Ion Collision Frequency Research Articles

The effects of ion-neutral collision frequency on the plasma sheath dynamics for oblique entrance of ions into the sheath

Recently it has been shown that the magnetic field has significant effects on the characteristics of ions which enter the collisionless plasma sheath with an oblique incidence angle. Here, we have investigated these effects in collisional plasma sheath. Considering the ion-neutral collision, the basic equations of fluid model in a plasma sheath have been numerically solved in the presence of an external magnetic field where the ion collision frequency has a power law dependency to the ion flow velocity. The results show that the effects of magnetic field on the plasma sheath dynamics strongly depend on the ion-neutral collision frequency and its dependency to ion flow velocity.

Development of drift-resistive-inertial ballooning transport model for tokamak edge plasmas

A new model is developed for transport driven by drift-resistive-inertial ballooning modes (DRIBMs) in axisymmetric tokamak plasmas. The model is derived using two-fluid reduced Braginskii equations in a generalized ŝ−α geometry. The unified theory includes diamagnetic effects, parallel electron and ion dynamics, electron inertia, magnetic perturbations, transverse particle diffusion, gyroviscous stress terms, electron and ion equilibrium temperature gradients, and temperature perturbations. A mixing length approximation is used to compute electron and ion thermal transport as well as particle fluxes from eigenvalues and eigenvectors of the linearized equations. The prediction for the saturation level is obtained by balancing the DRIBM growth rate against the nonlinear E×B convection. The parametric dependence of DRIBMs is investigated in systematic scans over density gradient, electron and ion temperature gradients, magnetic-q, collision frequency, magnetic shear, and Larmor radius. The DRIBM threshold is determined as a function of the collision frequency and the density and temperature gradients. The transition from DRIBM to the toroidal ion temperature gradient (ITG) mode is observed for small density gradients. For steep density gradients, the effect of ITG on DRIBM is found to be stabilizing. The transport seen in the DRIBM is of a scale that is consistent with the observed experimental anomalous transport, suggesting that the DRIBM mode could be the principle agent responsible for edge transport in Ohmic and L-mode discharges.

Electron–ion collision rates in atomic clusters irradiated by femtosecond laser pulses

In atomic clusters irradiated by femtosecond laser pulses, plasmas with high density and high temperature are created. The heating is mainly caused by inverse bremsstrahlung, i.e. determined by electron–ion collisions. In the description of the scattering of electrons on noble gas ions in such plasmas, it is important to account for the inner structure of the ions and the screening by the surrounding plasma medium which can be accomplished by using suitable model potentials. In the wide parameter range met in experiments, the Born approximation is not applicable. Instead, the electron–ion collision frequency is calculated on the basis of classical momentum transport cross sections. Results are presented for xenon, krypton and argon ions in different charge states. A comparison of these results to those for the scattering on Coulomb particles with the same charge shows an enhancement of the collision frequency. The Born approximation, however, leads to an overestimation.

Influence of collision frequency on neoclassical polarization current

A kinetic theory for the evolution of magnetic islands is considered in a tokamak plasma, in both the low (νi ≪ ϵω) and high (νi ≫ ϵω) collision frequency limits (νi is the ion collision frequency, ϵ is the inverse aspect ratio and ω is the island propagation frequency in the E × B rest frame). The calculation of the bootstrap current perturbation in the presence of a magnetic island is reviewed, and is confirmed to be independent of ω and the collision frequency regime. The neoclassical polarization current perturbation is calculated in the two collision frequency limits (within the banana regime). The result in the collisional limit is in agreement with a fluid theory. The effect of collisions in the ‘dissipation layer’ at the trapped/passing boundary is also considered, for νi ≪ ϵω. It is found that the dissipation layer provides an additional contribution to the neoclassical polarization current perturbation. Consequently, if the polarization current is stabilizing, it provides a critical island width for instability, which is found to scale as , where r is a weak logarithmic function of .

