Multipole Electrodynamic Ion Trap Geometries for Microparticle Confinement under Standard Ambient Temperature and Pressure Conditions
Bogdan M. Mihalcea, Liviu C. Giurgiu, Cristina Stan, Gina T. Visan, Mihai Ganciu, Vladimir E. Filinov, Dmitry S. Lapitsky, Lidiya V. Deputatova, Roman A. Syrovatka
MMultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement
Multipole Electrodynamic Ion Trap Geometries for Microparticle Confinement underStandard Ambient Temperature and Pressure Conditions
Bogdan M. Mihalcea, a) Liviu C. Giurgiu, Cristina Stan, Gina T. Vi¸san, MihaiGanciu, Vladimir E. Filinov, Dmitry Lapitsky, b) Lidiya Deputatova, and RomanSyrovatka National Institute for Laser, Plasma and Radiation Physics (INFLPR),Atomi¸stilor Str. Nr. 409, 077125 M˘agurele, Ilfov, Romania University of Bucharest, Faculty of Physics, Atomistilor Str. Nr. 405,077125 M˘agurele, Romania Department of Physics,
Politehnica
University, 313 Splaiul Independent¸ei,RO-060042, Bucharest, Romania Joint Institute for High Temperatures, Russian Academy of Sciences,Izhorskaya Str. 13, Bd. 2, 125412 Moscow, Russia
Trapping of microparticles and aerosols is of great interest for physics and chemistry.We report microparticle trapping in case of multipole linear Paul trap geometries,operating under Standard Ambient Temperature and Pressure (SATP) conditions.An 8-electrode and a 12-electrode linear trap geometries have been designed andtested with an aim to achieve trapping for larger number of particles and to studymicroparticle dynamical stability in electrodynamic fields. We report emergence ofplanar and volume ordered structures of microparticles, depending on the a.c. trap-ping frequency and particle specific charge ratio. The electric potential within thetrap is mapped using the electrolytic tank method. Particle dynamics is simulatedusing a stochastic Langevin equation. We emphasize extended regions of stable trap-ping with respect to quadrupole traps, as well as good agreement between experimentand numerical simulations.PACS numbers: 37.10.Rs, 37.10.Ty, 52.25Kn, 52.27.Aj, 52.27.Jt, 92.60.Mt, 92.60.SzKeywords: microparticle electrodynamic ion trap; strongly coupled Coulomb sys-tems; complex plasmas; dynamical stability; stochastic Langevin equation a) Electronic mail: bogdan.mihalcea@inflpr.ro b) Electronic mail: [email protected] a r X i v : . [ phy s i c s . p l a s m - ph ] M a r ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement I. INTRODUCTION
Coulomb systems represent many-body systems made of identical particles, that interactby means of electrostatic forces. When the potential energy associated to the Coulombinteraction is larger than the kinetic energy of the thermal motion, the system is stronglycoupled as it presents a strong spatial correlation between the electrically charged particles,similar to liquid or crystalline structures. Strongly coupled Coulomb systems encompassvarious many-body systems and physical conditions, such as dusty (complex) plasmas ornon-neutral and ultracold plasmas . Complex plasmas represent a unique type of low-temperature plasmas, characterized by the presence of highly charged nano or microparticles,by chemical reactions, and by the interaction of plasmas with solid surfaces . They areencountered in astrophysics as interstellar dust clouds, in comet tails or as spokes in thering systems of giant gas planets . Complex plasmas are also present in the mesosphereand troposphere of the Earth, near artificial satellites and space stations, or in laboratoryexperiments . Dust particle interaction occurs via shielded Coulomb forces , the so-called Yukawa interaction . Yukawa balls were reported in case of harmonically confineddusty plasmas . The dynamical time scales associated with trapped microparticles liein the tens of milliseconds range, while microparticles can be individually observed usingoptical methods . As the background gas is dilute, particle dynamics exhibits strongcoupling regimes characterized by collective motion . Dust particles may give birth tolarger particles which might evolve into grain plasmas . The mechanism of electrostaticcoupling between the grains can vary widely from the weak coupling (gaseous) regime tothe pseudo-crystalline one . Complex plasmas can be described as non-Hamiltoniansystems of few or even many-body particles. They are investigated in connection with issuesregarding fundamental physics such as phase transitions, self-organization, study of classicaland quantum chaos, pattern formation and scaling.The paper investigates strongly coupled Coulomb systems of finite dimensions, such aselectrically charged microparticles confined in electrodynamic traps. Particular examplesof such systems would be electrons and excitons in quantum dots or laser cooled ionsconfined in Paul or Penning type traps . We can also mention ultracold fermionicor bosonic atoms confined in traps or in the periodic potential of an optical lattice . Ex-perimental investigations of charged particles in external potentials have gained from the2ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementinvention of ion traps , as they have greatly influenced the future of modern physics andstate of the art technology . Using a classical (hyperbolic) Paul trap geometry in vac-uum, ordered structures of iron and aluminium microparticles with micron range diameterhave been observed since the 1960s . The particles repeatedly crystallized into a regulararray and then melted owing to the dynamical equilibrium between the trapping potentialand inter-particle Coulomb repulsion. In 1991 an experiment demonstrated the storage ofmacroscopic dust particles (anthracene) in a Paul trap , as friction in air was proven to bean efficient mechanism to cool the microparticles. The mechanism is similar with coolingof ions in ultrahigh vacuum conditions owing to collisions with the buffer gas molecules .The dynamics of a charged microparticle in a Paul trap near Standard (Ambient) Tem-perature and Pressure conditions was studied by Izmailov , using a Mathieu differentialequation with damping term and stochastic source, under conditions of combined periodicparametric and random external excitation. Particle