Time-averaged Potential Research Articles

Three-Dimensional Crystal Alignment Using a Time-Dependent Elliptic Magnetic Field

A theoretical study has been presented to show that it is possible to align three different diamagnetic susceptibility axes (chi(3) < chi(2) < chi(1) < 0) of a crystallite with respect to the laboratory coordinate system (x, y, z). The time-dependent magnetic field that periodically changes in direction and intensity on the xy plane in an elliptic manner (the intensity stronger in the x direction) at a rate quicker than the intrinsic rate of magnetic response causes the three-dimensional alignment, that is, chi(1) parallel x, chi(2) parallel y, and chi(3) parallel z. The fluctuation of the three susceptibility axes around the corresponding laboratory coordinates is estimated in terms of the fluctuation around the minimum of the time-averaged magnetic potential. This technique enables the three-dimensional alignment of the crystallographic axes.

Interspecies pharmacokinetic scaling of oltipraz in mice, rats, rabbits and dogs, and prediction of human pharmacokinetics

Dose-independent pharmacokinetics of oltipraz after intravenous and/or oral administration at various doses to mice, rats, rabbits and dogs were evaluated. After both intravenous and/or oral administration of oltipraz to mice (5, 10 and 20 mg/kg for intravenous and 15, 30 and 50 mg/kg for oral administration), rats (5, 10 and 20 mg/kg for intravenous and 25, 50 and 100 mg/kg for oral administration), rabbits (5, 10 and 30 mg/kg for intravenous administration) and dogs (5 and 10 mg/kg for intravenous and 50 and 100 mg/kg for oral administration), the total area under the plasma concentration-time curve from time zero to time infinity (AUC) values of oltipraz were dose-proportional in all animals studied. Animal scale-up of some pharmacokinetics parameters of oltipraz was also performed based on the parameters after intravenous administration at a dose of 10 mg/kg to mice, rats, rabbits and dogs. Linear relationships were obtained between log time-averaged total body clearance (Cl) x maximum life-span potential (MLP) (1 year/h) and log species body weight (W) (kg) (r=0.999; p=0.0015), log Cl (l/h) and log W (kg) (r=0.979; p=0.0209), and log apparent volume of distribution at steady state (V(ss)) (l) and log W (kg) (r=0.999; p=0.0009). The corresponding allometric equations were ClxMLP=49.8 W(0.861), Cl=5.20 W(0.523) and V(ss)=4.46 W(0.764). Interspecies scale-up of plasma concentration-time data for the four species using pharmacokinetic time of dienetichron resulted in similar profiles. In addition, concentrations of oltipraz in a plasma concentration-time profile for humans predicted using the four animal data fitted to the dienetichron time transformation of animal data.

Ion energy uniformity in high-frequency capacitive discharges

Ion energy distribution functions and ion fluxes in low-pressure, high-frequency (13.56–80MHz) capacitive discharges were investigated both theoretically and experimentally. In most of the conditions explored, the ion energy distribution function was a single peak centered at the time-averaged plasma potential. Lower energy ions with higher fluxes are obtained as the frequency increases. The uniformity of the ion energy across large-area electrodes (40cm2) was also studied in conditions under which the standing wave effect is important, i.e., conditions such that the rf voltage and the ion flux are strongly nonuniform. Unlike the latter quantities, the ion energy was uniform across the reactor at all frequencies, due to dc current flowing radially in the plasma and in the electrodes.

