Charge-state Fluctuations Research Articles

Temperature Equilibration due to Charge State Fluctuations in Dense Plasmas.

The charge states of ions in dense plasmas fluctuate due to collisional ionization and recombination. Here, we show how, by modifying the ion interaction potential, these fluctuations can mediate energy exchange between the plasma electrons and ions. Moreover, we develop a theory for this novel electron-ion energy transfer mechanism. Calculations using a random walk approach for the fluctuations suggest that the energy exchange rate from charge state fluctuations could be comparable to direct electron-ion collisions. This mechanism is, however, predicted to exhibit a complex dependence on the temperature and ionization state of the plasma, which could contribute to our understanding of significant variation in experimental measurements of equilibration times.

Scalability of supercurrent modulable with single Cooper-pair transistors connected in parallel

A single Cooper-pair transistor (SCPT) can work as a fast supercurrent switch. However, a direct combination of an SCPT with other superconducting-electronics circuits is not easy because of the smallness of the switchable supercurrent with it. In this work, scalability of the supercurrent that can be modulated with an SCPT structure is studied using multiple SCPTs connected in parallel having a common gate electrode. It is found that the magnitude of the maximum supercurrent is scaled up almost linearly with the increase in the number of SCPTs, N, and that it is modulated with the gate voltage as in the case for a single SCPT. The modulability, however, decreases with the increase in N, which is demonstrated to be mostly because of the charge-state fluctuations of either islands of the constituent SCPTs caused by the capacitive coupling among them. A practically possible method of improving the modulability is also discussed.

Introducing a Novel Multi-Level Method for Simulating the pH Dependence of Charge State Fluctuations and Conformational Ensembles of Intrinsically Disordered Proteins

Simulations of intrinsically disordered proteins (IDPs) use fixed charge models where the charge states of ionizable residues are set using model compound pKa values. Recent experiments have questioned the validity of fixed charge models. For a 100-residue IDP without sequence biases there can be roughly 103 or more unique possible charge states. Accurate and fully ergodic simulations require converged conformational sampling of each of the charge states. To facilitate this we have developed a multi-level Monte Carlo and free energy based method that leverages the ABSINTH implicit solvation model to enable efficient simulations of the conformational ensembles of all possible charge states for a given sequence. This is achieved by grouping charge states based on their net charge and adding auxiliary Markov chains that enable protonation/deprotonation of ionizable residues. At a given pH, the populations of thermodynamically accessible charge states and conformations are calculated using the Bennett Acceptance Ratio method and data from simulations obtained for all possible charge states. Key features of the ABSINTH model allow reductions in the number of replicas needed for free energy calculations. We also estimate shifts in free energies upon protonation / deprotonation relative to model compounds. Using these estimates, we quantify charge state fluctuations - known as charge regulation - to estimate pKa shifts within IDPs and extract the pH dependencies of the populations of charge states and conformational ensembles. In peptides excised from IDP sequences we find that local sequence contexts cause shifts in pKa values that can be larger than one pH unit. The method, with the incorporation of heuristics to enable increased efficiencies, is being deployed for simulations of charge states and conformational ensembles of a spectrum of IDPs.

Optical switching of defect charge states in 4H-SiC

We demonstrate optically induced switching between bright and dark charged divacancy defects in 4H-SiC. Photoluminescence excitation and time-resolved photoluminescence measurements reveal the excitation conditions for such charge conversion. For an energy below 1.3 eV (above 950 nm), the PL is suppressed by more than two orders of magnitude. The PL is recovered in the presence of a higher energy repump laser with a time-averaged intensity less than 0.1% that of the excitation field. Under a repump of 2.33 eV (532 nm), the PL increases rapidly, with a time constant 30 μs. By contrast, when the repump is switched off, the PL decreases first within 100–200 μs, followed by a much slower decay of a few seconds. We attribute these effect to the conversion between two different charge states. Under an excitation at energy levels below 1.3 eV, VSiVC0 are converted into a dark charge state. A repump laser with an energy above 1.3 eV can excite this charged state and recover the bright neutral state. This optically induced charge switching can lead to charge-state fluctuations but can be exploited for long-term data storage or nuclear-spin-based quantum memory.