dynamics in nonlinear traps has alsobeen investigated. It was found that ion motion is well described by the Duffing oscillatormodel with an additional nonlinear damping term . Regions of stable (chaos) and un-stable dynamics were illustrated, as well as the occurrence of strange attractors and fractalproperties for the associated dynamics.The Paul trap proved to be a very powerful tool to look into the physics of few-bodyphase transition since its very beginning . High-precision spectroscopy and mass spec-trometry measurements with unprecedented accuracy , quantum physics tests ,precise control of quantum states , study of non-neutral plasmas , optical fre-quency standards , quantum metrology and quantum information processing (QIP)experiments and use of optical transitions in highly charged ions for detection ofvariations in the fine structure constant , became all possible by using laser cooledatomic and molecular ions confined in electrodynamic and Penning traps .The paper is organized as follows: Section I introduces Coulomb systems (especiallystrongly coupled examples of such systems), as they encompass various many-body systemsand physical conditions. Because microparticles can be found as atmospheric aerosols or as-trophysical dusty plasmas, investigation of such mesoscopic systems requires high precisionmass measurements for micro and nanoparticles. Section II reviews different investigationmethods for micro and nanoparticles, as their presence in the atmosphere determines thequality of life. Section III reviews the equations that govern aerosol (microparticle) dy-3ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementnamics and the forces implied. The equation describing trapped particle dynamics in air isintroduced, using dimensionless variables. The trap geometries under test are presented inSection IV, together with experimental parameters and the electronic setup. The transversalsection of the electric field is mapped for the 12-electrode trap. Section V illustrates theoccurrence of ordered and stable structures of microparticles within the trap. A physicalmodelling is performed using a stochastic Langevin equation to account for microparticledynamics in Section VI. The equation that characterizes the trap potential is inferred, forexperimental trap parameters of interest. Regions of stable trapping are illustrated and mi-croparticle trajectories for the two trap geometries are investigated, by means of numericalsimulations. Section VII emphasizes compatibility with previous experiments (results) aswell as the good agreement between numerical theory and experiment. II. MICROPARTICLES. INVESTIGATION METHODS
Microparticles can be found as atmospheric aerosols , astrophysical dusty plasmas or plasma membranes in case of biological cells and bacteria. Recent investigations havedemonstrated a strong correlation between the presence of aerosols in the atmosphere andtheir effect on climate parameters such as local temperature, air quality and rainfalls, thingsdirectly related to the phenomenon of global warming and the quality of life . Aerosolparticles with diameter less than 10 µ m enter the pulmonary bronchi, while those whosediameter is lower than 2.5 µ m reach the pulmonary alveoli, a region where gas exchangetakes place. The presence of certain aerosols (especially anthropogenic ones, such as smoke,ashes or dust) is associated with high levels of industrial pollution and it is responsiblefor respiratory and cardiovascular diseases, as well as for the ever increasing incidence ofhuman allergies in town areas. Investigation of atmospheric aerosols, viruses, bacteria,and chemical agents responsible for environment pollution, requires high precision massmeasurements for micro and nanoparticles (with dimensions ranging between 10 - 10,000nm), in order to characterize and explain the underlying chemistry and physics of suchcomplex systems . Moreover, study of such mesoscopic systems is of large interest,as mesoscopic physics is linked to the fields of nanofabrication and nanotechnology.Since its early days the Paul trap has proven to be a versatile device that uses pathstability as a means of separating ions according to their specific charge ratio . Ion4ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementdynamics in Paul traps is characterized by linear, uncoupled equations of motion (Mathieuequations), that can be solved analytically . The Quadrupole Ion Trap Mass Spectrom-etry (QIT-MS) is a promising technique to perform mass analysis of micron-sized particlessuch as biological cells, aerosols and synthetic polymers . The trap can be operated in themass-selective axial instability mode by scanning the frequency of the applied a.c. field .When using the QIT as a electrodynamic balance to perform microparticle diagnosis, thefrequency of the a.c. field applied to the trap electrodes is typically in the range of 1 kHzor less. Because of this low frequency, in order to achieve high mass measurement accuracy(better than 1 ppm) only one particle is analyzed at a time, over a time period ranging fromseconds up to minutes.Fluorophore labeled polystyrene microparticles (with dimensions ranging between 2 to7 microns) have been trapped in vacuum, by means of three dimensional electrodynamicquadrupolar fields and probed using laser fluorescence spectroscopy and QIT-MS. Inves-tigation of single particle emission spectra and of associated optical resonance signaturesby using the Mie theory, supplies information regarding the particle size, shape and itsrefractive index . The absolute mass and electric charge of single microspheres can bedetermined by measuring their secular oscillation frequencies. Moreover, a microsphere canact as a three-dimensional optical cavity able to support optical resonances, also known asmorphology-dependent resonances (MDR). Using individual micron-sized particles dopedwith fluorescence dyes and confined within a quadrupole trap, MDR emission has beenobserved by means of confocal and two-photon fluorescence microscopes . Optical MDRresonances induced in the fluorescence spectrum were investigated in order to study laser-induced coalescence of two conjoined, polystyrene