Effect of the ion distribution over longitudinal velocities on the efficiency and separating parameters of the ICR method of isotope separation

In the context of the ICR method of isotope separation, resonance RF heating of the ions in an electric field propagating along a constant magnetic field while simultaneously rotating in the direction perpendicular to it is calculated in a linear approximation. The analysis is carried out for two types of the initial ion distribution function over longitudinal velocities: a function proportional to the first power of the velocity in the range of low velocities and a shifted semi-Maxwellian distribution function. The distribution function of the ions over transverse velocities is calculated under the assumption that their initial distribution over transverse velocities is Maxwellian. The ion fluxes onto the collector plates are estimated by integrating the corresponding ion distribution functions over the allowed range of the longitudinal and transverse velocities and the transverse coordinates of the guiding centers of the ion trajectories in front of the extractor. In the first part of the paper, calculations are carried out for a model binary mixture of isotopes with mass numbers of 6 and 7. The effect of the shape of the ion distribution function over longitudinal velocities on the heating efficiency and on the concentration of the target isotope ions at the collector, as well as the effect of the longitudinal ion temperature on the width of resonance curves for the ion heating efficiency, is investigated. In the second part, a study is made of the selectivity of heating of isotope ions in a gadolinium plasma, in particular, the effect of the longitudinal magnetic field on the selectivity of heating of neighboring isotopes with atomic masses of 156, 157, and 158 is examined.     

Calculation of the ion transverse velocity distribution function under ion cyclotron resonance heating

The ion transverse velocity distribution functions and the fraction η of ions heated above a certain energy W ₁ are calculated as applied to the ion cyclotron resonance heating method of isotope separation. It is assumed that the longitudinal ion velocity distribution in a plasma source is nonequilibrium. Under high heating temperatures, the averaged ion transverse velocity distribution becomes essentially nonequilibrium and exhibits two maxima. The ion heating efficiency η is calculated for W ₁=40 eV and various values of the parameter p=λ/L, where λ is the wavelength of the electric field of an antenna and L is the heating zone extension. The relative contributions of the time-of-flight and Doppler broadenings are evaluated.     

Hot-Electron Magneto-Transport in InSb

The balance equations are used to investigate the hot electron magneto-transport in narrowgap semiconductor InSb at 77 K in crossed weak magnetic field and electric field. In the case of vanishing transverse velocity, the drift mobility and the Hall mobility are calculated and it is shown that the Hall factor in InSb at 77K is less than 1 and decreases with electric field. In the case of vanishing transverse electric field, the longitudinal velocity and the transverse velocity are calculated as a function of the magnetic field and the electric field. The effect of the magnetic field on the longitudinal velocity is different from that on the transverse velocity.     

Dynamics of an ion flow in an electron layer

We study the acceleration of an ion flow in the electron layer formed by an electron flow moving in a transverse electric field and confined by the intrinsic magnetic field. The possibility of extraction of heavy ions with velocities lower than the ion sound velocity from the plasma, and the feasibility of their further acceleration by an external field is demonstrated.     

Die Geschwindigkeitsverteilung der Ionen in der Freifallsäule

The velocity distribution of the ions in the positive column of the free-fall type discharge is derived by means of the method of characteristics from collisionless Boltzmann equation extended by a source term in plane and cylindrical geometries. A homogeneous axial magnetic field and the initial distribution of ion velocities is taken into account. The formula of Tonks and Langmuir for ion density is reproduced in case of vanishing initial velocity of the ions and vanishing magnetic field.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one‐dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters ‐ like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons ‐ is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current‐carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geschwindigkeitsverteilungsfunktionen von Atomen und Ionen in verschiedenen Anregungs- und Ionisationsstufen in Niederdruck-Entladungen bei hohem Ionisationsgrad

Supposing free-fall conditions the velocity distribution functions of atoms and ions in various levels in gas discharges at low pressures are calculated. In particular, plasmas at high degrees of ionization are considered. Solving the Boltzmann equation for the motions transverse to the wall of the discharge tube it is shown that the velocity distribution functions can considerably deviate from the Maxwellian and become non-isotropic. Inelastic collisions with electrons and the ionization by electron impacts considerably determine the velocity distribution function of the neutral atoms. The velocity distribution function of the ions is also essentially determined by the electric field within the plasma. For the motions transverse to the wall the half widths of the velocity distribution functions do not only depend on the temperature of the wall, but on the electron density and on the electron temperature as well. At small electron densities the half widths for excited atoms and for ions can be narrower than the one for the ground state atoms. The charge exchange between atoms and ions is shortly taken into consideration.     

