Trapped Ion Cloud Research Articles

Ion energy distribution in an electron beam ion trap inferred from simulations of the trapped ion cloud.

We have inferred the energy distribution of trapped ions in an electron beam ion trap (EBIT) from simulations of the spatial distribution of Fe^{13+} ions and a comparison with measured visible light images of the ion cloud. We simulated the cloud of Fe^{13+} ions by computing ion trajectories in the EBIT for different ion energy distributions used to initialize the trajectories. We then performed a least-squares fit to infer the ion energy distribution that best reproduced the measured ion cloud. These best-fit distributions were typically non-Maxwellian. For electron beam energies of 395-475eV and electron beam currents of 1-9 mA, we find that the average ion energy is in the range of 10-300eV. We also find that the average ion energy increases with increasing beam current approximately as 〈E〉≈25I_{e}eV, where I_{e} is the electron beam current in mA. We have also compared our results to Maxwell-Boltzmann-distribution ion clouds. We find that our best-fit non-thermal distributions have an 〈E〉 that is less than half that of the T from the best-fit Maxwell-Boltzmann distributions (〈E〉/q)/T=0.41±0.05.

Possible Mechanisms of String Formation in Complex Plasmas at Elevated Pressures.

Possible mechanisms of particle attraction providing formation of the field aligned microparticle strings in complex plasmas at elevated gas pressures are theoretically investigated in the light of the Plasmakristall-4 (PK-4) experiment on board the International Space Station. The particle interaction energy is addressed by two different approaches: (i) using the dynamically screened wake potential for small Mach numbers derived by Kompaneets et al., in 2016, and (ii) introducing effect of polarization of the trapped ion cloud by discharge electric fields. Is is found that both approaches yield the particle interaction energy which is independent of the operational discharge mode. In the parameter space of the performed experiments, the first approach can provide onset of the particle attraction and string formation only at gas pressures higher than 40–45 Pa, whilst the mechanism based on the trapped ion effect yields attraction in the experimentally important pressure range 20–40 Pa and may reconcile theory and observations.

Effects of emitting surfaces and trapped ions on the sheath physics and current flow in multidimensional plasma systems

Recent one-dimensional simulations of planar sheaths with strong electron emission have shown that trapping of charge-exchange ions causes transitions from space-charge limited (SCL) to inverse sheaths. However, multidimensional emitting sheath phenomena with collisions remained unexplored, due in part to high computational cost. We developed a novel continuum kinetic code to study the sheath physics, current flow and potential distributions in two-dimensional unmagnetized configurations with emitting surfaces. For small negatively biased thermionic cathodes in a plasma, the cathode sheath can exist in an equilibrium SCL state. The SCL sheath carries an immense density of trapped ions, neutralized by thermoelectrons, within the potential well of the virtual cathode. For further increases of emitted flux, the trapped ion cloud expands in space. The trapped ion space charge causes an increase of thermionic current far beyond the saturation limit predicted by conventional collisionless SCL sheath models without ion trapping. For sufficiently strong emission, the trapped ion cloud consumes the entire 2D plasma domain, forming a mode with globally confined ions and an inverse sheath at the cathode. In situations where the emitted flux is fixed and the bias is swept (e.g. emissive probe), the trapped ions cause a large thermionic current to escape for all biases below the plasma potential. Strong suppression of the thermionic emission, required for the probe to float, only occurs when the probe is above the plasma potential.

β -delayed neutron emission studies of I137,138 and Cs144,145 performed with trapped ions

A detailed study of the $\ensuremath{\beta}$-delayed neutron emission properties of $^{137,138}\mathrm{I}$ and $^{144,145}\mathrm{Cs}$ has been performed by confining ions in the Beta-decay Paul Trap. The daughter ions following $\ensuremath{\beta}$ decay emerge from the trapped-ion cloud with negligible scattering allowing reconstruction of the recoil-ion energy from the time of flight. From this information, the neutron-emission branching ratios and neutron-energy spectra were deduced. The results for the $^{137}\mathrm{I}$ and $^{144,145}\mathrm{Cs}$ decays are in agreement with previous results performed using direct neutron-detection techniques. In the case of $^{138}\mathrm{I}$, a branching ratio of 6.18(50)% is obtained, yielding a value consistent with the more recent results, which are a factor of two larger than measurements made prior to 1978.