Spin-lattice relaxation of an individualMn2+ion in a CdTe/ZnTe quantum dot

We present the study of the spin-lattice relaxation of an isolated ${\mathrm{Mn}}^{2+}$ ion in a single CdTe/ZnTe quantum dot. The measurements are done in a wide range of magnetic field. The spin-lattice relaxation rate is determined in a time resolved experiment. The ion spin state is driven out of equilibrium using optical orientation of the ${\mathrm{Mn}}^{2+}$ spin in a system of two coupled dots. Then the light is switched off and the ${\mathrm{Mn}}^{2+}$ ion spin relaxes. The ${\mathrm{Mn}}^{2+}$ spin state is measured after switching the light on again. We discuss the magnetic field dependence of the spin-relaxation rate in light of two theoretical models: one based on scattering of transverse acoustic phonons in the presence of a finite uniaxial ${\mathrm{Mn}}^{2+}$ spin anisotropy, and the second relying on presence of quantum dot charge state fluctuations.

The ΔTOF detector for isobar separation at ion energies below 1 MeV/amu

The ΔTOF detector is a new approach for isobar separation at energies below 1MeV/amu. The specific energy loss after a degrader foil can be measured very precisely with time-of-flight (TOF). Small differences in the specific energy loss between isobars lead to clear separation even at low energies. The resolution is not deteriorated by angular scattering or charge state fluctuations. Highly homogeneous low stress silicon nitride foils are used as degrader foils which reduces energy-loss tails significantly. For 36Cl measurements at 0.5MeV/amu a reduction of 36S by 104 could be achieved. The proprieties of these foils for the ΔTOF detector are discussed and first AMS measurements of 36Cl at 0.5MeV/amu and 41Ca at 0.4MeV/amu with the 3MV tandem accelerator VERA are presented.

Ion charge state fluctuations in vacuum arcs

Ion charge state distributions of cathodic vacuum arcs have been investigated using a modified time-of-flight (TOF) method. Experiments have been done in double gate and burst gate mode, allowing us to study both systematic and stochastic changes of ion charge state distributions with a time resolution down to 100 ns. In the double gate method, two ion charge spectra are recorded with a well-defined time between measurements. The elements Mg, Bi and Cu were selected for tests, representing metals of very different properties. For all elements it was found that large stochastic changes occur even at the limit of resolution. This is in agreement with fast changing arc properties observed elsewhere. Correlation of results for short times between measurements was found but it is argued that this is due to velocity mixing rather than due to cathode processes. The burst mode of TOF measurements revealed the systematic time evolution of ion charge states within a single arc discharge, as opposed to previous measurements that relied on data averaged over many pulses. The technique shows the decay of the mean ion charge state as well as the level of material-dependent fluctuations.

Drastic enhancement of energy-loss straggling of relativistic heavy ions due to charge-state fluctuations

Stopping power and energy-loss straggling of 197Au, 208Pb, and 209Bi projectiles have been measured in different solids (4</=Z2</=82) in the energy range (100-1000) MeV/u. The experimental results clearly demonstrate the influence of the different charge states of the ions. Because of charge-state fluctuations the energy-loss straggling is up to 7 times larger than the pure collisional straggling. The selected energy domain in combination with the heavy projectiles allows for the first time an unambiguous interpretation of the long-standing problem of charge-changing collisions in energy-loss straggling.

Influence of initial charge and charge state fluctuations on high-energy ion ranges and track formation

A model used for calculating the depth distribution of implanted atoms and the energy deposited into the electron and nuclear subsystems of solids is studied. The model is based on the transport equations and takes into account the initial charge and the fluctuations of charge states of high-energy ions ( E > 1 MeV/amu). The critical dose of 250 MeV Xe + ions necessary for the formation of deep amorphous layers in Si, GaAs and InP have been estimated. The process of the formation of continuous track regions in InP by 250 MeV Xe + ions is studied.

