate analytical theory by invoking a jellium picture to predict the charge density profiles of the 2D planar configurations attained by the droplets. This approach reduces the system of equations into a set of dual integral equations, which is solved self-consistently via Hankel transform techniques. The theory predicts functional forms for the droplet density profiles and the size of the planar cluster as a function of the number of charged drops and the system parameters. As a part of validating the theory, numerical integration of the exact equations of motion of the interacting many-drop system has been carried out. Additionally, experiments were also conducted by levitating a large number of drops in an ED balance previously developed in our laboratory. A comparison of the predictions of the theory with those of the numerical simulations shows excellent agreement between the two. The experimental data on the spatial density distribution also seems to be consistent with the predictions of the theory. The results are further discussed.

Radiation and generalized uncertainty principle

This paper tries to investigate the effect of Generalized Uncertainty Principle (GUP) on one of the physical concepts. In this study which is based on our previous work Moayedi et al. (2013) [25], the radiating systems in the framework of GUP is investigated. We obtain the modified electric dipole fields and the total power radiated in the presence of a minimal length scale. Also, the magnetic dipole and electric quadrupole fields in the framework of GUP is found. We show that in the limit ħ2β→0, all of the modified electric dipole fields and modified quadrupole fields become the usual forms of them. We also, estimate the upper bound on the deformation parameter β.

Two-frequency operation of a Paul trap to optimise confinement of two species of ions

We describe the operation of an electrodynamic ion trap in which the electric quadrupole field oscillates at two frequencies. This mode of operation allows simultaneous tight confinement of ions with extremely different charge-to-mass ratios, e.g., singly ionised atomic ions together with multiply charged nanoparticles. We derive the stability conditions for two-frequency operation from asymptotic properties of the solutions of the Mathieu equation and give a general treatment of the effect of damping on parametric resonances. Two-frequency operation is effective when the two species’ mass ratios and charge ratios are sufficiently large, and further when the frequencies required to optimally trap each species are widely separated. This system resembles two coincident Paul traps, each operating close to a frequency optimised for one of the species, such that both species are tightly confined. This method of operation provides an advantage over single-frequency Paul traps, in which the more weakly confined species forms a sheath around a central core of tightly confined ions. We verify these ideas using numerical simulations and by measuring the parametric heating induced in experiments by the additional driving frequency.

Corrections to atomic ground state energy due to interaction between atomic electric quadrupole and optical field**Project supported by the National Natural Science Foundation of China (Grant Nos. 21503138, 11247324, 61405003, 11604225, 11404225, and 11474205) and the Fund from Beijing Education Committees, China (Grant No. KM201710028004).

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.

Simulation of the simultaneous dual-frequency resonance excitation of ions in a linear ion trap.

The process of ion resonance dipolar excitation in a linear ion trap by 2 ejection waveforms with close frequencies is studied. The physical mechanism of increasing the resolving power using the ion excitation is a nonlinearity of the electric radio frequency fields caused by space charge. Using 2 resonance forces with 2 close frequencies leads to the completion of 2 excitation processes. In the case of the perfect quadrupole electric field, the ion motion equations are linear, and as a result, the respondent ion ensemble is also a linear and valid superposition principle. Nevertheless, the resolution increases (20%) in the case of lack of a space charge in an operating mode with a dual-frequency. The numerical simulations show that the mass shift is removed, and the mass resolution is increased via dual-frequency resonance excitation when the frequency difference (approximately 2.5kHz) is relatively small and the phase difference of 2 harmonic signals is 0-π3 even at a high linear ion density of up to 50000 ions per radius field r0 .

The Størmer problem for an aligned rotator

The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed of a dipole magnetic and quadrupole electric fields. The geometry of the trapping regions is studied as a function of the magnetic field magnitude and the rotation speed of the body. Examples of the potential energy topology for different values of these parameters are given. The main difference from the classical St{\o}rmer problem is that the single toroidal trapping region predicted by St{\o}rmer is divided into equatorial and off-equatorial trapping regions. Applicability of the idealized model of a rotating uniformly magnetized sphere with a vacuum magnetosphere to real celestial bodies is discussed.

A Linear Ion Trap with an Expanded Inscribed Diameter to Improve Optical Access for Fluorescence Spectroscopy.