spheres levitated in a QIT .Thus, QIT-MS is an excellent tool that can be used to identify organic molecules incomplex samples. A specific charge m/z can be isolated in the ion trap by ejecting allother m/z particles (ions) by applying various resonant frequencies . Moreover, an iontrap can be coupled to an Aerosol Mass Spectrometer to investigate atmospheric aerosol(nano)particles.To minimize both micromotion and second-order Doppler shift owing to space chargerepulsion of ions from the trap node line, multipole electrodynamic (Paul) ion traps havebeen investigated, where ions are weakly bound with confining fields that are effectively zerothrough the trap interior and grow rapidly near the trap electrode walls . Multipole5ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementtraps are used as tools in analytical chemistry . Octupole RF traps are used as bufferzones or guides in order to transport ions from one region to another in similar applica-tions. Because ions in a multipole Paul trap spend relatively little time in the region ofhigh RF electric fields, the RF heating phenomenon is greatly reduced and low-temperatureion-molecule collisions can be studied in a well-controllable environment . This immunityto changes in the ion number comes together with a reduced sensitivity to changes in theambient temperature. Space-charge effects are not negligible in this situation. It is sup-posed that optical frequency standards based on multipole traps should be able to achievesensibly higher accuracy, required by applications such as satellite-based navigation (GPS),quantum metrology or precision measurements on variations of the fundamental constantsin physics . III. MICROPARTICLE DYNAMICS. STRONGLY COUPLED COULOMBSYSTEMS
Dust particles experience a certain number of forces. The prevailing forces acting uponthe micrometer sized particles of interest are the a.c. electric trapping field (whose outcomeis the ponderomotive force caused by particle motion within a strongly nonlinear electricfield) and gravity. The gravitational force can be expressed as F g = m g = 43 πa ρ d g , (1)where g stands for the gravitational acceleration, m represents the dust mass, a is the dustparticle radius and ρ d corresponds to the dust particle density. The electric field yields aforce F el = − Q e = − Ze E , (2)where Q = Ze is the dust particle electric charge and e = 1 . · − C is the electron electriccharge. When a temperature gradient is created within the neutral gas background, a forcecalled thermophoretic drives the particles towards regions of lower gas temperature. Anotherforce acting upon the particle is the ion drag force, owing to a directed ion flow . Toresume, the forces that act on an aerosol particle include the radiation pressure force, thethermophoretic force, the photophoretic force, electric forces, and possibly magnetic forces,in addition to aerodynamic drag and the force of gravity .6ultipole Electrodynamic Ion Trap Geometries for Microparticle ConfinementA one-component plasma (OCP) consists of a single species of charge submerged inthe neutralizing background field . Single component non-neutral plasmas confined inPenning or Paul (RF) traps exhibit oscillations and instabilities owing to the occurrenceof collective effects . The dimensionless coupling parameter that describes the correlationbetween individual particles in such plasma can be expressed asΓ = 14 π(cid:15) q a W S k B T , (3)where (cid:15) is the electric permittivity of free space, q stands for the ion charge, a W S is theWigner-Seitz radius, k B denotes the Boltzmann constant and T is the particle temperature.The Wigner-Seitz radius results from the relation43 πa W S = 1 n , (4)where n is the ion (particle) density. Although the Wigner-Seitz radius measures the averagedistance between individual particles, it does not coincide with the average inter-particledistance. The Γ parameter represents the ratio between the potential energy of the nearestneighbour ions (particles) and the ion thermal energy. It describes the thermodynamicalstate of an OCP. Low density OCPs can only exist at low temperatures. Any plasmacharacterized by a coupling factor Γ > <
174 thesystem exhibits a liquid-like structure, while larger values might indicate a liquid-solid phasetransition into a pseudo-crystalline state (lattice) . OCPs are supposed to exist in denseastrophysical objects. An example of a high temperature system would be a quark-gluonplasma (QGP), used to characterize the early Universe and ultracompact matter found inneutron or quark stars .Colloidal suspensions of macroscopic particles and complex plasmas represent other ex-amples of strongly coupled Coulomb systems. Trapped micrometer sized particles interactstrongly over long distances, as they carry large electrical charges. Friction in air com-bined with large microparticle mass results in an efficient particle cooling , which leads tointeresting strong coupling features. The signature of such phenomenon lies in the appear-ance of ordered structures, liquid or solid like, as phase transitions occur in case of suchsystems . The presence of confining fields maintains the particles localized togetherin an OCP. Trapped and laser cooled ions offer a good, low temperature realization of astrongly coupled ultracold laboratory plasma.7ultipole Electrodynamic Ion Trap Geometries for Microparticle ConfinementThe equation of motion for a particle trapped in air, can be expressed in a convenientform by introducing dimensionless variables defined as Z = z/z and τ = Ω t/
2, where z represents the trap radial dimension (a geometrical constant) and Ω stands for the frequencyof the a.c. trapping voltage. The nondimensional equation of motion then becomes d Zdt + γ dZdt + 2 βZ cos(2 τ ) = σ , (5)where γ stands for the drag parameter, β is the a.c. field strength parameter and σ representsa d.c. offset parameter, defined as γ = 6 πµd p κm Ω , β = 4 g Ω (cid:18) V ac V dc (cid:19) , σ = − g Ω z (cid:18) V dc V ∗ dc (cid:19) , (6)where V ∗ dc satisfies F z − mg = qC V ∗ dc z . (7) C and C are two geometrical constants ( C <