On the space-charge boundary layer inside the nozzle of a cutting torch

A numerical study of the space-charge sheath adjacent to the nozzle wall of a cutting torch is presented. The hydrodynamic model corresponds to a collision-dominated sheath and does not assume cold ions, so drift-diffusion-type equations are used. Also an improved expression for the ion-neutral momentum transfer is employed rather than the usual constant ion-mean-free-path or constant ion collision frequency approximations. Assuming a constant electron temperature in the sheath and neglecting the electron inertial term, the continuity and momentum equations for ions and electrons, together with Poisson’s equation, were solved for the electric potential, ion velocities (both normal and tangential components), and for the ion and electron densities. It was found that both the ion and electron densities present a sudden drop at the sheath-plasma edge. The ion density continues to decrease slowly inside the sheath, while the electron density presents a virtually zero value everywhere inside the sheath, the electron thermal conduction flux to the nozzle wall being negligible. These wall results thus become thermally isolated in spite of the high electron temperature in its adjacency. For a nozzle biasing voltage close to the gas breakdown, it was found that the electric field value is high, reaching a value of about 9×106 V m−1 at the exit of the nozzle wall. This value is higher than the average field value across the sheath and is on the order of the breakdown threshold value. This means that an undesired sheath breakdown could occur at the vicinities of the nozzle exit even if the average electric field across the sheath is not strong enough.

Unstable spectrum of a relativistic electron beam interacting with a quantum collisional plasma: application to the fast ignition scenario

Quantum and collisional effects on the unstable spectrum of a relativistic electron beam–plasma system are investigated through a two-fluids model. Application is made to the near target center interaction of the relativistic electron beam in the fast ignition scenario. Partial degeneracy effects are found to be negligible while the most influential factors are the beam temperature and the electron–ion collision frequency of the plasma. The introduction of the latter triggers some oblique unstable modes of much larger wavelength than the collisionless ones. Transition from the collisionless regime to the resistive one is thus documented and found discontinuous.

Rocket‐based measurements of ion velocity, neutral wind, and electric field in the collisional transition region of the auroral ionosphere

The JOULE‐II sounding rocket salvo was launched from Poker Flat Rocket Range into weak pulsating aurora following a moderate substorm at 0345 LT on 19 January 2007. We present in situ measurements of ion flow velocity and electric and magnetic fields combined with neutral wind observations derived from ground observations of in situ chemical tracers. Measured ion drifts in the 150–198 km and 92–105 km altitude ranges are consistent with × motion to within 16 m s−1 rms and with neutral wind velocity to within 20 m s−1, respectively. From these measurements we have calculated the ratio κ of the ion cyclotron and ion collision frequencies, finding κ = 1 at an altitude of 118 ± 0.3 km. Using direct measurements of ion current, we calculate the Joule heating rate and Pedersen and Hall conductivity profiles for this moderately active event and find height‐integrated values of 390 W km−2 and 0.59 and 2.22 S, respectively. We also find that these values would have errors of up to tens of percent without coincident neutral wind measurements, and presumably more so during more active conditions. Ion flow vectors were measured at a rate of 125 s−1; however, no significant fluctuations were observed at spatial/temporal scales below ∼350 m and 0.5 s. Observational limits were 5.5 m and 0.016 s.

Fluid model of current-carrying and magnetized fully ionized plasma confined by two coaxial cylinder electrodes

The steady state of a quasi-neutral bulk of a cylindrical, current-carrying, fully ionized, collisional plasma confined by two coaxial metallic cylinders was analysed both analytically and numerically, using a magneto-hydrodynamic model. The plasma is magnetized by a uniform magnetic field, imposed parallel to the wall. The analysis did not assume Boltzmann equilibrium for the electrons, and the dependence of the mean electron–ion collision frequency on the varying plasma density was considered. The first integral of the model equations was found to be an algebraic relation between the self-consistent electric potential and the ion radial velocity. Radial distributions of characteristic plasma parameters (electric potential, density, velocities and currents) in the quasi-neutral region were calculated, and their dependences on the magnetic field strength, voltage and current were analysed. Trial and error was used in numerical calculations to choose the ‘initial’ ion radial velocity at the inner cylinder so that boundary conditions at the outer cylinder were satisfied. The results show that the variation in the radial ion velocity determined is mainly by competition between the Amperian force, which accelerates the ions, and the centrifugal force, which decelerates them. The competition may lead to non-monotonic variation in the ion velocity and density with the radial coordinate, depending on the electric current, while the electric potential in the plasma bulk is a monotonic function of the radial coordinate. The plasma rotates around the system axis with the frequency proportional to the electric current to the outer wall. The plasma azimuthal velocity calculated taking into account the ion viscosity is a non-linear function of the distance from the system axis. The calculated dependence of the current to the wall from the potential drop in the plasma bulk shows a monotonic transition from ion to electron current to the wall by increasing the voltage from negative to positive magnitudes. The current decreases with the increase in the magnetic field.