We report a custom-geometry linear ion trap designed for fluorescence spectroscopy of gas-phase ions at ambient to cryogenic temperatures. Laser-induced fluorescence from trapped ions is collected from between the trapping rods, orthogonal to the excitation laser that runs along the axis of the linear ion trap. To increase optical access to the ion cloud, the diameter of the round trapping rods is 80% of the inscribed diameter, rather than the roughly 110% used to approximate purely quadrupolar electric fields. To encompass as much of the ion cloud as possible, the first collection optic has a 25.4 mm diameter and a numerical aperture of 0.6. The choice of geometry and collection optics yields 107 detected photons/s from trapped rhodamine 6G ions. The trap is coupled to a closed-cycle helium refrigerator, which in combination with two 50 Ohm heaters enables temperature control to below 25 K on the rod electrodes. The purpose of the instrument is to broaden the applicability of fluorescence spectroscopy of gas-phase ions to cases where photon emission is a minority relaxation pathway. Such studies are important to understand how the microenvironment of a chromophore influences excited state charge transfer processes. Graphical Abstract ᅟ.

Computation of stability regions for the cylindrical ion trap with no octupole electric field as compared to the corresponding results of the Paul trap.

The cylindrical ion trap is analyzed so that the octupole component of the electric field inside the trap is set to zero. As a consequence, the diameter to height ratio is computed to be 1.20 for which the quadrupole component of the cylindrical ion trap is dominant. Afterwards, it is concluded that the electric potential inside the trap as well as the corresponding stability regions are very similar to those obtained for an ideal Paul trap with pure quadrupole electric field. Furthermore, we drew a conclusion that the stability diagrams of the cylindrical ion trap without octupole term and the stability diagrams of the Paul trap have 5.6%, 3.7%, and 2.9% discrepancy for the first, second, and third stability diagrams, respectively. It should be noted that, expansion of the electric potential inside the cylindrical ion trap in terms of the multipole electric field components and making the advantages of the octupole term elimination has not been reported in the literature previously.

Single Strontium Rydberg Ion Confined in a Paul Trap

Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Technically, the ion trap will need to stay active while exciting the ions into the Rydberg state, else the strong Coulomb repulsion will quickly push the ions apart. Thus, a thorough understanding of the trap effects on Rydberg ions is essential for future applications. Here we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the quadrupolar electric trapping field. This effect leads to Floquet sidebands in the spectroscopy of Rydberg D-states whereas Rydberg S-states are unaffected due to their symmetry. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state which results from the strong polarizability of the Rydberg ion. We observe the resultant energy shifts as a line broadening which can be suppressed by cooling the ion to the motional ground state in the directions orthogonal to the excitation laser.

The effect of surface charge convection and shape deformation on the settling velocity of drops in nonuniform electric field

The electrohydrodynamic settling of a leaky dielectric drop suspended in another leaky dielectric medium of unbounded extent in the combined presence of gravity and a nonuniform (combination of uniform and quadrupole) electric field is investigated theoretically in the Stokes flow limit. The present study incorporates both the effects of surface charge convection and shape deformation on the drop settling speed. The drop settling speed in the presence of an electric field is governed by three dimensionless groups: (i) capillary number Ca (the ratio of viscous to capillary stresses), (ii) electric Reynolds number ReE (the ratio of charge relaxation to convection time scales), and (iii) Masson number M (the ratio of electric to viscous stresses). Depending on the material properties of the drop and suspending medium, the strength of the applied electric field, and the drop radius, the following two different kinds of physical systems are identified for which asymptotic solutions for the settling velocity is obtained: (i) weak charge convection and small shape deformation (i.e., ReE≪1, Ca≪1) but with appreciable electric field strength (M∼1) and (ii) weak electric field (i.e., M≪1) but with appreciable charge convection ReE∼1. For a perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium, the application of a uniform and/or quadrupole electric field always deforms the drop into a prolate shape which leads to an increase in drop settling speed. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the application of a quadrupole electric field can deform the drop into either a prolate or an oblate shape which leads to an increase or decrease in the drop speed depending on the drop to medium permittivity ratio. Combined presence of uniform and quadrupole fields induces a dielectrophoretic force on the drop which not only alters the drop speed but also can change the direction of drop motion depending on the values of physical parameters. The present study establishes that surface charge convection plays an important role in determining the drop settling speed for a leaky dielectric drop suspended in a leaky dielectric medium. It is shown that the charge-convection-induced correction in the drop settling speed is larger in magnitude in the presence of a quadrupole electric field as compared to a uniform electric field; this is due to a more intense circulation inside the drop in the presence of a quadrupole electric field.

Measuring the Second Chern Number from Nonadiabatic Effects.

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this Letter, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3/2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an overcomplete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally, I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.

