Initial Ion Density Research Articles

Study of the Pure Deuterium Fuel Burning Rate in Z-Pinch Devices with Magneto-Inertial Confinement

The burning rate of pure deuterium (D-D) fuel in Z-pinch devices with magneto-inertial confinement was studied in this paper. The system of particle and energy balance equations for D-D fuel burning with a mixed D-T-3He fusion cycle (D-D, D-T, and D-3He reactions) was solved numerically, taking into account the densities of all reacted and produced ions (protons, deuterium, tritium, helium-3, and alpha-particles). The obtained results indicate that effective D-D fusion in Z-pinch devices can be successfully achieved under conditions of a hot, dense plasma with an initial temperature of 31 keV or higher. The initial ion density of deuterium and electron density were equal due to quasi-neutrality condition of the plasma, with both reaching 1024 m−3. Although the obtained results show that the burning rate of D-D fuel is approximately 2.3 times slower and its power density notably lower than that of D-T fuel, pure deuterium plasma can be considered as a promising alternative to well-studied deuterium–tritium plasma, with potential future applications in magneto-inertial fusion (MIF) facilities.

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

Abstract For investigating efficiently the stagnation kinetic-process of Z-pinch, we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used. In our algorithm, the electric field in z-direction is solved by a parallel electrode-plate model, the azimuthal magnetic field is obtained by Ampere’s law, and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field. In simulation results of 2 MA deuterium plasma shell Z-pinch, the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation, and the plasma current also closely aligns with the external current. The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained. The main kinetic characteristic of electron motion is thermal equilibrium and oscillation, which should be oscillated around the ions, while that of ion motion is implosion inwards. In the region of stagnation radius, the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing, while of electrons is basically the equilibrium state. When the initial ion density and current peak are not high enough, the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

Behavior of ions from medium-density plasma in electric field created by plate–grid–plate geometry

The behavior of the ions from a medium-density plasma in an electric field created by the plate–grid–plate geometry was simulated with a two-dimensional one-fluid model in which electrons are assumed to be in thermal equilibrium, and the accuracy of the model was verified by comparing with other research results. The results show that the wire mesh parameters of the grid, including the wire mesh diameter and the spacing between the two wires of the grid, have an important influence on the ion extraction time and the ion collection ratio of the cathode plate. The blocking rate of the grid obtained by the theoretical simulation is almost equal to the geometrical blocking rate, and it is minimally affected by the initial ion density. These results can provide guidance for the optimization of wire mesh parameters of the grid, especially for the ion extraction and collection from a pulsed plasma.

Modification of the Alfvén wave spectrum by pellet injection

Alfvén eigenmodes driven by energetic particles are routinely observed in tokamak plasmas. These modes consist of poloidal harmonics of shear Alfvén waves coupled by inhomogeneity in the magnetic field. Further coupling is introduced by 3D inhomogeneities in the ion density during the assimilation of injected pellets. This additional coupling modifies the Alfvén continuum and discrete eigenmode spectrum. The frequencies of Alfvén eigenmodes drop dramatically when a pellet is injected in JET. From these observations, information about the changes in the ion density caused by a pellet can be inferred. To use Alfvén eigenmodes for MHD spectroscopy of pellet injected plasmas, the 3D MHD codes Stellgap and AE3D were generalised to incorporate 3D density profiles. A model for the expansion of the ionised pellet plasmoid along a magnetic field line was derived from the fluid equations. Thereby, the time evolution of the Alfvén eigenfrequency is reproduced. By comparing the numerical frequency drop of a toroidal Alfvén eigenmode (TAE) to experimental observations, the initial ion density of a cigar-shaped ablation region of length 4 cm is estimated to be m−3 at the TAE location (). The frequency sweeping of an Alfvén eigenmode ends when the ion density homogenises poloidally. Modelling suggests that the time for poloidal homogenisation of the ion density at the TAE position is ms for inboard pellet injection, and ms for outboard pellet injection. By reproducing the frequency evolution of the elliptical Alfvén eigenmode (EAE), the initial ion density at the EAE location () can be estimated to be m−3. Poloidal homogenisation of the ion density takes 2.7 times longer at the EAE location than at the TAE location for both inboard and outboard pellet injection.