β-delayed-neutron studies ofSb135,136andI140performed with trapped ions

Beta-delayed-neutron ($\beta$n) spectroscopy was performed using the Beta-decay Paul Trap and an array of radiation detectors. The $\beta$n branching ratios and energy spectra for $^{135,136}$Sb and $^{140}$I were obtained by measuring the time of flight of recoil ions emerging from the trapped ion cloud. These nuclei are located at the edge of an isotopic region identified as having $\beta$n branching ratios that impact the r-process abundance pattern around the A~130 peak. For $^{135,136}$Sb and $^{140}$I, $\beta$n branching ratios of 14.6(11)%, 17.6(28)%, and 7.6(28)% were determined, respectively. The $\beta$n energy spectra obtained for $^{135}$Sb and $^{140}$I are compared with results from direct neutron measurements, and the $\beta$n energy spectrum for $^{136}$Sb has been measured for the first time.

Attraction between trapped ions and beams of electrons

The attraction between 100 and 160 eV electron beams and a cloud of trapped calcium ions was observed experimentally. To explain the effect, analytical and numerical models were proposed. They are based on the well-known, classical, Rutherford scattering model. The experimental results and theoretical predictions are in very good agreement. The observed effect is important for studying propagation of electrons through plasmas.

A quartz amplifier for high-sensitivity Fourier-transform ion-cyclotron-resonance measurements with trapped ions.

Single-ion sensitivity is obtained in precision Penning-trap experiments devoted to light (anti)particles or ions with low mass-to-charge ratios, by adding an inductance coil to an amplifier connected to the trap, both operated at 4 K. However, single-ion sensitivity has not been reached on heavy singly or doubly charged ions. In this publication, we present a new system to reach this point, based on the use of a quartz crystal as an inductance, together with a newly developed broad-band (BB) amplifier. We detect the reduced-cyclotron frequency of 40Ca+ ions stored in a 7-tesla open-ring Penning trap. By comparing the detected electric signal obtained with the BB amplifier and the fluorescence signal obtained by collecting the photons emitted by a trapped ion cloud, we show a detection limit below 110 ions. Adding the crystal, the electrical signal increases by a factor of about 30 at room temperature, which combined with the measured equivalent resistance and voltage noise, proves the feasibility of the system to reach single-ion sensitivity at 4 K.

Analytical model of an ion cloud cooled by collisions in a Paul trap

A simple model of a trapped ion cloud cooled by collisions in a buffer gas in a Paul trap is presented. It is based on the customary decomposition of the ion motion in micro- and macro- (or secular) motions and a statistical treatment of hard-sphere collisions and ion trajectories. The model also relies on the evidence that the effective trapping area in real Paul traps is limited to a certain radius, where the harmonics of the potential of order >2 become non negligible. The model yields analytical formulae for the properties of the ion cloud and equilibration times, which are in good agreement for a wide range of parameters with the results of a numerical simulation, whose reliability has been verified with experimental observations. When the confining potential is efficient enough to suppress evaporation from the trap, the model yields an effective temperature for the ions T$_{eff}$=2T/(1-m$_{g}$/m), where T is the temperature of the buffer gas, m and m$_{g}$ are the masses of the ions and gas molecules respectively. The so-called rf heating effect, responsible for T$_{eff}$>T, is interpreted in light of the model as the result of an incomplete cooling of the ion motion, limited to the macromotion, while the net effect of the micromotion is to double the average ion kinetic energy for m/m$_{g}$ >>1. For m/m$_{g}$ <=1, the incomplete cooling is not sufficient to overcome the thermal agitation of the cloud to which the micromotion participates; the ions are therefore led out of the trap.

A numerical study on charging of an absorbing sphere in plasmas with different ion compositions

Results of a direct observation of the charging of spherical bodies in plasmas by means of a numerical experiment are presented. The prime objective of the simulation is to compare quantitative data obtained at different mass ratios of electrons and ions. It is established that the sphere acquires a greater charge at lesser values of the ratio, other things being equal. At high values of the sphere charge, contribution of trapped ions moving in finite orbits near the negatively charged sphere to its shielding by the plasma becomes quite significant. The net charge of the trapped-ion cloud also grows with decrease in the mass ratio as a parameter of the problem in the range of studied plasma parameters.

Energy transfer in elastic collisions between electrons and trapped ions

Heating of trapped ion clouds by interactions with free electrons crossing the trapping potential was observed. A model describing such a process was proposed and discussed. The presented approach predicts two effects: pushing and heating of the ions' ensemble by electrons. The former was found to be too weak for observation; however, the latter was investigated experimentally. For comparison between experimental results and theoretical predictions, molecular dynamics simulations for various ion ensembles in various temperatures were performed to determine the dependence between ion cloud geometry and its temperature. A heating rate coefficient was defined and determined together with temperatures of ion clouds bombarded with electrons. Good correlation between the two quantities was found, which agrees with the proposed model.

Modified Quadrupole Ion Trap Mass Spectrometer for Infrared Ion Spectroscopy: Application to Protonated Thiated Uridines.