1) and b = z C /C . For a negative chargedparticle, the right hand term of Eq. III is a positive quantity. When the d.c. potentialis adjusted to compensate the external vertical forces, V dc = V ∗ dc , σ = 0 and the particleexperiences stable confinement. Other relevant quantities are the gas viscosity coefficient µ ,the particle diameter d p , the particle mass m , while b represents the geometrical constant ofthe electrodynamic balance. IV. EXPERIMENTAL SETUPA. Microparticle physics using quadrupole and multipole traps
A linear Paul trap uses a combination of time varying and static electric potentials to cre-ate a trapping configuration that confines charged particles such as ions, electrons, positrons,micro or nanoparticles . A radiofrequency (RF) or a.c. voltage is used in order to generatean oscillating quadrupole potential in the y − z plane, which achieves radial confinement ofthe trapped particles. Axial confinement of positively charged ions (particles) is achievedby means of a static potential applied between two endcap electrodes situated at the trapends, along the trap axis ( x plane). The RF or a.c. field induces an effective potential whichharmonically confines ions in a region where the field exhibits a minimum, under conditionsof dynamic stability . As it is almost impossible to achieve quadratic a.c. and8ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementd.c. endcap potentials for the whole trap volume, it can be assumed that the potential in thevicinity of the trap axis region can be regarded as harmonic, which is a sufficiently accurateapproximation.Stable confinement of a single ion in the radio-frequency (RF) field of a Paul trap iswell known, as the Mathieu equations of motion can be analytically solved . Particledynamics in a multipole trap is quite complex, as it is described by non-linear, coupled, non-autonomous equations of motion. Solutions of such system can only be found by performingnumerical integration . The assumption of an effective trapping potential still holds,and ion dynamics can be separated into a slow drift (the secular motion ) and the rapidoscillating micromotion . The effective potential in case of an ideal cylindrical multipoletrap can be expressed as V ∗ ( r ) = 14 n ( qV ac ) m Ω r (cid:18) rr (cid:19) (2 n − , (8)where V ac is the amplitude of the radiofrequency field and n is the number of poles (forexample n = 2 for a quadrupole trap, n = 4 for an octupole trap and n = 6 for a 12-poletrap). The larger the value of n , the flatter the potential created within the trap centre andthe steeper the potential close to the trap electrodes.Further on we will review some of the most important milestones that describe exper-iments with microparticles in quadrupole traps and experiments with multipole traps, inan attempt to describe current status in the field. An electrodynamic trap, used for in-vestigating charging processes of a single grain under controlled laboratory conditions wasproposed in . A linear cylindrical quadrupole trap was used, where every electrode wassplit in half in order to achieve a harmonic trapping potential and thus perform precisemeasurements on the specific charge-to-mass ratio. The secular frequency of the grain wasmeasured in order to determine the charge to mass ratio, a method previously applied incase of microparticles . In the paper of Vasilyak and co-workers, mathematical simula-tions were used to investigate a dust particle’s behavior in a Microparticle ElectrodynamicIon Trap (MEIT) with quadrupole geometry. Regions of stable confinement of a singleparticle are reported, in dependence of frequency and charge-to-mass ratio. An increase ofthe medium’s dynamical viscosity results in extending the confinement region for chargedparticles. Ordered Coulomb structures of charged dust particles obtained in the quadrupoletrap operated in air, at atmospheric pressure, are also reported by the authors. Very recent9ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementpapers report on measuring the charge of a single dust particle , on the effective forcesthat act on a microparticle confined in a Paul trap , or trapping of microparticles in gasflow . Another paper reports micrometer sized particles dynamic confined in a linear elec-trodynamic trap, at normal temperature and pressure conditions, where time variations ofthe light intensity scattered by trapped microparticles were recorded and analyzed in thefrequency domain .A recent paper on electrodynamic traps and the physics associated to them studiesring electrode geometry and quadrupole linear trap geometry centimeter sized traps, astools for physics teaching labs and lecture demonstrations. The authors introduce a viscousdamping force to characterize the motion of particles confined in MEITs operating in air.For the microparticle species used, the authors show that Stokes damping describes wellthe mechanism of particle damping in air. The secular force in the one-dimensional caseis inferred. Nonlinear dynamics is also observed, as such mesoscopic systems are excellenttools to perform integrability studies and investigate quantum chaos.Investigations on higher pole traps intended to be used for frequency standards based ontrapped ions were first reported by Prestage and his group , that built a 12-pole trap andhave shuttled ions into it from a linear quadrupole trap. The outcome of the experiments wasa clear demonstration on trapping larger ion clouds with respect to a quadrupole trap. Thepaper also emphasizes on the issue of space charge interactions that are non-negligible in amulti-pole trap. The Boltzmann equation describing large ion clouds in the general multipoletrap of arbitrary order was solved. The authors state that fluctuations of the number oftrapped ions influence the clock frequency much less severely than in the quadrupole case,which motivates present and future quest towards developing and testing multipole traps forion trap based high-precision frequency standards . An interesting paper reports on theJPL multi-pole linear ion trap standard (LITS), which has demonstrated excellent frequencystability and improved immunity from two of its remaining systematic effects, the second-order Doppler shift and second-order Zeeman shift. The authors report