Energy of electrons at the interaction of femtosecond laser with argon nanocluster

The interaction of intense femtosecond laser pulses with argon nanoclusters is studied using nanoplasma model. Based on the dynamic simulations, ionisation process, heating, and expansion of an argon nanocluster irradiated by an intense femtosecond laser pulse are investigated. The analytical calculation provides ionisation rate for different mechanisms and time evolution of hydrodynamic pressure for various pulse shapes. In this work, the dependence of laser intensity, initial ion density and pulse shape on the electron pressure, the density of electrons and electron temperature are presented. It is noticed that the negative and positive chirped pulses and initial ion density implement some modifications on the current calculation models. It is found that reducing the initial ion density at a laser intensity of about $$1\times 10^{16} \, \hbox {W}/hbox{cm}^{2}$$ increases the energy of electrons. By applying a positive chirp laser pulse during interaction with nanoclusters, both electron density and ultimately electron pressure are improved by about 22%.

The evolution process of nonlinear cold-electron-plasma oscillations against fixed periodic ion density cavities

Using the one-dimensional Vlasov-Poisson simulation method, the nonlinear cold-electron-plasma oscillations against a fixed periodic ion background are studied. It is shown that a gradual loss of the phase coherence in the excited Langmuir wave dynamics occurs in such plasmas leading to wave-breaking at arbitrary low wave amplitudes. Not only the salient features of a steepening of the electric field gradient and large electron density peaks caused by the presence of the ion cavities have been found but also the change of phase-mixing and burst time with the initial ion density perturbation and electron temperature has been studied. The evolution processes of the electron distributions in phase space, especially the electron distribution at the phase-mixing and burst time, have been studied.

Three-dimensional kinetic modeling of streamer propagation in a nitrogen/helium gas mixture

A fully resolved kinetic model (particle-in-cell and direct simulation Monte Carlo for particle/photon collisions) of a near atmospheric pressure ionization wave is presented here. Fully resolving the required numerical spatial (sub-μm) and temporal scales (tens of fs) for atmospheric pressure discharges in three-dimensions is still a challenging task on modern super computers. To keep the overall problem tractable, the total number of elements are reduced by only simulating a 10° wedge rather than a full 360° geometry. The ionization wave is generated in a needle-plane configuration with a gap size of 250 μm and a background of nitrogen and helium gas. A voltage of 1500 V is applied to the anode and an initial electron and ion density of 109 cm−3 is seeded in a region near the anode electrode tip and extending towards the cathode. As these initial electrons are swept away, photoionization and photoemission create new electrons and allow the ionization front to propagate towards the cathode. Results from the 90% N2, 10% He discharge indicate that photoionization has minimal impact on plasma formation processes and cathode photoemission is the dominant mechanism for new electrons. In the 90% He, 10% N2 discharge case, however, photoionization likely has an impact as the observed locations of photoionization occur far enough away from the ionization front to allow for sufficient avalanche processes that contribute to the propagation of the ionization wave. Additionally, the electron energy distribution functions in the 90% He, 10% N2 case indicate that there is less energy loss to the low lying molecular N2 electronic states as well as the vibrational and rotational modes. This leads to higher electron energies and faster plasma development times of ∼0.4 ns for the 90% He, 10% N2 case, and ∼1.5 ns for the 90% N2, 10% He case. In addition to analysis of the ionization wave results, the overall challenges associated with simulations near atmospheric pressure discharges in three-dimensions are discussed, including the limitations of the 10° wedge that produces, at least qualitatively, minimal 3D effects.