Modifications to a Paul-type quadrupole ion trap mass spectrometer providing optical access to the trapped ion cloud as well as hardware and software for coupling to a table-top IR optical parametric oscillator laser (OPO) are detailed. Critical experimental parameters for infrared multiple photon dissociation (IRMPD) on this instrument are characterized. IRMPD action spectra, collected in the hydrogen-stretching region with this instrument, complemented by spectra in the IR fingerprint region acquired at the FELIX facility, are employed to characterize the structures of the protonated forms of 2-thiouridine, [s2Urd+H]+, and 4-thiouridine, [s4Urd+H]+. The measured spectra are compared with predicted linear IR spectra calculated at the B3LYP/6-311+G(d,p) level of theory to determine the conformers populated in the experiments. This comparison indicates that thiation at the 2- or 4-positions shifts the protonation preference between the 2,4-H tautomer and 4-protonation in opposite directions versus canonical uridine, which displays a roughly equal preference for the 2,4-H tautomer and O4 protonation. As found for canonical uridine, protonation leads to a mixture of conformers exhibiting C2'-endo and C3'-endo sugar puckering with an anti nucleobase orientation being populated for both 2- and 4-thiated uridine. Graphical Abstract ᅟ.

Numerical experiments on charging of a spherical body in a plasma with Maxwellian distributions of charged particles

New results of numerical simulation of collisionless plasma perturbation caused by a sphere absorbing electrons and ions are presented. Consideration is given to nonstationary phenomena accompanying the process of charging as well as to plasma steady state reached at long times. Corresponding asymptotic values of charges of the sphere and trapped-ion cloud around it have been found along with self-consistent electric field pattern depending on parameters of the unperturbed plasma. It is established that contribution of the trapped ions to screening of the charged sphere can be quite significant, so that the screening becomes essentially nonlinear in nature. A simple interconnection between the sphere radius, electron and ion Debye lengths has been revealed as the condition for maximum trapped-ion effect. Kinetic structure of the space charge induced in the plasma is discussed with relation to the specific form of the unperturbed charged particle distribution functions.

Simulation of perturbation produced by an absorbing spherical body in collisionless plasma

A steady plasma state reached in the course of charging of an absorbing spherical body is found using computational methods. Numerical simulations provide complete information on this process, thereby allowing one to find the spatiotemporal dependences of the physical quantities and observe the kinetic phenomena accompanying the formation of stable electron and ion distributions in phase space. The distribution function of trapped ions is obtained, and their contribution to the screening of the charged sphere is determined. The sphere charge and the charge of the trapped-ion cloud are determined as functions of the unperturbed plasma parameters.

Using GPU parallelization to perform realistic simulations of the LPCTrap experiments

The LPCTrap setup is a sensitive tool to measure the β − ν angular correlation coefficient, a βν , which can yield the mixing ratio ρ of a β decay transition. The latter enables the extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V Vud . In such a measurement, the most relevant observable is the energy distribution of the recoiling daughter nuclei following the nuclear β decay, which is obtained using a time-of-flight technique. In order to maximize the precision, one can reduce the systematic errors through a thorough simulation of the whole set-up, especially with a correct model of the trapped ion cloud. This paper presents such a simulation package and focuses on the ion cloud features; particular attention is therefore paid to realistic descriptions of trapping field dynamics, buffer gas cooling and the N-body space charge effects.

Trapping ions from a fast beam in a radio-frequency ion trap: The relaxation of the ion cloud and its resulting column density

The relaxation of trapped Cl${{}_{2}}^{\ensuremath{-}}$ ions and their resulting column density in a multipole radio-frequency (RF) ion trap have been investigated after loading the trap from an initial fast-moving beam exploiting a mechanism described recently [A. Svendsen et al., Phys. Rev. A 87, 043410 (2013)] where the injection is mediated through the exchange of energy between ions and the oscillating RF field. The temporal relaxation of the energy distribution of the trapped ion cloud was probed by observing the evolution of the resulting time-of-flight distribution of ions after extraction and fragment mass analysis in a quadrupole mass filter. The ion energy distribution was found to be essentially stationary after $\ensuremath{\sim}20$ ms. The resulting column density of trapped ions after relaxation was probed by two-dimensional position-resolved photodissociation of the trapped Cl${{}_{2}}^{\ensuremath{-}}$ ions. A detailed statistical analysis of the ion column density in the ring-electrode trap is given, and by comparison to the experimental data, a value of the maximum adiabaticity parameter of ${\ensuremath{\eta}}_{\mathrm{max}}\ensuremath{\simeq}0.28$ is inferred. It is further demonstrated how the present experimental system allows for time-resolved mass spectrometry by probing explicitly the populations of both parent (Cl${{}_{2}}^{\ensuremath{-}}$) and daughter (Cl${}^{\ensuremath{-}}$) ions as a function of time after closing the trap and after laser irradiation. Finally, it is discussed how the setup can be used to obtain absolute photodissociation cross sections via a tomographic method without assumptions on the decay law for the trapped ions.