Self-consistent particle-in-cell/Monte Carlo simulation of RF magnetron discharges of oxygen/argon mixture: effects of partial pressure ratio

The characteristics of RF planar magnetron discharges of O/sub 2//Ar mixture are clarified using the particle-in-cell/Monte Carlo method. The simulation is carried out for axisymmetrical magnetic fields. The spatial and temporal behavior of magnetron discharge is examined in detail. The O/sup -/ ions are trapped in the plasma bulk by the time-averaged potential. The O/sup -/ density is governed by a balance of generation and loss of O/sup -/. The positive ions Ar/sup +/, O/sub 2//sup +/, and O/sup +/ are distributed in such a way that the charge neutrality is kept in the plasma bulk. Since the peak point of O/sup -/ density does not coincide with that of electron density, the spatial distributions of Ar/sup +/, O/sub 2//sup +/, and O/sup +/ have two peaks. The number densities of Ar/sup +/ and O/sup -/ ions drastically increase when oxygen is added to the discharge gas Ar, and then saturated. In the case when the mole fraction of oxygen increases, the self-bias voltage on the target decreases. This phenomenon is investigated in detail and a clear physical explanation is presented.

Effects of the trapping dust particles on the sheath structure in radio-frequency discharges

The spatial distributions of the trapping dust particles under the interaction of the electrostatic, gravitational, ion-drag, and pressure gradient forces in a radio-frequency sheath are investigated with a self-consistent model. The effects of the trapping dust particles on the ion flux, ion mean velocity, ion and time-averaged electron densities, and time-averaged local potential in the sheath are studied in detail. The distribution for the particles with a finite temperature has a thermal broadening. The region where dust particles trapped is wider for a higher dust temperature or a smaller particulate radius. Due to the collection and scattering of ions by dust particles, the ion flux in the sheath with dust suspending is not constant but decreased. The ion and time-averaged electron densities in the region of trapping particles are also decreased. The time-averaged local sheath potential in the region of the trapping dust particles is even more negative and the local ion mean velocity is increased, which are qualitatively consistent with the experimental measurements of Arnas et al. [Phys. Plasmas 7, 4418 (2000)].

Analytical model of a dual frequency capacitive sheath

In recent years, there has been an increased interest in capacitively coupled plasma discharges which are operated with two frequencies. An analytical sheath model for a capacitively coupled radio-frequency plasma discharge operated with two frequencies is proposed and studied under the assumptions of a time-independent, collisionless ion motion. Expressions are obtained for the time-average electric potential within the sheath, nonlinear motion of the electron sheath boundary and nonlinear instantaneous sheath voltage. The derived model is valid under the condition that the low frequency (lf) electric field Elf in the sheath is much higher than the high frequency (hf) electric field Ehf. This condition is fulfilled within typical dual frequency conditions. It is shown, however, that the hf electric field modifies the sheath structure significantly because of the electron response to Ehf. This model has been compared to particle-in-cell plasma simulations, finding good quantitative agreement. We present the dependence of the maximum sheath width and the dc sheath voltage drop on the hf/lf current ratio and on the hf/lf frequency ratio.

Alternative representation of time-dependent Hamiltonians with application to laser-driven systems

A representation of time-dependent Hamiltonians that describe laser-driven systems is presented. Unlike the well-known time-independent dressed potentials that are functions of the characteristic parameter ${\ensuremath{\alpha}}_{0}=\sqrt{I}/{\ensuremath{\omega}}^{2},$ where $\ensuremath{\omega}$ and I are the laser frequency and intensity, this approach provides a time-averaged potential that depends explicitly on the field parameters; e.g., I, $\ensuremath{\omega},$ and shape of the laser pulse. The modified dressed potential is $\ensuremath{\Elzxh}$ independent and adds a classical time-independent potential barrier to the Kramers-Henneberger dressed potential. We show that this dynamical potential barrier is identical to the Kapitza effective classical potential energy obtained for the motion of a particle in a rapidly oscillating field. As an illustrative numerical example, a simple one-electron effective model Hamiltonian of xenon atom in strong laser field is studied. We show that the zero-order quasienergies obtained by our representation are reasonably accurate and the second order high-frequency perturbation calculations provide quite accurately the lifetime of the photoionized electron for a broad range of laser frequencies.

