Ion Velocity Profiles Research Articles

Ion acceleration in expanding plasma in small radio frequency plasma thruster with a magnetic cusp

Ambipolar electric field is formed in the expanding plasma of the small radio frequency plasma thruster using a cusp-shaped magnetic field. A highly energized group of ion energy distribution function is observed in the z-direction, indicating the presence of axial ion acceleration downstream the magnetic nozzle owing to the electric field. The mean velocity profile of the beam ions along the z axis is evaluated using the energy distribution functions along the z axis. The high axial ion velocity profile stretches downstream, although the evaluated dimensionless velocity profile is lower than that calculated using quasi-one-dimensional models. It is suggested that ion momentum loss can result from ion-neutral collision, leading to beam divergence in the magnetic nozzle of the proposed small thruster.

TriWaSp: a multi-faceted visible spectroscopy diagnostic on the ST40 tokamak

We present a new state-of-the-art Triple Wavelength Spectrometer (TriWaSp), recently deployed on ST40, a high field low aspect ratio spherical tokamak. The TriWaSp has a range of possible applications due to its flexible design; the current configuration focuses on charge exchange recombination spectroscopy from carbon and neon impurities in the ST40 plasma. This paper discusses the detailed setup of the system and presents initial charge exchange ion temperature measurements using a single line of sight, which show good agreement with other ion temperature diagnostics. Building on these commissioning results and forward modelling of the system, a new observation geometry has been implemented for the next experimental campaign which will considerably improve the localisation of ion temperature and velocity profile measurements.

Effects of initial ion velocity, magnetic field and plasma density profiles in simulating the plasma plume in a Hall thruster

Effects of initial ion velocity, magnetic field and plasma density profiles in simulating the plasma plume in a Hall thruster

Ion kinetic effects and instabilities in the plasma flow in the magnetic mirror

Kinetic effects in plasma flow due to a finite ion temperature and ion reflections in a converging–diverging magnetic nozzle are investigated with collisionless quasineutral hybrid simulations with kinetic ions and isothermal Boltzmann electrons. It is shown that in the cold ions limit, the velocity profile of the particles agrees well with the analytical theory, predicting the formation of the global accelerating potential due to the magnetic mirror with the maximum of the magnetic field and resulting in the transonic ion velocity profile. The global transonic ion velocity profile is also obtained for warm ions with isotropic and anisotropic distributions. Partial ion reflections are observed due to a combined effect of the magnetic mirror and time-dependent fluctuations of the potential as a result of the wave breaking and instabilities in the regions when the fluid solutions become multi-valued. Despite partial reflections, the flow of the passing ions still follows the global accelerating profile defined by the magnetic field profile. In simulations with reflecting boundary condition imitating the plasma source and allowing the transitions between trapped and passing ions, the global nature of the transonic accelerating solution is revealed as a constrain on the plasma exhaust velocity that ultimately defines plasma density in the source region.

On the mechanism of ionization oscillations in Hall thrusters

Low-frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0D) predator–prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has often been used for the characterization of such oscillations and scaling estimates. We investigate the properties of its continuum analog, the one-dimensional (1D) system of two nonlinearly coupled equations in partial derivatives (PDEs) for plasma and neutral density. This is a more general model, of which the standard 0D predator–prey model is a special limit case. We show that the 1D model is stable and does not show any oscillations for the boundary conditions relevant to Hall thrusters and the uniform ion velocity. We then propose a reduced 1D model based on two coupled PDEs for plasma and neutral densities that is unstable and exhibit oscillations if the ion velocity profile with the near-the-anode back-flow (toward the anode) region is used. Comparisons of the reduced model with the predictions of the full model that takes into account the self-consistent plasma response show that the main properties of the breathing mode are well captured. In particular, it is shown that the frequency of the breathing mode oscillations is weakly dependent on the final ion velocity but shows a strong correlation with the width of the ion back-flow region.

Characteristics of Magnetized Dusty Plasma Sheath With Two Ion Species and q-Nonextensive Electrons

The effect of q-nonextensive electrons, nature, and magnitude of dust charge on magnetized dusty plasma sheath with two ion species has been numerically investigated via fluid model. The initial common speed of ion species at the sheath entrance has been extended, which increases from subsonic to supersonic with the decrease in nonextensive parameter q and ion-neutral drag force as well. The presence of super extensive primary electrons ( q <; 1) has significantly affected the sheath parameters characterizing the dusty plasma sheath: dust charging, potential profile, ion and electron densities profile, ion velocity profile, and dust dynamics. It is found that the negatively charged dust grains accelerate in the region of weak electric field, whereas the fluctuation decreases in the region of strong electric field. A significant change has been observed in dust dynamics with the presence of two different natures of dust charges and its magnitudes. The velocity fluctuations of negatively and positively charged grains are in opposite phase. Furthermore, the comparative study of dust velocity in the presence and absence of dust-neutral collisions has been presented.