Observation of ion coalescence in Orbitrap Fourier transform mass spectrometry

Similar to other mass spectrometric technologies based on ion trapping in a spatially restricted area, the performance of Orbitrap Fourier transform mass spectrometry (FTMS) is affected by the interaction between the trapped ion clouds. One of the effects associated with Coulombic interaction inside the ion trap is the ion cloud coupling, known in ion cyclotron resonance (ICR) FTMS as coalescence, or a phase-locking phenomenon. Nevertheless, the direct observation of ion coalescence has not been reported for Orbitrap FTMS yet. We have performed experiments on ion coalescence with a pair of isobaric peptides in the state-of-the-art hybrid linear ion trap high-field compact Orbitrap Elite FT mass spectrometer using both standard and advanced signal processing modes. For the instrument configuration employed in this work we found that ion coalescence occurs when two singly charged peptides with the mass difference of 22 mDa and molecular weight of about 1060 Da have the total abundance of at least 7.5*10(4) charges. We experimentally demonstrate the existence of the ion coalescence phenomenon in Orbitrap FTMS for peptides for a wide range of total trapped ion population. Using the applicable modeling of the phase-locking threshold we estimate the effect of ion coalescence on the performance of Orbitrap FTMS.

Optimization of a quadrupole ion storage trap as a source for time‐of‐flight mass spectrometry

Designs of a quadrupole ion trap (QIT) as a source for time-of-flight (TOF) mass spectrometry are evaluated for mass resolution, ion trapping, and laser activation of trapped ions. Comparisons are made with the standard hyperbolic electrode ion trap geometry for TOF mass analysis in both linear and reflectron modes. A parallel-plate design for the QIT is found to give significantly improved TOF mass spectrometer performance. Effects of ion temperature, trapped ion cloud size, mass, and extraction field on mass resolution are investigated in detail by simulation of the TOF peak profiles. Mass resolution (m/Δm) values of several thousand are predicted even at room temperature with moderate extraction fields for the optimized design. The optimized design also allows larger radial ion collection size compared with the hyperbolic ion trap, without compromising the mass resolution. The proposed design of the QIT also improves the ion-laser interaction volume and photon collection efficiency for fluorescence measurements on trapped ions.

Temperature measurement of 6He + ions confined in a transparent Paul trap

The LPCTrap setup is a transparent Paul trap dedicated to the measurement of the β-ν correlation coefficient aβν in the β decay of trapped radioactive nuclides. In a first experiment, the system has been used to record ∼105 coincidences between the β particles and recoiling ions emitted from the decay of 6He+ ions. The analysis of the collected data has already shown that the size of the 6He+ ion cloud confined in the Paul trap is a critical parameter, potentially limiting the accuracy on the aβν measurement. We report here the precise determination of the trapped ion cloud temperature and size. This was performed by extracting the trapped ions toward a position sensitive micro channel plate detector at different phases of the RF driving field. We find a temperature Texp = 0.107(7) eV, consistent with the temperature values inferred using two other observables but 20% higher than the temperature Tsim = 0.09 eV predicted by realistic simulations of the ions interacting with the H2 buffer gas.

Formation of a Trapped-Ion Cloud Around a Dust Particle in Low-Density Plasma

A self-consistent model for trapped-ion-cloud formation around a dust particle immersed in low-temperature low-density plasma is presented. The model is based on the solution of an integral balance equation for trapped-ion density, the free ion and electron densities, and the Poisson equation for electric potential distribution. It is shown that, in a weakly collisional regime in plasma, trapped ions form a spread “shell” with the maximum located at some distance from the negatively charged core (dust particle) proportional to an ion Debye length. The estimated polarizability of such dusty “quasi atoms” in an external electric field is very high, and their induced dipole moments can be responsible for the alignment of dust particles, the formation of chain and multilayer structures, and the coagulation of dust grains.

Trapping and cooling of Sr+ ions: strings and large clouds

This paper reports on trapping and laser cooling of singly ionized strontium ions in a linear Paul trap. We describe the loading technique based on two-photon absorption of femtosecond pulses at a wavelength of 431 nm and we compare this technique to electron-bombardment ionization. We perform Doppler cooling of the ions in the few-ions regime as well as in the case of large clouds. The analysis of the fluorescence spectra and direct imaging of the cloud allows us to identify the Coulomb-crystal regime. These experiments open the way to the use of a large cold trapped-ion cloud as a medium for quantum optics and quantum information experiments.