Modulated plasma potentials and cross field diffusion in a Helicon plasma

As the input rf power to a helicon plasma is increased there is a discontinuous increase in the density which is identified with a change from a capacitive to an inductive/wave coupling to the plasma. The radial distribution of the density is much narrower in the inductive (high) mode than in the capacitive (low) mode. Although the time average plasma potential (Vp) decreases markedly at this mode change, the radial profile of Vp is flat in both modes. Measurements with an emissive probe show that in the capacitive mode Vp is strongly modulated (ΔV is order of Vp) at the rf drive frequency indicating the presence of large rf fields in the source. There is also a large radial gradient in the amplitude of this modulation. In the inductive mode the modulation decreases significantly but can still be observed in measurements of the ion energy distribution. It is suggested that in the capacitive mode, the radial diffusion of electrons is driven by the large gradients in the rf fields. As the density increases, the fields are screened out, diminishing the radial electron loss and consequently, the radial ion loss. The reduced radial diffusion of both charged species produces a still higher density as the major loss surface is now reduced to the ends only.

Comparison of all atom, continuum, and linear fitting empirical models for charge screening effect of aqueous medium surrounding a protein molecule

To investigate the role hydration plays in the electrostatic interactions of proteins, the time-averaged electrostatic potential of the B1 domain of protein G in an aqueous solution was calculated with full atomic molecular dynamics simulations that explicitly considers every atom (i.e., an all atom model). This all atom calculated potential was compared with the potential obtained from an electrostatic continuum model calculation. In both cases, the charge-screening effect was fairly well formulated with an effective relative dielectric constant which increased linearly with increasing charge–charge distance. This simulated linear dependence agrees with the experimentally determined linear relation proposed by Pickersgill. Cut-off approximations for Coulomb interactions failed to reproduce this linear relation. Correlation between the all atom model and the continuum models was found to be better than the respective correlation calculated for linear fitting to the two models. This confirms that the continuum model is better at treating the complicated shapes of protein conformations than the simple linear fitting empirical model. We have tried a sigmoid fitting empirical model in addition to the linear one. When weights of all data were treated equally, the sigmoid model, which requires two fitting parameters, fits results of both the all atom and the continuum models less accurately than the linear model which requires only one fitting parameter. When potential values are chosen as weighting factors, the fitting error of the sigmoid model became smaller, and the slope of both linear fitting curves became smaller. This suggests the screening effect of an aqueous medium within a short range, where potential values are relatively large, is smaller than that expected from the linear fitting curve whose slope is almost 4. To investigate the linear increase of the effective relative dielectric constant, the Poisson equation of a low-dielectric sphere in a high-dielectric medium was solved and charges distributed near the molecular surface were indicated as leading to the apparent linearity.

Collision dynamics of two Bose–Einstein condensates in the presence of Raman coupling

A collision of two-component Bose-Einstein condensates in the presence of Raman coupling is proposed and studied by numerical simulations. Raman transitions are found to be able to reduce collision-produced irregular excitations by forming a time-averaged attractive optical potential. Raman transitions also support a kind of dark soliton pair in two-component Bose-Einstein condensates. Soliton pairs and their remnant single solitons are shown to be controllable by adjusting the initial relative phase between the two colliding condensates or the two-photon detuning of Raman transitions.

A proposal for ac magnetic guide and trap of cold atoms

We propose a novel ac electro-magnetic wave guide for cold neutral atoms in an Ioffe tube, which is based on the interaction of a magnetic dipole moment of a guided atom with both an ac quadrupole magnetic field in the transverse direction and a dc-bias magnetic field along the guiding axis. The time-averaged magnetic potential and force for the guided atoms in the magnetic guiding tube are calculated. The results show that the potential is high enough to collect and guide nearly all cold atoms from a standard magneto-optical trap with a temperature of ∼120 μK. We also estimate the atomic losses from collisions with background thermal atoms, quantum tunneling and spin-flip transitions in the guiding process. Our study indicates that a cold and dense atomic beam with a guiding efficiency of ∼92% and a beam intensity of about 10 11 atoms/cm 2/s can be output from the magnetic guide tube, and the guiding scheme proposed here could be used to manipulate spin-polarized cold atoms.