Untersuchung von run-away-Elektronen im Neutralgas

The theory of run-away electrons is applied to a special device, where electrons of a given initial velocity move in a neutral gas through a homogeneous electric field. The average velocity of the electrons as a function of the space coordinate for different initial velocities and relative electric fieldsE/p is calculated. In an experimental investigation of this case the velocity distribution of the electrons after their passage of the field space for different initial velocities and relative fieldsE/p is analyzed. Within the range of experimental errors the measured average velocities agree with the calculated ones. On the basis of these experimental velocity distributions the runaway effect at large initial velocities but medium electric fields can be demonstrated.     

Numerical simulation of intense helical electron beams with the calculation of the velocity distribution functions

The method of calculation of intense helical electron beams which allows to find the distribution function of electrons with respect to their transverse (oscillatory) and longitudinal velocities is developed. The initial velocity distribution function can be arbitrary. The data obtained in numerical simulation and experimental measurements for beams with various topologies are compared. The evolution of the transverse velocity distribution function with the beam current growth is traced. It is found that the transformation of the velocity distribution function may indicate a possible instability in a real beam.     

A Corrugated Mirror-Cyclotron Frequency Direct Conversion System (COMI-CYFER)

In this scheme the plasma escaping from a mirror machine is split into an array of long narrow beams by means of a grid of iron slabs. For proper shaping of the slabs, the increased mirror ratio at the iron causes acceptably low beam interception. After spherical expansion of the magnetic field containing the escaping plasma, the electrons are repelled by non-intercepting grids. A spatially alternating electric and/or magnetic field which follows is converted to an alternating or rotating force by the motion of the ions. At sufficiently low velocity, this force resonates with the cyclotron frequency and sweeps the ions to collector plates. With average ion energies of 293 keV an efficiency of 85% can be obtained in a system whose size is much smaller than other proposed direct conversion systems. For a 74% efficienicy, only 186 keV ions are required and the system becomes extraordinarily compact.     

Influence of the temperature of positive ions on the sheath formation and parameter space region in magnetized electronegative plasmas

The parameter space regions and the sheath formation in an electronegative discharge in the presence of thermal positive ions and oblique magnetic field are investigated. It is assumed that the negative species are in thermal equilibrium and the positive ions have a finite temperature. Three regimes of uniform, multilayer stratified and pure stratified are found as functions of positive and negative ion temperature, electronegativity and the magnetic field. The influence of positive ion temperature in the presence of magnetic field on the profiles of the positive ion density, positive ion velocity and electric potential are investigated. The positive ion flux at the sheath edge as a function of magnetic field is obtained for different collisionality and positive and negative ion temperatures. Finally, the influence of the magnetic field, collision frequency and the positive ion temperature on the parameter space regions are discussed.     

Distribution function for relativistic charges in the vicinity of cyclotron resonance

The function of charge distribution over the momentum projections in a preset field of a circularly polarized rf transverse electromagnetic wave propagating along a constant uniform magnetic field with phase velocity u > c is obtained by solving the relativistic collisionless kinetic equation. The peculiarities in energy associated with the nonlinearity of the cyclotron resonance for various values of the phase velocity are analyzed in the limits of single-valuedness of the resonance curve. Some distribution functions are considered.     

Formation of Suprathermal Particle Fluxes in a Strongly Turbulent Plasma

We consider the problem on the formation of suprathermal particle fluxes by electrostatic structures in strongly turbulent cosmic plasmas. It is shown that regions with a strong plasma turbulence can be large accelerators of charged particles. We give solutions of the stationary kinetic equation in a turbulent layer for different acceleration regimes and estimate the efficiency of diffusion over the longitudinal and transverse velocities of particles with respect to the magnetic field. The transverse diffusion in velocity space is more efficient for ions and leads to strong isotropization of ion fluxes. Electrons move almost along the magnetic field. We reveal the conditions under which the regular force in a nonuniform magnetic field influences the stochastic-acceleration process. The average energy of axial motion of the particles and the particle fluxes at large distances from the injection region are estimated. Ions and electrons can be accelerated up to comparable energies. We analyze the characteristic features of the motion of the relativistic-particle beams. It is shown that strong plasma turbulence can form particle beams with specific energies. The proposed mechanism is useful for explanation of the properties of energetic particles in cosmic plasmas with magnetic-field-aligned currents, e.g., in high-latitude regions of planetary magnetospheres, force-free configurations of the solar corona, and the solar wind.     

