Thermal Motion Of Ions Research Articles

Kinetic ion effect on geodesic acoustic Alfvén modes in tokamaks

Using a quasitoroidal set of coordinates with coaxial circular magnetic surfaces, the Vlasov equation is solved for collisionless plasmas, and the dielectric tensor is found for large aspect ratio tokamaks in a low frequency band. Taking into account q-profile and charge separation parallel electric field, it is found that the Alfven wave continuum is deformed by ion geodesic effects producing continuum minimum at the rational magnetic surfaces. Low frequency geodesic ion induced Alfven waves are found below the continuum minimum where collisionless damping has a gap for Maxwell distribution. In kinetic approach, the ion thermal motion defines the geodesic effect but the mode frequency is strongly corrected due to parallel motion of electrons.

Effects of bound electrons and radiation on shock Hugoniot

Hydrodynamic flow of materials, initiated by shock waves, is determined by their equation of state (EOS). For comparatively weak shocks, the zero-temperature isotherm and thermal motion of ions, mainly, determine the EOS. However, in processes involving high energy density, as in inertial confinement fusion, astrophysical phenomena, nuclear explosion, etc., very strong shocks $(Pg\text{few}\text{ }\text{megabars},\phantom{\rule{0.3em}{0ex}}Tg\text{few}\text{ }\text{eV})$ are encountered. Such shocks give rise to many thermal effects leading to dissociation of molecules, ionization of electrons, radiation emission, etc., in addition to the quantum-mechanical pressure ionization in materials. Therefore, hydrodynamics due to strong shocks crucially depend on the behavior of electrons and the radiation emitted by the electrons. This paper aims at developing a simple but quantitative model of electronic binding in plasmas and its effects on compressibility of materials. An improved version of the screened hydrogenic model is developed for this purpose. The effect of radiation emission is incorporated using Stefan-Boltzmann law. The Hugoniot of various elements such as Al, Be, Fe, etc., are, then, computed. These are in excellent agreement with those obtained using sophisticated self-consistent field calculations, and the oscillations in Hugoniot are shown to be due to ionization of electrons from different shells. Shell effects are also reflected in the variation of electronic specific heat with temperature and the relation between shock velocity and fluid velocity. Further, at very high temperature and pressure, equilibration between radiation and matter increases the compressibility of materials. The limiting compression of all materials, via a strong shock, is found to be 7 unlike 4, which is the limit for free-electron gas or ideal monoatomic gas. The model reported here can be employed in lieu of Thomas-Fermi-type theories used in global EOS packages such as quotidian equation of state (QEOS).

Sheath analysis in collisional electronegative plasmas with finite temperature of positive ions

The sheath which occurs in front of a plane metallic surface immersed in an electronegative plasma is analysed taking into account the positive ion collisions and thermal motion. Collisions do not affect the equations of the sheath but have a significant influence on the initial conditions, which are obtained from the plasma solution. The combined influence of collisions and positive ion thermal motion on the sheath, the sheath thickness, the positive ion saturation current and the floating potential is analysed.

Reflection of Solitons at Critical Density of Negative Ions: Contribution of Thermal and Gyratory Motions of Ions

On the basis of appropriate modified Korteweg-deVries (mKdV) equation derived for three cases of nn0 ne0 together with nn0 ne0.

Relic Crystal-Lattice Effects on Raman Compression of Powerful X-Ray Pulses in Plasmas

Powerful x-ray pulses might be compressed to even greater powers by means of backward Raman amplification in ultradense plasmas produced by ionizing condensed matter by the same pulses. The pulse durations contemplated are shorter than the time for complete smoothing of the crystal lattice by thermal motion of ions. Although inhomogeneities are generally thought to be deleterious to the Raman amplification, the relic lattice might, in fact, be useful for the Raman amplification. The x-ray frequency band gaps can suppress parasitic Raman scattering of amplified pulses, while enhanced dispersion of the x-ray group velocity near the gaps can delay self-phase-modulation instability, thereby enabling further amplification of the x rays.

Soliton propagation in an inhomogeneous plasma at critical density of negative ions: Effects of gyratory and thermal motions of ions

The effects of gyratory and thermal motions of ions on soliton propagation in an inhomogeneous plasma that contains positive ions, negative ions, and electrons are studied at a critical density of negative ions. Since at this critical negative ion density the nonlinear term of the relevant Korteweg–deVries (KdV) equation vanishes, a higher order of nonlinearity is considered by retaining higher-order perturbation terms in the expansion of dependent quantities together with the appropriate set of stretched coordinates. Under this situation, time-dependent perturbation leads to the evolution of modified KdV solitons, which are governed by a modified form of the KdV equation that has an additional term due to the density gradient present in the plasma. On the basis of the solution of this equation and obliquely applied magnetic field, the effects of gyratory and thermal motions of ions are analyzed on the soliton propagation for three cases, nn0<ne0, nn0=ne0, and nn0>ne0, together with nn0 (ne0) as the density of negative ions (electrons). The role of the negative ions in the evolution of the modes and the solitons is also discussed. Under the limiting cases, our calculations reduce to the ones obtained by other investigators in the past. This substantiates the generality of the present analysis.