developments thatreduce the residual systematic effects to less than 6 × − , and the highest ratio of atomictransition frequency to frequency width (atomic line Q ) ever demonstrated in a microwaveatomic standard operating at room temperature.An Electron Spectrometer MultiPole Trap (ES-MPT) setup was devised by Jusko andco-workers . A radio-frequency (RF) ion trap and an electron spectrometer were used in the10ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementexperiment, with an aim to estimate the energy distribution of electrons produced within thetrap. Results of simulations and first experimental tests with monoenergetic electrons fromlaser photodetachment of O − are presented. Other papers of the group from the CharlesUniv. of Prague approach the study of associative photodetachment of H − + H using a22-pole trap combined with an electron energy filter , study of capture and cooling of OH − ions in multipole traps or H − ions in rf octopole traps with superimposed magneticfield .Multipole ion traps designs based on a set of planar, annular, concentric electrodes arepresented in . Such mm scale traps are shown to exhibit trap depths as high as tens ofelectron volts. Several example traps were investigated, as well as scaling of the intrinsictrap characteristics with voltage, frequency, and trap scale. Stability and dynamics of ionrings in linear multipole traps as a function of the number of poles were investigated in .Multipole traps present a flatter potential in their centre and therefore a modified densitydistribution compared to quadrupole traps. Crystallization processes in multipole traps areinvestigated in , where the dynamics and thermodynamics of large ion clouds in traps ofdifferent geometry is studied. Applications of these traps span areas such as QIP, metrologyof frequencies and fundamental constants , production of cold molecules and the studyof chemical dynamics at ultralow temperatures (cold ion–atom collisions). B. Multipole trap geometries and electronic setup
We report two simple setups of Multipole Microparticle Electrodynamic Ion Traps(MMEITs). The first geometry consists of eight brass electrodes of 6 mm diameter, equidis-tantly spaced on a 20 mm radius, and two endcap electrodes located at the trap ends. Thetrap length is around 65 mm. The second trap geometry consists of twelve brass electrodes(a - a ) equidistantly spaced, and two endcap electrodes ( b and b ). The electrode diam-eter is 4 mm, the trap radius is 20 mm, while the length of the electrodes does not exceed85 mm. A sketch of the 8-electrode trap geometry we designed is shown in Fig. 1.The 12-electrode (pole) trap geometry is shown in Fig. 2. Both setups are intendedfor studying the appearance of stable and ordered patterns for different electrically chargedmicroparticle species. Alumina microparticles (with dimensions ranging from 60 microns upto 200 microns) were used in order to illustrate the trapping phenomenon, but other species11ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement FIG. 1. A sketch of the 8-electrode linear Paul trap geometry. a) cross-section;b) longitudinal section; c) electrode wiring can be considered. Specific charge measurements over the trapped microparticle speciesare expected to result, as the setup will be refined. The 12-electrode Paul trap which wedesigned is characterized by a variable geometry. The b endcap electrode is located on apiston which slides along the x axis of the trap. Hence, the trap length can vary between10 mm up to 75 mm.An electronic supply system was designed and realized. It supplies the a.c. voltage V ac ,with an amplitude of 0 − −
800 Hz range, requiredin order to achieve radial trapping of charged particles. A high voltage step-up transformer,driven by a low frequency oscillator (main oscillator) O , delivers the V ac voltage as shownin Fig. 3. An auxiliary oscillator O is used to modulate the amplitude of the V ac voltage.The modulation ratio can reach a peak value of 100%, while the modulation frequency liesin the 10 −
30 Hz range.Photos of both the 8-electrode and 12-electrode traps are presented in Fig. 4. The elec-tronic system also supplies a variable d.c voltage U z (also called diagnose voltage), appliedbetween the upper and lower multipole trap electrodes, used to compensate the gravita-tional field and shift the particle position along the z axis. Ions confined in such trapsunder ultrahigh vacuum conditions do arrange themselves along the longitudinal x axis andwithin a large region around it, where the trapping potential is very weak. The situation is12ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement FIG. 2. A sketch of the 12-electrode linear Paul trap geometry. a) cross-section;b) longitudinal section; c) electrode wiring sensibly different in case of electrically charged microparticles, which we explain in SectionVI. Another d.c. variable voltage U x is applied between the trap endcap electrodes, in orderto achieve axial confinement and prevent particle loss near the trap ends. The U z and U x voltages have values ranging between 50 −
700 V, while their polarity can be reversed.Both U z and U x voltages are obtained using a common d.c. double power supply, whichdelivers a voltage of ±
700 V at its output. Because the absorbed d.c. current is very low,the d.c. voltages are supplied to the electrodes by means of potentiometer voltage dividersas shown in Fig. 3.The supply system is a single unit which delivers all the necessary trapping voltages, asshown in Fig. 5. A microcontroller based measurement electronic circuit allows separatemonitoring and displaying of the supply voltage amplitudes and frequencies (for the a.c.voltage and modulation voltage). In order to visualize and diagnose the trapped particles,the experimental setups have been equipped with two different illumination systems. Thefirst system is based on a halogen lamp whose beam is directed normal to the trap axis. The13ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement
FIG. 3. Block scheme of the electronic supply unit second system consists of a laser diode whose beam is directed parallel to the trap axis, asone of the endcap electrodes is pierced.