Ion velocities of laser desorbed ions passing through quadrupole electric fields

This paper is a study of the effects of quadrupole electric fields on the velocities of ions generated by laser desorption ionization (LDI). We used a charge detector to measure ion flight time in the absence of electric and magnetic fields to obtain the initial velocity distribution of ions generated in the LDI process. It was found that the measured ion velocity of fullerene and matrix ions was proportional to the energy of the laser pulse. Then we measured velocity distributions of fullerene ions in rf-only quadrupoles. It was observed that the electric field in the fringing field region was proportional to pseudo-potential well depth (Dz) and that ions gained velocity in the fringing field region and speeded up as the Dz was increased due to transfer of rotational energy into translational energy in the high-order field region. Initial velocity of ions passing through different stages of quadruple was increased at every stage. In addition, the mass spectrometric analysis showed when the rf amplitude was low, the quadrupole field allowed stable motion of low mass ions; when the rf amplitude was increased, effective potential well depth was reduced. This is evident that the gradient of ion velocity drops as the difference in Dz increases for C60 and high mass Cn cluster ions.

Multimodal Nonlinear Optical Imaging of Live Cells Using Plasmon-Coupled DNA-Mediated Gold Nanoprism Assembly.

Multiphoton excitation microscopy techniques are the emerging nonlinear optical (NLO) imaging methods to watch the biological world due its ability to penetrate deep into living tissues. Driven by the need to develop multimodal NLO imaging probe, current article reports the design of DNA-mediated gold nanoprisms assembly based optical antennas to enhance multiphoton imaging capability in biological II window. Reported experimental data show a unique way to enhance second harmonic generation (SHG) and two-photon fluorescence (TPF) properties by several orders of magnitudes via plasmon coupled organization into gold nanoprism assembly structures. Experimental and theoretical modeling data using finite difference time domain (FDTD) simulations indicate that huge enhancement of SHG and TPF properties are mainly due to the electric quadrupole contribution and electric field enhancement. Using 1100 nm biological II window light, reported results demonstrated that antibody conjugated assembly structures are capable of exhibiting highly selective and very bright multimodal SHG and TPF imaging of human Hep G2 liver cancer cells.

Photoionization microscopy of hydrogen in magnetic and quadrupolar electric fields

The photoionization microscopy of hydrogen in magnetic and quadrupolar electric fields is studied on the basis of the semiclassical theory. Potential for the studied system possesses saddle points lying in the [Formula: see text]-direction, rather than the [Formula: see text]-direction in the common case, such as atom in the electric field. We find the electron current recorded by cylindrical surface detector shows symmetric interference patterns along [Formula: see text]-direction, and predict that the interference pattern presents the list structure, instead of the cyclic structure observed in the electric field. Besides, the interference structures are assigned to different types of trajectories. As the scaled energy increases, the structure of the interference pattern evolves smoothly and more types of trajectories emerge.

Dynamics of a charged drop in a quadrupole electric field

Quadrupole electric fields are commonly employed for confining charged conducting drops in Paul traps for studying Rayleigh instability characteristics. We investigate the effect of these fields on the deformation and stability characteristics of a charged liquid drop, using the axisymmetric boundary integral method (BIM). Different combinations of the amount of charge and strength of the electric field give rise to different equilibrium shapes. Interestingly, unlike in the case of uniform fields, stable oblate equilibrium drop shapes are sustained in quadrupole fields. In a positive endcap configuration of the quadrupole setup a drop carrying a small negative charge displays a transition from oblate to prolate as the field strength increases. On the other hand, for the case of a highly charged drop, a shift in the Rayleigh critical charge is observed in the presence of a weak quadrupole field. The Rayleigh instability displays imperfect transcritical bifurcation characteristics with respect to imposed prolate and oblate perturbations. Results are of significance in i) interpreting deformation and the Rayleigh stability effects using Paul traps with quadrupole fields, ii) designing more efficient quadrupole-field–based technologies for emulsification of water in oil.

Bound states of a charged particle in the field of an electric quadrupole in two dimensions

The Schrodinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy and find that the particle can be bound by a quadrupole of any magnitude. This result is remarkably different from the one for a charged particle in the field of a nonrelativistic electric dipole in three dimensions where a minimum value of the dipole strength is necessary for capture. Present results differ from those obtained earlier by other author.

Experimental investigation of preset electrostatic fields in a quasi-electrode system

We describe the results of implementation and breadboard investigations of the method for obtaining constant electric fields of a preset form in a quasi-electrode system. We have constructed a prototype (12 cm in diameter and 30 cm in length) with 36 filamentary electrodes fed with potentials from divider systems with azimuthal distribution laws corresponding to cosθ′, cos2θ′, and cos3θ′ laws with the maximal voltages up to ±2.4 kV. As a result, the electric dipole, quadrupole, and sextupole fields are formed. These fields are analyzed for a 2D cross section of the prototype by physical simulation on a specially developed device with conducting paper. The distributions of the families of equipotential curves measured using the bridge circuit are considered and the strengths of the three types of electric fields are calculated. The results indicate the attainment of all predicted fields with preset parameters and a working area of the aperture of ≥84%. Some other favorable features are also outlined and a number of technical recommendations for producing such fields are given.