A few remarks on ‘combined action of DC and AC magnetic fields on ion motion in a macromolecule’

Zhadin and Barnes [2005:26:323-330] concluded that they solved the differential equation describing combined action of DC and AC magnetic fields on thermal motion of ions in a biological macromolecule and, as a result, a diversity of biological phenomena could be explained. It is shown here that biological phenomena cannot be explained based on this model. Adair [2006:27:332-334] gave several arguments for the statement that the interaction of weak magnetic fields with ions trapped in protein cavities cannot produce detectable biological effects through changing the character of the ion orbits. The arguments are analyzed here and some are shown to be questionable or unjustified. We stress the difference between the conclusion made by Adair and that stated in this article.

Heating of ions by low-frequency Alfven waves

This paper reports a new physical mechanism that enables the heating of ions by a low-frequency parallel propagating Alfven wave of finite amplitude in a low beta plasma. The heating does not rely on ion cyclotron resonance. The process has two stages: First, ions, whose initial average velocity is zero, are picked up in the transverse direction by the Alfven wave and obtain an average transverse velocity. Second, at a given location the parallel thermal motions of ions produce phase differences (randomization) between ions leading to the heating of ions. The randomization (or heating) process saturates when phase differences are sufficiently large. The time scale over which ions are significantly heated is ∼π∕(kvth) (vth is the initial ion thermal speed and k is the wave number). The heating is dominant in the perpendicular (to the background magnetic field) direction. Subsequently, a large ion temperature anisotropy is produced. During the heating process, ions are also accelerated in the parallel direction and obtain a bulk flow speed along the background magnetic field.

Trapped Ion Quantum Computation with Transverse Phonon Modes

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.

Low-frequency wave instabilities in magnetoactive plasma with spatial inhomogeneity of temperature

The dispersion relation (DR) has been considered for low-frequency waves in a hot magnetoactive collisional plasma with 'longitudinal' large-scale electric field E 0 (t) and weak spatial inhomogeneity of temperature. The electric field was assumed to be extremely weak ('subdriecer' field) and the quasi-static time variation of its amplitude allows us to use the 'direct initiation' mechanism to describe the instability development. Taking into account the ion thermal motion has not changed the form of the DR. which has remained the polynomial of the fourth order, hut it has essentially complicated the form of its coefficients. As compared with previous investigations, these changes have resulted in the changes of the solutions of the DR. Two of the roots of the DR have remained of the same type ('kinetic Alfven-like waves), but another two have become quite different and get to the range of slow magneto-acoustic waves. Investigation of these new waves has shown that corresponding instability has clearly expressed threshold character, and the value of this threshold depends essentially on the reduced value of the electric field amplitude E 0 (t) and ratio of electron and ion temperatures.

Influence of the positive ion thermal motion on the stratified presheath for spherical and cylindrical Langmuir probes immersed in electronegative plasmas

When a cylindrical or spherical Langmuir probe is immersed in an electronegative plasma, for certain plasma conditions, the solution of the radial Poisson's equation consists of an oscillatory electric potential profile before the sheath is formed. The influence of the positive ion thermal motion on the plasma parameter space region in which the stratified presheath takes place is analysed.

Frequency and amplitude windows in the combined action of DC and low frequency AC magnetic fields on ion thermal motion in a macromolecule: Theoretical analysis

We solved the differential equation describing combined action of DC and AC magnetic fields on thermal motion of ions in a biological macromolecule. The solution showed the occurrence of a new set of resonant peaks for ion oscillations under the influence of magnetic fields. After establishment of steady ion oscillations in the macromolecule interior that is well shielded from the action of small particles of the medium surrounding this molecule, the change in energy of ion thermal motion could be sufficient to alter the conformation state of the macromolecule. On this basis, a diversity of biological phenomena can be explained, including the appearance of the known "frequency" and "amplitude" windows, without any resort to the ideas of participation of cyclotron or parametric resonances in these effects.

Theoretical Aspects of the Metal-Electronegative Plasma Interface in Collisional Plasmas for Finite Positive Ion Temperature

The interface between a metallic plane surface and an electronegative plasma is analyzed by using a theoretical model. The model includes ionization, positive ion collisions and positive ion thermal motion. Some physical quantities of great interest in plasma surface treatment and plasma diagnostic are analyzed, such as the positive ion current collected by the metal and the floating potential. The effect produced by each process (collisions, ionizations and positive ion thermal motion) is analyzed.

Sheath structure in electronegative plasmas with finite positive ion temperature

An earlier theoretical work, concerning the sheath structure in electronegative plasmas, is extended to include the effect of the positive ion thermal motion. A significant change is observed in the quantities characterizing the sheath with respect to the cold ion assumption. The sheath is contracted when the positive ion thermal motion is considered causing a decrease in the sheath thickness. The ion saturation current and the floating potential are shown to be distinguished quantities in plasma diagnosis of electronegative plasmas by using plane Langmuir probes.