FIG. 4. Photos of the 8-electrode and 12-electrode linear Paul trap geometries
If the a.c. potential is not too high (usually less than 3 kV), stable oscillation will occuruntil the d.c. potential is adjusted to balance vertical forces such as gravity. When suchcondition is achieved, the oscillation amplitude becomes vanishingly small and the particleexperiences stable trapping . The traps under test are fitted to study complex Coulombsystems (microplasmas) confined in multipole dynamic traps operating in air, at SATPconditions. The paper brings new evidence on microparticle trapping, while it demonstrates14ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement FIG. 5. Electronic supply unit used for the 8-pole and 12-pole traps that the stability region for multipole traps is larger with respect to a quadrupole trap(electrodynamic balance configuration) .We have used the electrolytic tank method to map the radiofrequency field potentialwithin the 12-electrode trap volume. We have designed and realized a precision mechanicalsetup that has enabled us to chart the field within the trap. The electrolyte solution usedwas distilled (dedurized) water. Two a.c. supply voltage values were used: 1 V and 1.5 V,respectively. We emphasize that these represent the amplitude values measured. Measure-ments were performed for an a.c. frequency value of Ω = 2 π ×
10 Hz. Figures 6 and 7 showthe contour and 3 D maps of the trap potential (rms values) that we have obtained.
V. RESULTS
We have investigated different linear multipole electrodynamic trap geometries operatingin air, under SATP conditions. We have focused on an 8-electrode and a 12-electrode trapgeometry respectively, intended for charged microparticle confinement and for illustrating15ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement
FIG. 6. Contour and 3D plots for the 12-electrode Paul trap potential when V ac = 1 V the appearance of planar and volume structures for these microplasmas. Microparticles areradially confined due to the a.c. trapping voltage V ac , which we set at a value of 2.5 kV.The microplasmas can be shifted both axially and vertically, using two d.c. voltages: U x and U z . The geometry of the 8-electrode trap has proven to be very critical, different radiihave been tested and the trap has gone through intensive tests with an aim to optimize it.It presents a sensibly higher degree of instability compared to the 12-electrode geometry.The 12-electrode (pole) trap has been studied more intensively as particle dynamics ismore stable for such geometry. We have loaded the traps with microparticles by means ofa miniature screwdriver. The peak of the screwdriver is inserted into the alumina powder.When touching the screwdriver to one of the trap electrodes, the particles are instantlycharged and a small part of them are confined, depending on their energy and phase of thea.c. trapping field. Thus a trapped particle microplasma results (very similar to a dusty16ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement FIG. 7. Contour and 3D plots for the 12-electrode Paul trap potential when V ac = 1 . V plasma, which is of great interest for astrophysics), consisting of tens up to hundreds ofparticles. Such a setup would be suited in order to study and illustrate particle dynam-ics in electromagnetic fields, as well as the appearance of ordered structures, crystal likeformations.Practically, stable confinement has been achieved especially in the 12-electrode (pole)trap, as we have observed thread-like formations (strings) and especially 2D (some of themzig-zag) and 3D structures of microplasmas. The stable structures observed have the ten-dency of aligning with respect to the z component of the radial field. The ordered formationswere not located along the trap axis, but rather in the vicinity of the electrodes. The laserdiode has been shifted away from the initial position (along the trap axis), towards outerregions of the trap. We report stable confinement for hours and even days. Laminary airflows within the trap volume break an equilibrium which might be described as somehow17ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementfragile and some of the particles can get lost at the electrodes. Nevertheless, we have alsotested the trap under conditions of intense air flows and we have observed that most of theparticles remain trapped, even if they rearrange themselves after being subject to intenseand repeated perturbations. When a transparent plastic box was used in order to shield thetrap, a sensible increase in the dynamical stability of the particle motion has been achieved.In Fig. 8 we present a few pictures which illustrate the stable structures we have been ableto observe and photograph. All photos were taken with a high sensitivity digital camera,using the halogen lamp in order to illuminate the trap. Pictures taken using the laserdiode were less clear due to reflection of light on the trap electrodes and this is the reasonwhy they are not included. We report filiform structures consisting of large number ofmicroparticles far from the trap center, where the trapping potential is extremely weak.This leads to the conclusion that microparticle weight is not balanced by the trapping fieldin the region located near the trap center. Moreover, most of the ordered structures observedwere generally located very close to the trap electrodes, at distances about 2-10 mm apartfrom them. The a.c. frequency range was swept between Ω = 2 π ×
50 Hz up to Ω = 2 π × frozen , which meansthey can be considered motionless due to the very low amplitude of their oscillation. Theoscillation amplitude increases as one moves away from the trap center. We also reportregions of dynamical stability for trapped charged microparticles located far away from the18ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement FIG. 8. Photos of the ordered structures observed in the 12-electrode Paul trap . × − C/kg to 0 . × − C/kg . The measuredmicroparticle density is around 3700 kg/m .The experimental results we report deal with trapping of microparticles in multipolelinear ion (Paul) traps (LIT) operating in air, under Standard Ambient Temperature andPressure (SATP) conditions. We suggest such traps can be used to levitate and studydifferent microscopic particles, aerosols and other constituents or polluting agents whichmight exist in the atmosphere. The research performed is based on previous results andexperience . Moreover, the paper brings new evidence with respect to recent workof the authors . Numerical simulations were run in order to characterize microparticledynamics. VI. PHYSICAL MODELLING AND COMPUTER SIMULATION