Effect of the initial charge and charge-state fluctuations on the range parameters of high-energy ions

A model used in calculating the depth distribution of implanted atoms, and the energy released into the electron and nuclear subsystems of the solid is studied. It takes into account the initial charge and the fluctuations of charge states of high-energy ions with energies E⩽1 MeV amu−1. The results of calculations are obtained on the basis of solutions of transport equations. Satisfactory agreement between theoretical predictions and experimental results is observed for a broad class of ion-target systems.

Modification of diamond films by high-energy ion irradiation: “track channelling” and ion charge fluctuation effects

A model of ion implantation in diamond with an energy of 1 MeV per nucleon is formulated taking into account the two effects: (i) ion channelling through latent tracks, and (ii) ion charge state fluctuations on the basis of a set of the Boltzmann and Fokker–Planck transport equations. Comparison with the experimental data on the implantation of Ni and Xe ions in diamond leads to the conclusion that these effects are essential to the accurate calculation of the depth distributions of impurity and defects at the high energy ion implantation.

Charge state fluctuations: a master equation approach

A stochastic theory of charge exchange fluctuations in ion transport is introduced based on a master equation for the probability of finding ions in appropriate phase space locations. When energy losses are absent, a forward master equation is obtained which is solved exactly in the binary charge state case. The equilibrium probability distribution is shown to be a binomial distribution and differs from that at small depths. In the more general case a backward master equation is derived for the multi-point probability distribution function, from which an equation for the average charge state is obtained.

Angular straggling associated with fluctuations in charge state of the projectile in grazing ion-surface scattering

We have studied the angular straggling of a few keV ions scattered off metal surfaces at grazing scattering condition. The angular straggling of scattered particles is large when the charge state of the particle fluctuates significantly in the surface region. The important physical parameters responsible for the angular straggling are the particle induced density of states and the rate of change of the energy of the atomic level with distance from the surface. An implication for the mechanism underlying skipping motion is discussed.

Charge state fluctuations and energy loss straggling of fast ions in cold and in plasma targets

The energy loss and straggling of fast ions in solid and plasma targets were calculated. In particular, the role of charge state fluctuations in determining the straggling profiles was investigated. It is found that in foil targets charge state fluctuations can drastically increase the width of the energy spectrum upon exit. In plasma targets they can drastically smear the ideally sharp Bragg peak in the energy deposition profile. A comparison of the results of calculations for beam-foil interaction with an experiment which is briefly described is made.

The transport equation approach for the simulation of charge state fluctuation effects during ion penetration into solids

A model for high-energy ion implantation taking account of ion charge state fluctuations is proposed and the corresponding forward and backward kinetic equations are formulated. The results of simulation ny numerical solution of the transport equations are given. It is shown that taking account of high-energy fluctuations results in an increase in straggling of the implanted impurity and radiation defect distributions and gives better agreement with experiments than the standard simulations.

The ion charge state fluctuation effect during high energy ion implantation: Monte Carlo simulation

A model of energetic ion implantation based on a Monte Carlo method with regard to ion charge state fluctuations is considered. It is shown that a model taking into account energetic ion charge fluctuations gives a better agreement with experiment than standard Monte Carlo codes or kinetic equation-based approaches.

Energy straggling of light-ion beams.