Impurity transport caused by blob and hole propagations

It is for the first time demonstrated by means of the three-dimensional electrostatic particle-in-cell simulation that the impurity ion transport caused by blob and hole propagations might not be negligible as compared with other types of transport. The simulations have shown that the impurity ion density profile in the blob/hole structure becomes a dipolar profile and the dipolar profile of the impurity ion density propagates with the blob/hole. Furthermore, the simulations in which the initial impurity ion density has a radial gradient have revealed that the estimated effective radial diffusion coefficient for impurity ions by a single blob/hole is comparable to the Bohm diffusion coefficient.

Collisionless expansion of pulsed radio frequency plasmas. I. Front formation

The dynamics during plasma expansion are studied with the use of a versatile particle-in-cell simulation with a variable neutral gas density profile. The simulation is tailored to a radio frequency plasma expansion experiment [Schröder et al., J. Phys. D: Appl. Phys. 47(5), 055207 (2014)]. The experiment has shown the existence of a propagating ion front. The ion front features a strong electric field and features a sharp plasma potential drop similar to a double layer. However, the presented results of a first principle simulation show that, in general, the ion front does not have to be entangled with an electric field. The propagating electric field reflects the downstream ions, which stream with velocities up to twice as high as that of the ion front propagation. The observed ion density peak forms due to the accumulation of the reflected ions. The simulation shows that the ion front formation strongly depends on the initial ion density profile and is subject to a wave-breaking phenomenon. Virtual diagnostics in the code allow for a direct comparison with experimental results. Using this technique, the plateau forming in the wake of the plasma front could be indirectly verified in the expansion experiment. Although the simulation considers profiles only in one spatial dimensional, its results are qualitatively in a very good agreement with the laboratory experiment. It can successfully reproduce findings obtained by independent numerical models and simulations. This indicates that the effects of magnetic field structures and tangential inhomogeneities are not essential for the general expansion dynamic. The presented simulation will be used for a detailed parameter study dealt with in Paper II [Schröder et al., Phys. Plasma 23, 013512 (2016)] of this series.

Effect of space charge on the ion mobility spectrum with two close lines

In ion mobility spectrometers, space-charge field has a significant effect on the diffusion and drift of ions, if the initial ion density is higher than 106 cm−3. Owing to this effect, the ion distribution in time and space cannot be described by a Gaussian curve any longer. These non-Gaussian ion distributions change the shape of the spectra not only quantitatively, but also qualitatively, which can lead to a misinterpretation of the spectra.

Ionic Distribution in Plasma for the Process of Electron-Beam Physical Vapor Deposition

This paper investigates ionic distribution generated by electron beam (EB) during Physical Vapor Deposition (PVD). EB-PVD has a wide range of applications in thermal barrier coatings (TBCs) due to favorable characteristics compared with other coating processes. EB-PVD is an important material coating method that utilizes electron beams as heat sources to evaporate materials, which are then deposited on a substrate. Therefore EB-induced ionic distribution dominates the quality and thickness of the final coating on the substrate. Assuming the EB-generated plasma to be only a function of radial direction, the steady-state equations of continuity and motion combined with Posson’s equation were utilized to analyze the plasma distributions along the radial direction. The available experimental data are also used to validate the model. The results show that the coating efficiency can be improved by decreasing the ratio of the electron thermal energy to the initial ion energy and increasing the ratio of the initial ion density to the initial electron density. The uniformity of coating can be achieved by reducing the initial ion density.

Numerical simulation of back discharge ignition

Back discharge refers to any discharges initiated at or near a dielectric layer covering a passive electrode (Czech et al 2011 Eur. Phys. J. D 65 459–74). Back discharge activity is commonly observed in electrostatic precipitators. This study aims to contribute to increasing the fundamental understanding of back discharge phenomena by using a plasma fluid model. The modelling strategy only considers the region of back discharge development as a first approach, and the numerical simulation is complemented by an experimental study. Back discharge ignition is studied with a pinhole of radius 100 µm set in a dielectric layer. First, we have considered the criterion for back discharge ignition from an electrostatic point of view, and the numerical results confirm the major role of the surface charge density deposited on the dielectric layer. Then the dynamics of back discharge in the ‘onset-streamer’ regime (Masuda and Mizuno 1977/1978 J. Electrostat. 2 375–96) is described: the discharge ignites inside the pinhole, develops outside as a cathode-directed ionizing wave, before stopping. This regime is characterized by a current pulse and the corresponding optical emission. Results obtained in experiments and simulations are in good agreement. Furthermore, this discharge regime is independent of the pinhole radius (ranging from 75 to 150 µm) despite a change in the discharge shape. Finally, an increase in the initial negative ion density or Laplacian electric field is found to be responsible for the transition from ‘onset-streamer’ to ‘space streamer’ regime, which corresponds well with experimental observations.