Space Environment Simulation for Material Processing by Acoustic Levitation

Single-axis acoustic levitation of four polymer samples has been realized inair under the ground-based laboratory conditions forthe purpose of space environment simulation of containerless processing.The levitation capabilities are investigated bynumerical calculations based on a model of the boundary element method corresponding to our levitatorand following Gor'kov and Barmatz's method.The calculated results, such as the resonantdistance between the reflector and the vibrating sourceand the positions of levitatedsamples, agree well with experimental observation,and the effect of gravity on the time-averaged potential for levitationforce is also revealed. As an application, thecontainerless melting and solidification of aliquid crystal, 4-Pentylphenyl-4'-methybenzoate,is successfully accomplished, in which undercoolingup to 16 K is obtained and the rotation andoscillation of the sample during solidificationmay result in fragmentation of the usual radiating surface growth morphology. PACS: 43. 25. Uv, 81. 20. Zx

Effect of space-charge limited emission on measurements of plasma potential using emissive probes

Effects of space-charge limitation have been considered for an analytical estimation of plasma potential with use of emissive probes, taking account of a correct expression of emission current under space-charge limited condition. The analytical results are obtained for the floating potential method of emissive probe and for the differential emissive probe method, both without and with an oscillating ac potential. In the case of the floating potential method, the operating condition is discussed for different plasma parameters at several probe temperatures. These results indicate that the floating potential of the emissive probe gives us the plasma potential to an accuracy of the order of the plasma electron temperature Te/e for a strong probe emission. In the case of the differential emissive probe method, the relations among space-charge effects, the ratio of thermoelectron emission current to plasma electron collection current, the plasma electron temperature, the probe temperature, and the amplitude of the oscillating ac potential are discussed in terms of determination of plasma potential. In addition, the analytical results also indicate that the midpoint of the two peaks in the derivative d〈Iem〉/dV curve is a good method for measuring the time-averaged plasma potential.

Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap

We propose and demonstrate a scheme for a blue-detuned optical dipole trap for cold atoms which consists of a single, rapidly rotating laser beam. We characterize a parameter range in which the optical potential can be accurately described by a quasistatic time-averaged potential. The trap is loaded with $&gt;{10}^{6}$ Rb atoms, and is then compressed adiabatically by a factor of 350 to a final density of $5\ifmmode\times\else\texttimes\fi{}{10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}3}.$ $\mathrm{A}\ensuremath{\sim}4$ times adiabatic increase in the peak phase-space density of the trapped atoms is obtained due to the change in the shape of the trap potential. The two-body elastic and inelastic collision rates of atoms in the compressed trap are determined.

Asymmetric plasma potential fluctuation in an inductive plasma source

Time-averaged plasma potential in an inductive source with a ground wall has been measured by using an emissive probe. The inflection point method in the limit of zero emission is employed to determine the plasma potential. In this source, capacitive coupling results in a fluctuating plasma potential. The peak-to-peak value of the radiofrequency (RF) fluctuations, which is approximately given by the separation of the two peaks in the derivative of an I-V characteristic curve, has been reduced by introducing a gap between the antenna and the quartz window and by various electrostatic screens. Experimental data show that the lower potential peak, representing the lowest plasma potential, was approximately constant as the RF fluctuation level was reduced, while the higher potential peak, indicating the more positive plasma potential, changed and approached the lower potential peak. For very low fluctuation level, the lower potential peak becomes the dc plasma potential and only the higher potential peak responds to the RF fluctuation.