Deformation and breakup of a leaky dielectric drop in a quadrupole electric field

AbstractThe deformation and breakup of a leaky dielectric drop suspended in a leaky dielectric medium subjected to a quadrupole electric field are studied. Analytical (linear and nonlinear asymptotic expansions in the electric capillary number, $C{a}_{Q} $, a ratio of electric to capillary stress) and numerical (boundary element) methods are used. A complete phase diagram for the drop deformation in the $R$–$Q$ plane is presented, where $R$ and $Q$ are the non-dimensional ratios of the resistivities and dielectric constants, respectively, of the drop and the medium phase. The prolate and oblate deformations are mapped in the phase diagram, and the flow contours are also shown. The large deformation and breakup of a drop at higher $C{a}_{Q} $ are analysed using the boundary element method. Several non-trivial shapes are observed at the onset of breakup of a drop. A prolate drop always breaks above a certain critical value of $C{a}_{Q} $. In the oblate deformation cases, breakup as well as steady shapes are observed at a higher value of $C{a}_{Q} $. A detailed study of prolate and oblate deformation tendencies due to the normal and tangential electric stresses and the countervailing role of viscous stresses is presented. The circulation inside a drop is found to be more intense for a quadrupole field as compared with a uniform electric field. More intense internal circulations can lead to enhanced mixing characteristics and will have implications in microfluidic devices.

33S NMR spectroscopy. 4. Substituent effects on the 33S nuclear quadrupole coupling constants and electric field gradient in 3- and 4-substituted benzenesulphonates studied by DFT calculations in vacuo and in aqueous solution

33S nuclear quadrupole coupling constants (χ) and the principal component of the electric field gradient (qzz) in 3- and 4-substituted benzenesulphonates are dependent on the electronic properties of substituents. Previously reported experimental results were interpreted with the support of theoretical calculations in vacuo and in aqueous solution. To obtain good reproducibility of the experimental data, the introduction of the solvent effect into the calculations was mandatory. The best results were obtained at the B3LYP/6-311++G(3d,p) level using the Integral Equation Formalism for the Polarisable Continuum Model (IEF-PCM) to reproduce the solvent effect. In vacuo, for neutral substituents, the substituent effect on sulphur qzz can be mainly ascribed to electronic interactions (i.e., inductive and mesomeric effects transmitted through the aromatic ring). For charged substituents (3-NH3+,4-NH3+,4-NH(CH3)2+,3-SO3-,4-SO3-,3-O-,4-O-) there is also a relevant contribution of coulomb origin, owed to the electric charge on the substituent itself, which polarises the S–O and C–S bonds. In aqueous solution, short-range solute–solvent interactions (i.e., hydrogen bonding) can be neglected, and the solvent effect can be adequately described considering the electrostatic interactions between the C–SO3- moiety and the electric charges on the surface of the cavity embedding the molecule within the solvent. These interactions amplify the electronic contribution transmitted through the aromatic ring and partially annihilate the coulomb contribution of the intrinsic charges of substituents. The results of the Natural Bond Orbital (NBO) analysis support these results and demonstrate that the polarisation of the S–O and S–C bonds and oxygen lone pairs due to solvent interactions produces only a redistribution of the electron density around the sulphur nucleus, thus inducing the variations of qzz.

Design of a unique open-geometry cylindrical Penning trap

The Texas A&M University Penning trap facility is an ion trap system currently under construction, and will be used for precision nuclear physics experiments with radioactive beams provided by the Cyclotron Institute. Its primary focus is to carry out experiments to search for possible scalar currents in T=2 superallowed β-delayed proton decays, which, if found, would be an indication of physics beyond the standard model. In addition, TAMUTRAP will provide a low-energy, spatially localized source of ions for various other applications. The experiment is centered around a unique, compensated cylindrical Penning trap that employs a specially optimized length/radius ratio in the electrode structure that is not used by any other facility. This allows the electrode structure to exhibit an unprecedented 90mm inner radius, which is larger than in any existing trap, while at the same time remaining a tractable overall length. The trap geometry was designed from first principles to be suitable for a wide range of nuclear physics experiments. In particular, the electrode structure allows for a near quadrupole electric field at the trap center, a feature necessary for performing precision mass measurements.