Systematic Characterization of Carbon Nanotubes Functionalized in CF4 Plasma

We functionalize the surface of carbon nanotubes (CNTs) with different numbers of graphitic layers in a capacitively driven radio-frequency (RF) CF4 plasma. We investigate the resulting structural and bonding properties by transmission electron microscopy (TEM), Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS). XPS analysis shows that carbon-to-fluorine bonds form on the CNTs and the ratio of the intensity of the F 1s peak to that of the C 1s peak greatly depends on RF power. TEM analysis clearly shows that fluorination is initiated at the outermost graphitic layer and proceeds to the inner layers of CNTs with increasing RF power, whereas the depth of fluorination is limited to the surface area. Therefore, we suggest that fluorination in the CF4 plasma at low RF powers involves attaching fluorine atoms to carbon atoms of graphitic layers. We also discuss the correlation between the number of graphitic layers in a CNT and fluorination resistance, and show that an increase in the number of graphitic layers increases fluorination resistance. By estimating primary plasma parameters with a Langmuir probe, we conclude that ion density, i.e., the collision frequency of plasma ions with the surface of CNTs, is closely related to the rate of plasma fluorination.

A magnetized plasma sheath where the ion collision frequency depends on ion flow velocity

Recently some correlative works have been done to investigate the effects of collisions between ion and neutral gas atoms on the characteristics of plasma sheath in an external magnetic field. In general, the momentum transferring cross section (and thus the ion collision frequency) has a power law dependence on the ion flow velocity in the depth direction. Usually in the literature, constant collision frequency and constant mean free path are treated. Here, by using a collisional fluid model, we investigate the characteristics of a magnetized plasma sheath where the ion cross section depends on the ion flow velocity. The numerical calculations show that the effects of collisions on ion characteristics are more powerful when the momentum transferring cross section is constant. However, some parameters such as the electron density distribution are independent of this dependence.

Experimental characterization of a density peak at low magnetic fields in a helicon plasma source

We investigated characteristics of a density peak observed in a magnetic field B0 lower than 100 G in the case of using helicon plasma sources with particular wavelength. For B0 > 30 G, the antenna launches an electromagnetic wave as a slow wave, the phase velocity of which becomes close to the electron thermal velocity under the density-peak condition for various gas pressures. The Landau damping frequency is higher than the electron–neutral and the electron–ion collision frequencies, which indicates that the wave produces the plasma via Landau damping at low B0. The wavelengths estimated from the density ne and B0 for the density peaks agree with those of the electromagnetic field generated by helicon antennas of various lengths. The measured density is found to vary under the condition of the agreement between wavelengths of the propagating wave and the antenna-excited field during the density increase. One of the causes of the density peak appearing as a function of B0 is considered to be the wavelength variation and the corresponding change of phase velocity of the slow wave which is enabled to propagate in the plasma by the introduction of B0.

Fluid theory of magnetized plasma dynamics at low collisionality

Finite Larmor radius (FLR) fluid equations for magnetized plasmas evolving on either sonic or diamagnetic drift time scales are derived consistent with a broad low-collisionality hypothesis. The fundamental expansion parameter is the ratio δ between the ion Larmor radius and the shortest macroscopic length scale (including fluctuation wavelengths in the absence of small scale turbulence). The low-collisionality regime of interest is specified by assuming that the other two basic small parameters—namely, the ratio between the electron and ion masses and the ratio between the ion collision and cyclotron frequencies—are comparable to or smaller than δ2. First significant order FLR equations for the stress tensors and the heat fluxes are given, including a detailed discussion of the collisional terms that need be retained under the assumed orderings and of the closure terms that need be determined kinetically. This analysis is valid for any magnetic geometry and for fully electromagnetic nonlinear dynamics with arbitrarily large fluctuation amplitudes. It is also valid for strong anisotropies and does not require the distribution functions to be close to Maxwellians. With a subsidiary small-parallel-gradient ordering for large-aspect-ratio toroidal plasmas in a strong but weakly inhomogeneous magnetic field, a new system of reduced two-fluid equations is derived, rigorously taking into account all the diamagnetic effects associated with arbitrary density and anisotropic temperature gradients.