Variation of Velocity of Ions in a Magnetized Plasma Sheath for Different Magnetic Field

The kinetic trajectory simulation method has been used to study ion velocity profile in a plasma sheath for varying magnetic field at fixed obliqueness. As the electrons have higher velocity compared to that of ions the wall is charged up negatively with respect to the core plasma. The negative potential then attracts the ions and repels electrons forming a thin positive space charge region in front of the wall. This positive space charge region, known as the ‘sheath’ separates the negatively charged wall from the quasineutral ‘presheath’ plasma. The ions moving towards the wall have to satisfy the Bohm criterion to ensure the stability of the overall plasma. The mean value as well as oscillation frequency of velocity of ions change as the magnetic field is varied from 1.5 to 10.5 mT. The maximum amplitude of normal component of velocity is almost independent of the magnetic field but the maximum amplitude of other components of velocity change and shows oscillating nature as the magnetic field changes.

Influence of collisions in a fluid model for the warm-ion sheath around a cylindrical Langmuir probe

A long cylindrical Langmuir probe immersed in a collisional plasma is modelled by using fluid equations in which the collision term is introduced assuming a constant ion mean free path. The physical magnitudes of the system are expanded in a perturbation series in the collision parameter, that is, the ratio between the Debye length and the ion mean free path, and the system is thus separated into zeroth-order and first-order perturbation systems. The ion temperature is arbitrary and a continuous solution from the plasma to the probe is obtained for the perturbation systems. Using this methodology, a continuous solution for the ion sheath around a cylindrical Langmuir probe is obtained for long ion mean free path, for any ion temperature with no need of two-scale study or asymptotic matching. It is found that the collisions and the ion temperature have opposite effects, and these effects are quantified. The solution for cold ions cannot be obtained directly using this method, but it can be recovered from the warm-ion solution. The methodology is usable for long cylindrical probes in which the scale of the probe is much higher than the scale of the sheath, so that the geometry is essentially cylindrical. The model is numerically solved to obtain the potential profile, the ion temperature profile, the ion density profile and the ion velocity profile, and the dependence of the sheath on the ion mean free path and the ion temperature is studied. The ion-current to probe-potential profiles for different probe radius are obtained. Finally, the Sonin plot is calculated, in order to use the solution in plasma diagnosis.

On channel interactions in nested Hall thrusters

Nested Hall thrusters use multiple, concentric discharge channels to increase thrust density. They have shown enhanced performance in multi-channel operation relative to the superposition of individual channels. The X2, a two-channel nested Hall thruster, was used to investigate the mechanism behind this improved performance. It is shown that the local pressure near the thruster exit plane is an order of magnitude higher in two-channel operation. This is due to the increased neutral flow inherent to the multi-channel operation. Due to the proximity of the discharge channels in nested Hall thrusters, these local pressure effects are shown to be responsible for the enhanced production of thrust during multi-channel operation via two mechanisms. The first mechanism is the reduction of the divergence angle due to an upstream shift of the acceleration region. The displacement of the acceleration region was detected using laser induced fluorescence measurements of the ion velocity profile. Analysis of the change in beam divergence indicates that, at an operating condition of 150 V and 30 A, this effect increases the thrust by 8.7 ± 1.2 mN. The second mechanism is neutral ingestion from the adjacent channel resulting in a 2.0 + 0/−0.2 mN increase in thrust. Combined, these mechanisms are shown to explain, within uncertainty, the 17 ± 6.2 mN improvement in thrust during dual channel operation of the X2.

In situ electrostatic characterisation of ion beams in the region of ion acceleration

In situ and ex situ techniques have been used to measure directional ion beams created by a sharp axial potential drop in low pressure expanding plasmas. Although Retarding Field Energy Analysers (RFEAs) are the most convenient technique to measure the ion velocities and plasma potentials along with the plasma density, they are bulky and are contained in a grounded shield that may perturb the electric potential profile of the expanding plasma. In principle, ex situ techniques produce a more reliable measurement and Laser Induced Fluorescence spectroscopy (LIF) has previously been used to characterise the spatial velocity profile of ion beams in the same region of acceleration for a range of pressures. Here, satisfactory agreement between the ion velocity profiles measured by LIF and RFEA techniques has allowed the RFEA method to be confidently used to probe the ion beam characteristics in the regions of high gradients in plasma density and DC electric fields which have previously proven difficult.