In addition to experimental work, numerical simulation of charged particle dynamics wascarried out, under conditions close to the experiment. Brownian dynamics has been usedin order to study charged microparticle motion and thus identify regions of stable trapping.Numerical simulations take into account stochastic forces of random collisions with neutralparticles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltageand the gravitational force. Thus, microparticle dynamics is characterized by a stochasticLangevin differential equation : m p d rdt = F t ( r ) − πηr p drdt + F b + F g (9)where m and r p represent the microparticle mass and radius vector, η is the dynamic viscosityof the gas medium with η = 18 . µ Pa · s, and F t ( r ) is the ponderomotive force. The F b termstands for the stochastic delta-correlated forces accounting for stochastic collisions withneutral particles, while F g is the gravitational force. We have considered a microparticlemass density value ρ p = 3700 kg/cm . In order to solve the stochastic differentialequation (9), the numerical method developed in was used.The average Coulomb force acting on a microparticle owing to the contribution of eachtrap electrode can be expressed as the vector sum of forces of point-like charges uniformlydistributed along the electrodes, as demonstrated :20ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement | F t ( r ) | = (cid:88) s LU q N ln (cid:16) R R (cid:17) ( r s − r ) , (10)where L is the length of the trap electrodes, U is the trapping voltage: V ac sin(Ω t ) or V ac sin(Ω t + π ), q is the microparticle charge, N is the number of point-like charges for eachtrap electrode, R and R represent the radii of the grounded cylindrical shell surroundingthe trap and trap electrode respectively, while r and r s denote the vectors for microparticleand point-like charge positions respectively. Numerical simulations were run considering thefollowing trap parameters: length of electrodes L = 6 . V ac = 2 kV, R = 25 cm, R = 3mm, and a trap radius value r t = 2 cm. For such model the results of the computationsdepend on Φ p , defined as Φ p = V ac q (cid:0) R R (cid:1) . The cross sections of the equipotential surfaces for the 8-electrode and 12-electrode lineartrap are shown in Fig. 9. The equation which characterizes the trap potential can beexpressed as: U ( x, y ) == N el (cid:88) j =1 (cid:88) s ( − j LU/N ln (cid:16) R R (cid:17) (cid:114)(cid:16) x − r t cos (cid:16) πjN el (cid:17)(cid:17) + (cid:16) y − r t sin (cid:16) πjN el (cid:17)(cid:17) + z s . (11)We found that regions of stable microparticle confinement depend on the a.c. voltage, trapvolume, number of trapped microparticles, average interparticle distance and consequently,on the repulsive forces produced by interparticle interactions defined by the particle charge q . To further minimize the influence of these physical factors, we used a higher value of thea.c. trapping voltage electrode V ac = 2 kV. In such case, the electric charge of the capturedparticles will be lower and results of the simulations will be more or less universal.In Fig. 9 hills correspond to potential barriers and pits correspond to potential wellsthat attract microparticles. White holes inside the hills correspond to the cross section ofthe trap electrodes. Every half cycle of the a.c. voltage barriers and wells swap positionsand each charged particle oscillates between them. Such a physical mechanism of particleoscillation results in dynamic, stable confinement .Figure 10 illustrates the trapping regions for a charged microparticle in an 8-electrodeand 12-electrode trap, respectively. The confinement regions are located between correlated21ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement a) b)FIG. 9. 3D plots for the 8-electrode (a) and 12-electrode (b) traps. lines: for an 8-electrode trap between gray lines and for 12-electrode trap between blackdash lines. Outside these regions traps cannot confine particles. For small values of theparticle charge, the trap a.c. field cannot compensate the gravity force and particles flowthrough the trap. When the particle electric charge is large enough, the trap field is strongenough to push the microparticles out of the trap. FIG. 10. The regions for single particle confinement in air, depending on the frequency f ofthe a.c. voltage and electric charge q . Numerical simulations used the following characteristics:microparticle radius r p = 5 µ m and electrical charge ranging between q = 3 · e to 5 · e .Vertical lines 1 – 4 correspond to electric charge values q = 6 , , , · e we have considered inorder to estimate oscillation amplitudes within the trap. To study the influence of the number of trap electrodes on the stability of alumina (dust)particles, we have investigated the average amplitude of particle oscillations. We considered22ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementthe dynamics of a number of 20 microparticles confined within the trap while averagingthe amplitudes of particle oscillations. To achieve that, we have chosen a period of timelarge enough (around ten periods of the a.c. trapping voltage) as to obtain stable particleoscillations. In order to evaluate the average oscillation amplitude, the amplitudes of all20 particles were averaged. Trajectories for 20 particles confined in 8- and respectively 12-electrode traps, are shown in Fig. 11. Particle trajectories are shifted downwards in the12-electrode trap with respect to an 8-electrode trap, owing to a smaller gradient of the a.c.electric field. a) b)FIG. 11. End views of the microparticle tracks in 8-electrode (a) and 12-electrode (b) traps at f = 60 Hz. Big black dots correspond to trap electrodes (not in scale). The microparticle electriccharge value was chosen q = 8 · e . The d.c. voltage was not considered in the simulations. The dependence between particle oscillation amplitude and the number of trap electrodesis shown in Fig. 12. Such dependence is complex as it also depends on the particle charge.The physical reason explaining non-monotonic decay of some dependences on frequencyand break in Fig. 12 a) for an 8-electrode trap, might be associated with the occurrence ofresonance effects. For example, in an 8-electrode trap a resonance effect is found at ∼ ÷ q = 8 · e . In such case the particlesare pushed out of the trap, despite of the fact that all parameters are characteristic to theconfinement region (Fig. 10). As it follows from Fig. 10 for fixed particle charge values, thedependence of the averaged oscillation amplitude on the frequency in Fig. 12 a) is beyondthe confinement region when the frequency reaches a value of 120 Hz. Other pictures inFig. 12 b) - d) describe confinement regions with frequency values ranging from 40 up to23ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement200 Hz. a) b)c) d)FIG. 12. Dependency of average oscillation amplitude on the number of trap electrodes andparticle charge q . Numerical simulations were performed for electric charge values ranging between q = 6 · e to 1 . · e . VII. CONCLUSIONS