Comparison of the directional characteristics of swift ion excitation for two small biomolecules: glycine and alanine

The characteristics of ions that enter the plasma sheath with an oblique incident angle have been investigated in the presence of an external magnetic field. The ion dynamics in a collisional and collisionless magnetized plasma sheath have been numerically calculated by using a fluid model. Several values for the ion velocity at the sheath edge, orientation and strength of the magnetic field and the ion-neutral collision frequency have been considered. The results show that in a collisionless magnetized plasma sheath, the behaviour of ions that obliquely enter the sheath with some specific velocities at the sheath edge and at some specific orientations and strengths of magnetic field, is more complicated than that of ions with normal entrance angles. For the oblique entrance of ions, the weak magnetic fields cause some fluctuations in ion velocity around its boundary value, i.e. the ion velocity does not accelerate. However, the numerical calculations show that the ion dynamics in a collisional magnetized plasma sheath are the same for both normal and inclined entrance of ions into the sheath.     

基于双向偏振态激光诱导荧光方法的离子速度分布函数测量

为了评估利用发散磁场构型双电层效应的紧凑式螺旋波等离子体推力器的离子加速效果,探索了一种双向偏振态激光诱导荧光测量方法来对螺旋波等离子体源近出口端的离子速度分布函数进行测量。实验中采用Ar作为螺旋波等离子体源工质,中心波长为611.662 nm的激光以轴向方式注入等离子体,以激励一价Ar离子获得波长为461.086 nm的诱导荧光光谱。为了消除磁化等离子体中逆塞曼效应对激光诱导荧光光谱带来的分裂影响,通过四分之一波片将入射激光分别调制为左旋和右旋圆偏振态,并对其诱导光谱进行了分别测量,结果发现不同磁场强度下两次测量结果的偏移值与理论高度吻合,证明了双向偏振态激光诱导荧光测量方法的理论可行性。进一步,采用高斯型滤波器反卷积算法从测量光谱中去除自然展宽和能量饱和效应,再通过对两次相反偏振态测量结果进行平移处理消除逆塞曼效应,从而分离得到实际的多普勒效应。测量了射频能量600 W,不同轴向位置、磁场大小以及气体压力下的螺旋波Ar等离子体激光诱导荧光光谱,结果表明在该实验条件下离子并没有因双电层效应而达到期望值的加速效果,离子速度的形成可能只是一种磁约束作用下的双极电场所导致,并不能产生好的推力性能。     

Laser-induced fluorescence measurement of the ion-energy-distribution function in a collisionless reconnection experiment

Observations in space and laboratory plasmas suggest magnetic reconnection as a mechanism for ion heating and formation of non-Maxwellian ion velocity distribution functions (IVDF). Laser-induced fluorescence measurements of the IVDF parallel to the X line of a periodically driven reconnection experiment are presented. A time-resolved analysis yields the evolution of the IVDF within a reconnection cycle. It is shown that reconnection causes a strong increase of the ion temperature, where the strongest increase is found at the maximum reconnection rate. Monte Carlo simulations demonstrate that ion heating is a consequence of the in-plane electric field that forms around the X line in response to reconnection.     

Hot Ion Production in a Modified Penning Discharge

Ions with Maxwellian energy distributions and kinetic temperatures up to seven keV have been observed in a modified Penning discharge. Investigation of the plasma revealed two distinct spoke-like concentrations of charge, consisting respectively of ions and electrons, rotating with different velocities in the sheath between the plasma and the anode ring. Theoretical expressions are derived for the frequency of the ion and electron spoke rotation, for the ion kinetic temperature resulting from the ion spoke velocity, and for the ion heating efficiency. An extensive series of experimental measurements were made to check these theoretical expressions, and approximate agreement was obtained. It is shown that the ion kinetic temperature in the modified Penning discharge scales according to the relation Vi ~ Vani1/4/B1/2 where Va is the applied anode voltage, ni is the ion density in the sheath, and B is the magnetic field strength. The observed data demonstrate that the ion heating efficiency can be as high as several tens of percent.     

The effect of a longitudinal magnetic field on the plasma-dust structures in strata in a glow discharge

The plasma-dust structures in strata in a glow discharge exposed to a longitudinal magnetic field are studied in detail. In a weakly ordered structure, the angular velocity has a vertical gradient. A reversal of rotation of the structure in a magnetic field corresponding to the magnetization of electrons is found. With the help of the pair distribution function of particles, changes in the degree of order of the structure in the magnetic field are revealed. These changes correlate with changes in the angular velocity of rotation. To explain this effect, it is assumed that the dust structure is subjected to the action of ions in crossed electric and magnetic fields.