One-dimensional plasma sheath model in front of the divertor plates

A new model of the stationary electrostatic plasma sheath in front of divertor plates is developed, which takes into account strong inelastic processes. Using particle-in-cell simulations and analytic estimates it is demonstrated, that the properties of the tokamak divertor plasma sheath can significantly deviate from the properties of the classical sheath model. The most significant deviations are the increased energy flux to the plates and non-monotonic potential and ion velocity profiles in the presheath. Two main reasons for these deviations are identified: strong inelastic collisionality of the plasma presheath and the presence of super-thermal plasma particles originating from the upstream scrape-off layer.

Kinetic simulations of electron heat flux in the scrape-off layer

Parallel electron heat flux qe|| on open field lines is studied with the 1D2V kinetic Vlasov-Fokker-Planck (VFP) code KIPP [15–17]. In order to assess the importance of kinetic effects on the scrape-off layer heat transport in a systematic way, a series of self-similar KIPP cases with the stagnation point and one target, logical sheath condition, parabolic ion velocity profiles reaching ion sound speed at the target were run. The variable parameter was upstream electron collisionality v* (collisionality scan cases) and for each collisionality two different numerical schemes of particle source were implemented for comparison. It shows no significant difference between the results with two different schemes of particle source for any scanned collisionality. In high collisionality cases, heat flux converges to Braginskii formula as expected, while in comparatively low collisionality cases transport coefficients deviate far away from classical value due to target cut-off effect implicating that fluid model is not applicable near the target.Enhanced radiation near the target, forcing Te drop by factor 10 for low upstream v* comparable to that expected at the separatrix in the ITER baseline H-mode scenario, was required in KIPP runs. Pairs of such cases with two different ways of radiation power sink, by modeling sink (a) evenly from all velocity space, and (b) only from high energy electrons, were compared. The simulation results show almost no difference between the two cases in the steady-state, despite the presence of a strong heat flux limiting upstream and enhancement downstream.

Self-similar two-electron temperature plasma expansion into vacuum

AbstractA theoretical model is developed to describe self-similar plasma expansion into vacuum with two different electron temperature distribution functions. The cold electrons are modeled with a Maxwellian distribution while the hot ones are supposed to be non-thermal obeying a kappa distribution function. It is shown that ion density and velocity profiles depend only on cold electron distribution in early stage of expansion whereas ion acceleration is mainly governed by the hot electrons at the ion front and is strongly enhanced with the proportion of kappa distributed electrons. It is also found that when the kappa index is decreasing, the critical value of temperature ratio Teh/Tec, limiting the application of quasi-neutrality, becomes larger than the $5 + \sqrt {24} \approx 9.9$ value obtained in the two-electron Maxwellian Bezzerides model [Bezzerides, B., Forslund, D. W. &amp; Lindman, E. L. (1978). Phys. Fluids21, 2179–2185].

The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study

The electro-osmotic flow of an aqueous solution of NaCl between two parallel silicon walls is studied through a molecular dynamics simulation. The objective here is to examine the dependency of the electro-osmotic flow on the surface charge density by considering the changes made in the structural properties of the electric double layer (EDL). The ion concentration, velocity profiles, and electric charge density of the electrolyte solution are investigated. Due to the partially charged atoms of the water molecules, water concentration is of a layered type near the wall. The obtained profiles revealed that an increase in the surface charge density, at low surface charges where the governing electrostatic coupling regime is Debye–Huckel, increases both the electro-osmotic velocity and the EDL thickness; whereas, a decreasing trend is observed in these two parameters in the intermediate regime. For high values of surface charge density, due to the charge inversion phenomenon, the reversed electro-osmotic flow will be generated in the channel. Results indicate that the absolute value of the reversed electro-osmotic velocity rises with an increase in the surface charge density.

Effect of the q-nonextensive electron velocity distribution on a magnetized plasma sheath

In this work, a sheath model has been developed to investigate the effect of the q-nonextensive electron velocity distribution on the different characteristics of a magnetized plasma. By using Segdeev potential method, a modified Bohm criterion for a magnetized plasma with the nonextensive electron velocity distribution is derived. The sheath model is then used to analyze numerically the sheath structure under different q, the parameter quantifying the nonextensivity degree of the system. The results show that as the q-parameter decreases, the floating potential becomes more negative. The sheath length increases at the lower values of the q-parameter due to the increase in the electron population at the high-energy tail of the distribution function. As q-parameter decreases, the effective temperature of the electrons increases which results in a more extended plasma sheath. The ion velocity and density profiles for the different nonextensivity degrees of the system reflect the gyro-motion of the ions in the presence of the magnetic field. Furthermore, the results coincide with those given by the Maxwellian electron distribution function, when q tends to 1.