A universal approach to Rydberg spectral line shapes in plasmas

A universal approach for the calculation of Rydberg atom line shapes in plasmas is developed. This approach goes far beyond the calculation capabilities of the standard models. It is based on analytical formulae for the intensity distribution in radiation transitions n − n′ between highly excited atomic states with large values of principal quantum numbers n, n′ ≫ 1, with Δn = n − n′ ≪ n, and on the frequency fluctuation model to account for ion thermal motion effects. The theory allows us to describe a transition from the static to the impact broadening domains for every hydrogen spectral line. The specific cases of broadening of Hn−α(Δn = 1) and Hn−β(Δn = 2) lines are considered in detail for various values of plasma parameters. The line shapes are presented in a universal manner as functions of the relative frequency splitting and of the fluctuation rate ν of the ion plasma microfield, using dimensionless variables. For small values of ν, the static line shapes which generalize the well-known Underhill–Waddell data for the Rydberg state case are presented. For large values of ν, the transition to impact ion broadening is observed, resulting in a narrowing effect. A comparison with the hydrogen Hα line shape calculations shows a good agreement between the universal approach for Rydberg lines and traditional spectral line shapes.

Analytical fit of the I–V probe characteristic for finite ion temperature values: Justification of the radial model applicability

This article deals with an extension of the radial model for the sheath that surrounds a cylindrical or spherical Langmuir probe immersed in a plasma in which positive ion thermal motion is taken into account. The dependence of the electric potential profile and of the I–V characteristic on the positive ion temperature is obtained. Moreover, a different parameterization is established from a numerical fit of the I–V characteristic as a function of the probe radius, the biasing potential, and the ratio between the positive ion temperature and the electron temperature. This parameterization allows us to obtain an analytical approximation to the potential profile and the sheath edge. Finally, it also gives us a means of justifying under what conditions the radial model can be applied in plasmas with finite positive ion temperature.

Influence of the positive ion thermal motion on the stratified presheath in electronegative plasmas

As the Bohm criterion becomes multivalued in electronegative plasmas, when the ionization rate is low, the solution of Poisson's equation consists of an oscillatory electric potential profile before the sheath is formed (stratified presheath). By including the positive ion thermal motion these oscillations may be attenuated. The influence of this thermal motion on the parameter space region in which the stratified presheath takes place in the case of plane geometry is analysed.

Theory of electrical noise induced in a wire loop by the thermal motions of ions in solution

Continuous Markov process theory is used to model the electrical noise induced in a passive wire loop by the thermal motions of ions in a nearby solution. The ions, being charged particles in Brownian motion, generate a fluctuating magnetic field, and that in turn induces a fluctuating electromotive force (emf) that augments the loop’s Johnson emf. It is shown that the spectral density function of the equilibrium current in the wire loop is thereby increased, for moderate cycle frequencies ν, by approximately a factor (1+αν2), where α is determined by the geometry of the system, the resistance of the loop, and the charges, diffusion coefficients, and concentrations of the solution ions. It is also shown that the temporal trajectory of the loop current becomes “thickened,” in a randomly fuzzy way, by an approximate factor of the form (1+β)1/2, where β depends not only on the aforementioned parameters that determine α, but also on the hydrated masses of the ions. These findings may be useful for estimating the intrinsic background noise in the detector coil of a medical magnetic resonance imaging machine, or any other sensitive electronic circuit that is required to operate in an immediate “salt water” environment.

Turbulent Velocities and Ion Temperatures in the Solar Corona Obtained from SUMER Line Widths

Turbulent plasma velocities and ion temperatures were determined from the line widths recorded by the Solar Ultraviolet Measurements of Emitted Radiation instrument on the Solar and Heliospheric Observatory spacecraft. From the widths of the lines of five light elements (Ne, Na, Mg, Si, and S) and a heavy element (Fe), it was possible to determine the contributions of turbulent plasma motion and ion thermal motion to the line widths. The results indicated that the turbulent velocity was approximately 22 km s-1 at 30'' above the limb and decreased to less than 10 km s-1 at 109'' and 209'' above the limb. At 30'' above the limb, the ion temperatures of the hotter lines were comparable to the electron temperatures for ionization equilibrium. The ion temperatures of the cooler lines were higher than the ionization equilibrium temperatures; at 109'' and 209'' above the limb, the ion temperatures were at least a factor of 2.5 higher than the ionization equilibrium temperatures.

Theoretical ion current to cylindrical Langmuir probes for finite ion temperature values

A new theoretical model for the potential distribution in the surroundings of a cylindrical conductor placed inside a neutral plasma permitted us to analyse the effect of the positive ion thermal motion on the ion current collected by a cylindrical Langmuir probe. The new theoretical model includes the ABR (Allen - Boyd - Reynolds) theory as a limiting case, which is that of a negligible ion temperature compared to the electron temperature.