Comparison of high‐altitude production and ionospheric outflow contributions to O+ loss at Mars

AbstractThe Mars Test Particle model is used (with background parameters from a magnetohydrodynamic code) to simulate the transport of O+ ions in the near‐Mars space environment to study the source processes responsible for ion escape. The MHD values at this altitude are used to inject an ionospheric outflow source of ions for the Mars Test Particle (MTP). The resulting loss distributions (in both real and velocity space) from this ionospheric source term are compared against those from high‐altitude ionization mechanisms, in particular photoionization, charge exchange, and electron impact ionization, each of which has its own source regions, albeit overlapping. For the nominal MHD settings, this ionospheric outflow source contributes only 10% to the total O+ loss rate at solar maximum, predominantly via the central tail region. This percentage has very little dependence on the initial temperature, but a change in the initial ion density or bulk velocity directly alters this loss through the central tail. A density or bulk velocity increase of a factor of 10 makes the ionospheric outflow loss comparable in magnitude to the loss from the combined high‐altitude sources. The spatial and velocity space distributions of escaping O+ are examined and compared for the various source terms to identify features specific to each ion source mechanism. For solar minimum conditions, the nominal MHD ionospheric outflow settings yield a 27% contribution to the total O+ loss rate, i.e., roughly equal to any one of the three high‐altitude source terms with respect to escape.

Investigation of ion–ion-recombination at atmospheric pressure with a pulsed electron gun

For future development of simple miniaturized sensors based on pulsed atmospheric pressure ionization as known from ion mobility spectrometry, we investigated the reaction kinetics of ion-ion-recombination to establish selective ion suppression as an easy to apply separation technique for otherwise non-selective ion detectors. Therefore, the recombination rates of different positive ion species, such as protonated water clusters H(+)(H(2)O)(n) (positive reactant ions), acetone, ammonia and dimethyl-methylphosphonate ions, all recombining with negative oxygen clusters O(2)(-)(H(2)O)(n) (negative reactant ions) in a field-free reaction region, are measured and compared. For all experiments, we use a drift tube ion mobility spectrometer equipped with a non-radioactive electron gun for pulsed atmospheric pressure ionization of the analytes. Both, ionization and recombination times are controlled by the duty cycle and repetition rate of the electron emission from the electron gun. Thus, it is possible to investigate the ion loss caused by ion-ion-recombination depending on the recombination time defined as the time delay between the end of the electron emission and the ion injection into the drift tube. Furthermore, the effect of the initial total ion density in the reaction region on the ion-ion-recombination rate is investigated by varying the density of the emitted electrons.

Calculation of Ion Equilibrium Temperature in Ultracold Neutral Plasmas

We provide a fast iteration method to calculate the ion equilibrium temperature in an ultracold neutral plasma (UNP). The temperature as functions of electron initial temperature and ion density is obtained and compared with the recent UNP experimental data. The theoretical predictions agree with the experimental results very well. The calculated ion equilibrium temperature by this method can be applied to study the UNP expansion process more effectively.

Recombination during expansion of ultracold plasma

Signals of ultracold plasma are observed by two-photon ionization of laser-cooled caesium atoms in a magneto-optical trap. Recombination of ions and electrons into Rydberg atoms during the expansion of ultracold plasma is investigated by using state-selective field ionization spectroscopy. The dependences of recombination on initial electron temperature (1–70 K) and initial ion density (∼1010 cm−3) are investigated. The measured dependence on initial ion density is N1.547+0.004 at a delay time of 5 μs. The recombination rate rapidly declines as initial electron temperature increases when delay time is increased. The distributions of Rydberg atoms on different values of principal quantum number n, i.e. n = 30–60, at an initial electron temperature of 3.3 K are also investigated. The main experimental results are approximately explained by the three-body recombination theory.