Experimental Investigation of Ion Mass Dependency of Magnetic Reconnection Outflow by using High Precision Ion Doppler Spectroscopy

Doppler spectroscopy diagnostics with a new reconstruction method has been developed to evaluate local ion velocity profile of magnetic reconnection outflow. The multi-chord ion Doppler diagnostic can simultaneously measure spectral profiles of line-integrated emission from 90 chords across the plasma using three monochromators and three intensified CCD cameras. Under an assumption of axisymmetry, 2-dimensional profiles of reconnection outflow ion velocity are achieved with satisfactory accuracy by a vector-based tomography technic for the first time.

Finite Element Analysis on Multi-field Coupling of Cross-flow Nanofiltration of Polymeric Membrane

The application of nanofiltration in industrial fields is increasing rapidly in recent years, especially in drinking water treatment. Nevertheless, the mechanism of mass transport through these membranes has not yet been fully understood. And the optimal design of nanofiltration processes still faces challenges. At first, the Donnan Steric Pore Model (DSPM) is described in this paper, which is constructed on the basis of the extended Nernst-Planck equation for the prediction of the nanofiltration process of polymeric membrane. Then the DSPM model is used to characterize three kinds of membranes (AFC40, CA30 and NTR7450) for the nanofiltration of 50 mol/m(3) NaCl solution and NTR7450 membrane for the nanofiltration of NaCl and MgSO4 solution with different concentrations. The simulated results and their comparison with experimental results show that the DSPM model can effectively predict the membrane performance. And then a description of the Pores and Polarization Transport Model (PPTM) is presented, which is developed on the basis of the DSPM model, in order for characterizing cross-flow nanofiltration. The PPTM model combines the convection-diffusion-migration transport in the nanopores with the transport through the concentration polarization layer. To improve the PPTM model in the aspect of using an empirical model to describe the velocity field of solution above the membrane, the velocity profile in solution is solved by Navier-Stokes equation and continuity equation in this paper. The cross-flow nanofiltration of polymeric membrane is simulated using the finite element method, by coupling mass transfer in the membrane with ion concentration and velocity profile in solution above the membrane. By the comparison with experimental results and traditional PPTM results, it can be found that the modified method can reflect the change tendencies of ion concentration and velocity profile in solution, and their values are more in line with the values of experiments. The improved model can provide more reliable theoretical basis for the optimal design of cross-flow nanofiltration processes of polymeric membrane.

Comparison of azimuthal ion velocity profiles using Mach probes, time delay estimation, and laser induced fluorescence in a linear plasma device

We compare measurements of radially sheared azimuthal plasma flow based on time delay estimation (TDE) between two spatially separated Langmuir probes, Mach probes and laser induced fluorescence (LIF). TDE measurements cannot distinguish between ion fluid velocities and phase velocities. TDE and Mach probes are perturbative, so we compare the results against LIF, a non-perturbative, spatially resolved diagnostic technique that provides direct measurements of the ion velocity distribution functions. The bulk ion flow is determined from the Doppler shift of the Argon absorption line at 668.6139 nm. We compare results from all the three diagnostics, at various magnetic fields, which acts as a control knob for development of drift wave turbulence. We find that while Mach probes and LIF give similar profiles, TDE measurements typically overestimate the velocities and are also sensitive to the drift wave modes being investigated.

Reevaluation of the Braginskii viscous force for toroidal plasma

AbstractThe model by Braginskii [1] (Braginskii, S. I. 1965 Transport processes in plasma. In: Review of Plasma Physics, Vol. 1 (ed. M.A. Leontovich). New York, NY: Consultants Bureau, pp. 205–311) for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation, which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force, which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium, which indicates qualitative agreement between theory and measurement for impure plasma discharges with strong toroidal flow.

Electric fields and neutral winds from monostatic incoherent scatter measurements by means of stochastic inversion

[1] A new method utilizing stochastic inversion in determining the electric field and neutral wind from monostatic beam swing incoherent scatter measurements is described. The method consists of two stages. In the first stage, beam-aligned ion velocities from a chosen F region height interval and a set of subsequent beam directions are taken as measurements. The unknowns are the two electric field components and the field-aligned ion velocity profile. The solution gives the most probable values of the unknowns with error estimates. In the second stage, the measurements consist of beam-aligned ion velocities from the E region, and the electric fields given by the first inversion problem are also used as measurements. The number of applied beam directions may be greater than in the first inversion problem. This is a feasible approach since the neutral wind usually changes more slowly than the electric field. The solution of the second inversion problem gives the most probable values of the three neutral wind components. Results of the method are shown for 11 September 2005, when the European Incoherent Scatter (EISCAT) UHF radar was running in the CP2 experiment mode, which is a four-position 6 min monostatic cycle. In addition, from each beam direction a tristatic measurement at one F region range gate was made using two additional receivers. That allowed comparison between the monostatic and tristatic electric field results, which were in excellent agreement. The calculated neutral wind components were in good accordance with previous measurements during disturbed conditions from the same site.