Stability of the lower hybrid instability excited by longitudinal currents in a collisional, multi-ion plasma

We have investigated the stability of the lower hybrid wave in a collisional plasma containing hydrogen and positively and negatively charged oxygen ions. The collisions of all the species in the plasma have been considered. The electrons, streaming parallel to the magnetic field, can excite the instability if their drift velocity exceeds the parallel phase velocity of the wave. This is true for both the weakly as well as the strongly collisional cases. If the ion collisions are neglected, the growth/damping rate depends on the electron collision frequency and is modified by a factor dependent directly on the number densities and square of the charges on the oxygen ions and inversely on the masses of these ions. Ion collisions, however only damp the wave; this damping being dependent also on the ion collision frequencies, in addition to the above dependencies. We find that the dispersion relation in the low collisional limit can account for lower hybrid waves in the observed frequency range.

Edge turbulence in RFX-mod virtual-shell discharges

In the Reversed Field Pinch eXperiment RFX-mod a Gas Puffing Imaging Diagnostic (GPID) is used to investigate the dynamical structure of plasma edge turbulence. The GPID measures the radiation emitted from He gas puffed in H discharges and allows the investigation of edge plasma properties with high time and space resolution at high plasma current during the entire discharge. The characterization of edge turbulence has been carried out in terms of power spectrum, cross-correlation and toroidal velocity of structures. The scaling of such velocity with the density corresponds to different values of the dimensionless ratio νci/νei (ion cyclotron frequency/electron–ion collision frequency) ranging from below to above unity. The toroidal characteristic length of intermittent structures at different time scales has been determined by applying the conditional average technique on the structures identified by the continuous wavelet transform. These lengths are in the range 15–45mm, while the number of structures increases with the electron density, the propagation velocity, opposite to the plasma current, decreases with the density and saturates at −20km/s.

Viscous relaxation of drift-Alfvén waves in tokamaks and its application for triggering improved confinement regimes

Viscous damping of the drift-Alfvén modes in tokamaks and its application for triggering improved confinement regimes are considered. It is shown that these waves are effectively damped by the neoclassical viscosity with the upper limit for their frequency ω equal to the collision frequency of slow ions νi∕ϵ, where ϵ is the inverse aspect ratio. Quasistationary plasma poloidal and toroidal velocities and current drive produced by damping of these waves are estimated. Evaluations of the viscosity effects on the Alfvén waves which were induced by the dynamic ergodic divertor in the Tokamak Experiment for Technology Oriented Research tokamak [K. H. Finken et al., Phys. Rev. Lett. 94, 015003 (2005)] are made.

Weak effect of ion cyclotron acceleration on rapidly chirping beam-driven instabilities in the National Spherical Torus Experiment

The fast-ion distribution function in the National Spherical Torus Experiment is modified from shot to shot while keeping the total injected power at ∼2 MW. Deuterium beams of different energy and tangency radius are injected into helium L-mode plasmas, producing a rich set of instabilities, including compressional Alfvén eigenmodes, toroidicity-induced Alfvén eigenmodes (TAE), 50–100 kHz instabilities with rapid frequency sweeps or chirps, and strong, low frequency (10–20 kHz) fishbones. The experiment was motivated by a theory that attributes frequency chirping to the formation of holes and clumps in phase-space. In the theory, increasing the effective collision frequency of the fast ions that drive the instability can suppress frequency chirping. In the experiment, high-power (≲3 MW) high harmonic fast wave (HHFW) heating accelerates the fast ions in an attempt to alter the nonlinear dynamics. Steady-frequency TAE modes diminish during the HHFW heating but there is little evidence that frequency chirping is suppressed.

Measurement of the flow velocity in unmagnetized plasmas by counter propagating ion-acoustic waves

The diffusion velocity of an inhomogeneous unmagnetized plasma is measured by means of the phase velocities of ion-acoustic waves propagating along and against the direction of the plasma flow. Combined with the measurement of the plasma density distributions by usual Langmuir probes, the method is applied to measure the ambipolar diffusion coefficient and effective ion collision frequency in inhomogeneous plasmas formed in an asymmetrically discharged double-plasma device. Experimental results show that the measured flow velocities, diffusion coefficients, and effective collision frequencies are in agreement with ion-neutral collision dominated diffusion theory.