Power laws for the spatial dependence of electrical parameters in the high-voltage capacitive RF sheath

Following the analytical description of the collisionless high-voltage capacitive RF sheath in Lieberman (1988) and of the collisional high-voltage capacitive RF sheath in Lieberman (1989), electrical sheath parameters are calculated for a square-wave RF discharge current. The interest in the square-wave current lies in the analytical simplicity of the solutions. The spatial dependences of the time-averaged electrostatic potential /spl Phi/~ electric field E~ net-charge carrier density n~, and ion density n/sub i/ are related to the distance x from the plasma/sheath edge by power laws. For the collisionless RF sheath, /spl Phi/~/spl prop/x/sup 3/2/ E~/spl prop/x/sup 1/2/, n~/spl prop/x-/sup -1/2/and n/sub i//spl prop/x/sup -3/4/ (the respective exponents for the collisionless RF sheath are 4/3, 1/3, -2/3, -2/3), For the collisional RF sheath, /spl Phi/~/spl prop/x/sup 2/ E~/spl prop/x/sup 0/ and n/sub i//spl prop/x/sup -1/2/ (the respective exponents for the collisional DC sheath are 5/3, 2/3, -1/3, -1/3). The RF sheath solution is compared with Lieberman's solution for the sinusoidal RF discharge current. The spatial dependences of /spl Phi/~, E~, n~, and n/sub i/ are almost identical for the two current waveforms. For fixed ionic sheath charge and ion current, the sheath width and the time-averaged sheath voltage are similar for the two current waveforms.

Downstream Control of Negative-Ion Plasma Parameters in Helicon Discharge

Plasma parameters, such as electron temperature, plasma density and potential oscillation were controlled by applying a negative potential to a grid in the downstream region of an electronegative plasma excited by an m = ± 1 mode helical antenna. The fine mesh grid, with spacing comparable to the Debye length was found to quench the plasma characteristics in the source region whereas the coarse mesh grid did not. The fine mesh grid performed better cooling of the electron temperature and lowered the plasma oscillation. Oscillating amplitude was found to increase with an increase in the SF6 gas concentration, while the time-averaged space potential was found to decrease, implying the effect of negative ions. The measurement of positive ion energy distribution functions predicted an ion beam travelling from the plasma source region towards the diffused region because of the potential difference between the two regions separated by the grid bias.

A note on the contributions to the wave-drift damping matrix from the time-averaged second order potential

A note on the contributions to the wave-drift damping matrix from the time-averaged second order potential

Time-orbiting-potential quadrupole magnetic trap for cold atoms

An analytical theory of the time-orbiting-potential quadrupole magnetic trap for cold atoms is developed. It is shown that the rotating magnetic field used to create the time-averaged harmonic potential is responsible for the formation of quasienergy states of an atom in the trap. It is found that the motion of an atom near the origin of the trap can be represented as consisting of slow motion in the time-averaged potential and fast oscillations with small amplitude. Eigenstates and eigenfunctions for the motion are found. The eigenfunctions are used to calculate the coordinate and momentum distributions for a single atom. It is concluded that at low temperature the quantum-statistical momentum distribution for a single atom exhibits a ring shaped structure due to the fast oscillations in the atomic linear momentum.

Dynamics of cold atoms in a quadrupole magnetic trap with an orbiting potential

We study the dynamics of atoms confined to a quadrupole magnetic trap with an orbiting potential. For typical values of the experimental parameters of the trap, the rotating magnetic field is shown to produce high-frequency modulation of atomic momenta with an amplitude comparable to the widths of the momentum distributions for the lowest oscillation states of atoms in the time-averaged potential. We find the quantum-statistical momentum and position distributions of atoms and show that at temperatures much higher than the effective vibrational temperature of the atoms in the trap the quantum-statistical momentum and position distributions are Gaussian. We also establish that at temperatures comparable to the effective vibrational temperature of the atoms the quantum-statistical momentum distribution has an annular structure in the trap’s symmetry plane, which is due to the deep modulation of the atomic momenta caused by the rotating magnetic field.