The dielectric function method is applied to investigate the energy straggling of protons and helium ions using the atomic and the solid local-electron-density models. A partially stripped ion is treated as well as point charges. At low energies, the conventional stragglings of a proton (${\ensuremath{\Omega}}_{{\mathrm{H}{}^{+}}^{2})}$ and of helium ions (${\ensuremath{\Omega}}_{{\mathrm{He}{}^{+}}^{2}}$,${\ensuremath{\Omega}}_{\mathrm{He}}^{2+}$ $^{2}$) due to the fluctuation in electronic excitations are proportional to the kinetic energies of the ions even when the local-electron-density models are adopted, and at high energies they approach the values predicted by Bohr. Here we do not consider the bunching term since we assume the probability of exciting an electron is small. The straggling ratio ${\ensuremath{\Omega}}_{{\mathrm{He}{}^{+}}^{2}/{\ensuremath{\Omega}}_{{\mathrm{H}{}^{+}}^{2}}}$ shows a remarkable feature that it is nearly constant up to \ensuremath{\sim}50 keV/amu, and increases gradually beyond this energy for solid targets. The estimation of the collisional straggling of helium-ion beams is performed using the charge-state fractions, resulting in displaying ${Z}_{2}$ (target atomic number) oscillations similar to those of ${\ensuremath{\Omega}}_{{\mathrm{He}{}^{+}}^{2}}$ and ${\ensuremath{\Omega}}_{{\mathrm{He}{}^{2+}}^{2}}$. The straggling caused by charge-state fluctuations, which enhance the ${Z}_{2}$ oscillations of the total straggling of helium-ion beams more sharply at the energies considered, is also estimated.

The gas-solid density effect for MeV/u ions: Charge changing cross sections and the effective charge

It is commonplace to describe projectile ion charge-state fluctuations within gaseous and solid targets in terms of “charge-changing cross sections”. However the physical meaning of such cross section has been unclear in solids, where a significant proportion of the ions may be in excited states. For the case of a charge-state distribution dominated by fully stripped and one-electron ions, formulae for the charge-changing cross sections are derived in terms of more fundamental cross sections for projectile excitation, ionisation and electron capture. Density effects in the electron loss and capture cross sections, described in an informal way by Bohr and Lindhard, are presented in simple closed form. Quantitative estimates are given for the density effect in the loss cross section for one-electron ions. The results are supported by experimental data for 3 MeV/u C ions in gaseous and solid C targets. The corresponding density effect in the effective stopping-power charge q eff is considered, both for nearly fully stripped ions and for many-electron ions; and is compared with available experimental data for light and heavy ions at MeV/u energies.

Projected range distributions of low-, intermediate-, and high-energy ions

At incident ion energies E i significantly below and significantly above that of the electronic stopping-power maximum E m, major differences are to be found in the physics of nuclear and electronic collisions which give rise to the ion range distribution. In the present paper a Monte Carlo method is used to span the energy range between these low- and high-energy regimes. Good agreement is found with recent results on the parameters and shape of the distribution obtained from transport calculations at low energy and from a recently developed semi-analytical model at high energy. The changing character of the projected range distribution as a function of energy is discussed in terms of the statistics of nuclear collisions. The fwhm of the projected range distribution is found to be dominated by electronic straggling for incident energies above a few time E m, while as expected for significantly lower energies the fwhm arises predominantly from multiple nuclear collisions. The fwhm can also be increased significantly by charge-state fluctuations in the transitional region just above the stopping-power maximum. Quantitative predictions for the mean projected range, and the fwhm of the projected range distribution, are presented for the cases of 4He, 12C and 16O ions incident on A1 in the energy range 10 keV/u to 10 MeV/u.

Straggling in energy loss of energetic hydrogen and helium ions

The straggling in energy loss for protons and alpha particles is discussed, with special emphasis on correlation effects, stemming from the bunching of electrons in atoms and molecules and from charge-state fluctuations. It is shown that for gaseous targets, the correlation effects give rise to an increased straggling relative to that calculated from an electron-gas picture. For an amorphous, uniform solid, the contribution from correlation is much reduced, and the total energy straggling should approximately be given by the Lindhard-Scharff electron-gas expression. The theoretical description is in good agreement with accurate measurements of energy straggling for hydrogen and helium ions on a variety of atomic and molecular gases. Measurements in solids are often obscured by the influence of target non-uniformity and texture. A simple method to check for such effects is discussed and demonstrated by an example.