Nonlinear quantum dust acoustic waves in nonuniform complex quantum dusty plasma

The quantum hydrodynamic model for plasmas is employed to study the dynamics of the nonlinear quantum dust acoustic (QDA) wave in a nonuniform quantum dusty plasma (QDP). Through the reductive perturbation technique, it is shown that the quantum hydrodynamical basic equations describing the nonlinear QDA waves yield a modified Korteweg-de Veries equation with slowly varying coefficients in the system inhomogeneity. Applying generalized expansion method, it is found that the system admits only rarefactive solitons. The properties of the solitons such as the velocity, the amplitude and the width of the nonlinear QDA waves are analyzed using appropriate choice for initial ion and electron density numbers. For the homogeneous QDP, no critical value is found. Because of the system inhomogeneity, a new criticality is found forcing with the usage of new stretching coordinates. A higher evolution equation with third-order nonlinearity is derived at the critical values. The solution of the latter equation admits rarefactive shock wave attached with an amplitude factor. The present investigations should be useful for researches on astrophysical plasmas as well as for ultra small micro- and nano-electronic devices.

Influence of a finite initial ion density gradient on plasma expansion into a vacuum

The influence of a finite initial ion density gradient on a plasma expansion into a vacuum is studied with a numerical model that takes into account the charge-separation effects and assumes a Boltzmann equilibrium for the electrons. The cases of a semi-infinite plasma and of a finite plasma slab are treated. In both cases it is shown that the finite initial ion density gradient of the plasma surface leads to two phases in the plasma expansion, separated by a wave breaking of the ion flow. An ion front forms after the wave breaking and, in the semi-infinite plasma case, the plasma expansion becomes closer and closer to the initially sharp boundary case, the maximum ion velocity increasing logarithmically with time. In the finite plasma slab case, the energy conservation has to be taken into account, the thermal electron energy being progressively converted into the kinetic energy of the ions. When the initial ion density scale length lss is larger than a few percent of the total plasma slab width, the final maximum ion velocity decreases with lss.

Experimental study and computer simulations of the implantation of laser plasma ions in pulsed electric fields

Results are presented from experimental studies of pulsed plasma flows generated by nanosecond laser pulses with an intensity of 7 × 108 W/cm2 from a solid-state target in a strong electric field. The current pulses through the laser target and the depth distributions of the iron ions implanted in a silicon substrate to which a negative high-voltage pulse was applied are measured. The physical processes occurring in laser plasma with an initial iron ion density of 6 × 1010 cm−3 are simulated numerically by the particle-in-cell method for different delay times and different shapes of the accelerating high-voltage pulse. The model developed allows one to calculate the ion flows onto the processed substrate, the electron flows onto the target, and the energy spectra of the implanted ions. The results from computer simulations are found to be in good agreement the experimental data.

Influence of grid and target radius and ion–neutral collisions on grid-enhanced plasma source ion-implantation process

Grid-enhanced plasma source ion implantation (GEPSII) is a newly proposed technique for inner surface modification of materials with cylindrical geometry. In this paper, a collisional fluid model is used to investigate the ion sheath dynamics between the grid electrode and the inner surface of a cylindrical bore during the GEPSII process. Assuming the initial ion density along the radial direction is not uniform but determined by diffusion mechanisms, the effects of grid electrode radius, target radius and ion–neutral collisions on the ion dose and impact energy are investigated by solving fluid equations for ions coupled with Boltzmann assumption for electrons and Poisson's equation. The results show that small gap distance between grid electrode and target is favourable to increase the ion dose and impact energy on the target. In addition, ion–neutral collisions can reduce both the ion dose and impact energy.