The paper suggests use of Multipole Microparticle Electrodynamic Ion Traps (MMEITs)for trapping aerosols and microparticles, while bringing new experimental evidence on theadvantages associated to such geometries. The mathematical model we propose and thenumerical simulations performed simply create a clear and thorough picture of the phenom-ena we investigate. The pictures in are similar to those we have obtained, apart from thefact that we have achieved such phenomena in multipole traps, under better stability andless sensibility to environment fluctuations (flows of air). The 12 electrode trap exhibits a24ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementvariable geometry, which is one of the unique features that characterize the linear Paul trapswe have tested since 1996. We emphasize on the fact that the stability region for multipolePaul traps is larger with respect to a quadrupole trap (electrodynamic balance configura-tion), a feature which we demonstrate by charting the electric field map within the trapusing the electrolytic tank method, validated by experimental observations and numericalsimulations.The trap geometries investigated are characterized by more regions of stable trapping,some of them located close to the trap electrodes. Photos taken illustrate such phenomenon.By comparing the experimental data recorded, we can ascertain that stronger confinement,increased stability and larger microparticle numbers are achieved under conditions of dy-namical stability in case of a 12-electrode trap. We also probe that the trap geometriesinvestigated and especially the linear 12-electrode Paul trap, exhibit an extended regionwhere the trapping field almost vanishes. The amplitude of the field rises abruptly in thevicinity of the trap electrodes, which leads to stable trapping and the appearance of planarand volume structures in a layer of about a few millimeters thick. Particle oscillations aroundequilibrium positions occur, where gravity is balanced by the trapping potential. Close tothe trap center particles are almost frozen , which means that they can be considered asmotionless due to the very low amplitude of their oscillation. The oscillation amplitudeincreases as one moves away from the trap center. Regions of dynamical stability are alsoobserved for trapped charged microparticles located far away with respect to the trap center.Experimental data recorded are backed up by numerical simulations results, which allowsus to ascertain that a multipole trap exhibits a very extended region where the a.c. fieldintensity is weak, compared to a quadrupole trap. Due to the fact that the specific charge ofthe microparticles is very different compared to the specific charge of an ion, we suggest thatminiaturized multipole trap geometries might be suited for ions trapped in ultrahigh vacuumconditions. Microparticles are thermalized by air friction or air drag, an effect similar withcooling of ions by collisions with neutral background molecules or sympathetic cooling. Inspite of that, microparticle energy is still high and a lot of them are lost when loading thetrap. For ions confined in multipole traps under ultrahigh vacuum conditions, there exists alarge region where the trapping field is effectively zero. This drastically minimizes perturbingeffects among which the foremost is the second-order Doppler shift, making these traps verysuitable for high-resolution spectroscopy, quantum optics, quantum metrology and quantum25ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinementinformation processing (QIP) experiments .Brownian dynamics has been used in order to study charged microparticle motion andthus identify regions of stable trapping. A novel model is suggested for multipole Paul traps,as there were no other previous models to characterize such traps up to date. We have in-vestigated microparticle dynamics in multipole traps by considering a Langevin differentialequation, which takes into account stochastic forces of random collisions with neutral parti-cles, viscosity of the gas medium, regular forces produced by the a.c. trapping voltage andthe gravitational force. Regions of stable particle trapping have been identified by experi-mental observations, in good agreement with the numerical simulations results. To studythe influence of the number of trap electrodes on the dynamics and stability of alumina(dust) particles we have confined, the average amplitude of particle oscillations in the trapwas investigated. Numerical simulations clearly emphasize the influence of resonance effectson the confinement region.MMEITs represent versatile tools that enable study complex Coulomb systems (mi-croplasmas). The traps under test operate in air, at Standard Ambient Temperature andPressure (SATP) conditions. The microplasmas we have studied provide a basis for the studyof microparticle dynamics and phenomena associated to such kind of experiments, as well asthe appearance of ordered structures, crystal like formations, corresponding to phase tran-sitions. Such traps can be adapted to work in ultrahigh vacuum conditions. Moreover, anion trap can be coupled to an Aerosol Mass Spectrometer to investigate atmospheric aerosol(nano)particles, which makes them very well suited for environment monitoring studies,coupled with other techniques such as LIDAR.The most prominant advantage of multipole traps lies in the fact that the spatial extentof the region of confinement expands with the number of electrodes, and our results stronglysupport this hypothesis. And it is an aspect of utmost importance, as recent highly accurateabsolute frequency measurements of several microwave and optical frequency standards haveyielded sensitive probes of possible temporal and spatial changes of some of the fundamentalconstants. In these and other experiments, greater sensitivity would be possible using atomicfrequency standards with inaccuracy below 1 part in 10 typical of the best, present-dayatomic standards. This motivates the quest for new ion trap geometries, with an increasedsignal-to-noise ratio (SNR). 26ultipole Electrodynamic Ion Trap Geometries for Microparticle Confinement VIII. ACKNOWLEDGEMENTS
The authors would like to acknowledge support provided by the Ministery of Education,Research and Inovation from Romania (ANCS-National Agency for Scientific Research),contracts PN09.39.03.01, UEFISCDI Contract No. 90/06.10.2011, and ROSA Contract No.53/19. 11. 2013.Mathematical model and Brownian dynamics simulations have been carried out in theJoint Institute for High Temperatures, Moscow, Russian Academy of Sciences (RAS), underfinancial support by the Russian Foundation for Basic Research (grant No. 15-08-02835).
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