A modeling study of ionospheric conductivities in the high‐latitude electrojet regions

It is important to accurately determine the ionospheric conductivities for a better estimation of energy deposition in the upper atmosphere, particularly at high latitudes. It is a common practice to assume that enhancements in the conductivities are caused by solar radiation and particle precipitation, which can be regarded as external origins. However, little attention has been paid to effects caused by the presence of electrojet currents themselves. We call this effect an internal origin for influencing the ionospheric conductivities. The presence of electrojet current changes the conductivities, and, in turn, the already changed conductivities modify the current systems. That is, a feedback process is expected to take place in magnetosphere‐ionosphere coupling current systems. We use a one‐dimensional high‐latitude ionospheric model in which the continuity equations, as well as momentum and energy equations, are solved self‐consistently to study the conductivities in auroral regions where electrojets exist. The heating effect from the Farley‐Buneman instability, which possibly occurs in the electrojet regions, is considered. Electrojet‐related joule heating and frictional heating are also taken into account. Thermal processes are analyzed in response to the electrojet current. As a result of changes in the thermal structure, we demonstrate the response of the conductivities due to changes in the chemical reaction rate, which results in a higher electron density. The response of altitude profiles of the conductivities is determined by changes in the collision frequency of ions and electrons with neutral components, while an enhancement in the conductance is mainly caused by the electron density. The results show that both the Hall and Pedersen conductances, i.e., the height‐integrated conductivities, increase significantly. The ratio between Hall and Pedersen conductances also changes considerably.

Modeling of metal ablation induced by ultrashort laser pulses

Ablation of metal targets by femtosecond laser pulses is studied numerically by using a one-dimensional hydrodynamic model. The model describes the absorption of laser radiation, electronic heat conduction, electron–phonon and electron–ion energy exchange and material motion. The temperature dependencies of heat capacities, thermal conductivities and electron–ion collision frequencies are taken into account. The ablation mechanisms are investigated in the intermediate laser fluence range, which is typical for surface processing applications. The employed hydrodynamic model shows that the ablation is driven by a total pressure gradient, which induces a compression (shock) wave propagating into the bulk and an unloading (rarefaction) wave leading to the material expansion. A phenomenon similar to the spallation is observed at fluences close to the ablation threshold. In addition, a fast overheating of the liquid material is observed, which may result into a decomposition of the material to a mixture of gas and droplets. The calculated initial conditions for plasma plume expansion are presented.

Fast type‐I waves in the equatorial electrojet: Evidence for nonisothermal ion‐acoustic speeds in the lower E region

There is plenty of evidence to suggest that the phase velocity of large amplitude irregularities produced by the modified two‐stream and the gradient‐drift instabilities are the same as the threshold speed, namely, the nominal ion‐acoustic speed in the modified two‐stream case. In this context, it is rather puzzling to note that the phase velocity of type‐I waves in the equatorial electrojet is known to easily exceed 400 m/s during strong electrojet conditions. This is puzzling because the ion‐acoustic speed of the medium is expected to be 100 m/s slower than these observations. Explaining the observations as an increase in the nominal ion‐acoustic speed through much higher neutral temperatures than expected or through electron heating by plasma waves is problematic at best. The first explanation violates everything we know about the neutral atmospheric temperature near the mesopause, while in the latter case, we only have to recall the emerging view that electron heating is done, at high latitudes, by parallel wave fields and that there is no evidence for the existence of such fields in the equatorial case. By contrast, we show that, contrary to what is normally assumed, electron thermal fluctuations cannot be neglected in the theoretical treatment of the instability when the ion collision frequency becomes large compared to the wave frequency and the wave aspect angle is small. These electron thermal fluctuations are caused by electron adiabatic heating and cooling effects related to the wave dynamics. When the electron thermal fluctuations are included in the calculations the derived instability threshold speeds match the upper limit reached by the observations. The increase becomes detectable at 108 km altitude and increases rapidly with decreasing altitude to become roughly 1.5 times as large as the isothermal ion‐acoustic speed below 100 km altitude. We show in this paper that the new threshold speed provided by the nonisothermal threshold calculations provides an excellent match for the largest vertical type‐I phase speeds that were observed during a very strong daytime electrojet event.