Cold Ion Source Research Articles

Laser-induced delayed electron emission of Co−4 anions

SynopsisThe cryogenic trap for fast ion beams (CTF) located at the Max-Planck-Institut für Kernphysik has been used to study laser-induced delayed electron emission of various molecular and metal-cluster anions. We will discuss recent experiments investigating the radiative cooling respectively heating of Co−4 anions produced in hot and cold ion sources. The experiments will be continued at the cryogenic storage ring (CSR), which is presently being commissioned, to disentangle laser-induced electron emission from atom or cluster dissociation.

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

AbstractA general formalism for calculating the potential distribution Φ(z) in the quasineutral region of a new class of plane Tonks–Langmuir (TL)-type bounded-plasma-system (BPS) models differing from the well-known ‘classical’ TL model (Tonks, L. and Langmuir, I. 1929 A general theory of the plasma of an arc. Phys. Rev. 34, 876) by allowing for arbitrary (but still cold) ion sources and arbitrary electron distributions is developed. With individual particles usually undergoing microscopic collision/sink/source (CSS) events, extensive use is made here of the basic kinetic-theory concept of ‘CSS-free trajectories’ (i.e., the characteristics of the kinetic equation). Two types of electron populations, occupying the ‘type-t’ and ‘type-p’ domains of electron phase space, are distinguished. By definition, the type-t and type-p domains are made up of phase points lying on type-t (‘trapped’) CSS-free trajectories (not intersecting the walls and closing on themselves) and type-p (‘passing’) ones (starting at one of the walls and ending at the other). This work being the first step, it is assumed that ε ≡ λD/l → 0+ (where λD and l are a typical Debye length and a typical ionization length respectively) so that the system exhibits a finite quasineutral ‘plasma’ region and two infinitesimally thin ‘sheath’ regions associated with the ‘sheath-edge singularities’ | dΦ/dz|z→±zs → ∞. The potential in the plasma region is required to satisfy a plasma equation (quasineutrality condition) of the form ni {Φ} =ne (Φ), where the electron density ne (Φ) is given and the ion density ni {Φ} is expressed in terms of trajectory integrals of the ion kinetic equation, with the ions produced by electron-impact ionization of cold neutrals. While previous TL-type models were characterized by electrons diffusing under the influence of frequent collisions with the neutral background particles and approximated by Maxwellian (Riemann, K.-U. 2006 Plasma-sheath transition in the kinetic Tonks–Langmuir model. Phys. Plasmas 13, 063508) or bi-Maxwellian (Godyak, V. A. et al. 1995 Tonks–Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23, 728) electron velocity distribution functions (VDFs), which satisfy the zero-CSS-term (Vlasov) kinetic equation and imply zero electron currents, we here propose a more general class of electron VDFs allowing, in an approximate manner, for non-zero CSS terms and finite electron currents inside the plasma region. The sheath-edge and floating-wall potentials are calculated by balancing the ion and electron current densities at sheath-edge singularities. In a first detailed application, the type-t and type-p electron VDFs are assumed to be ‘inner’ and ‘outer’ cut-off Maxwellians respectively, with different amplitudes and ‘formal’ temperatures, implying the perfectly CSS-free limit. For the special case of equal type-t and type-p electron VDF amplitudes and formal temperatures, the classical Boltzmann distribution for electrons is formally retrieved. Special cases with other amplitude and formal-temperature ratios show significant deviations from the classical case.

Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

A plasma–sheath transition analysis requires a reliable mathematical expression for the plasma potential profile Φ(x) near the sheath edge xs in the limit ɛ≡λD/ℓ=0 (where λD is the Debye length and ℓ is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation (ɛ=0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys. D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann’s formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since “the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity” [Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann’s general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and “water-bag” ion source velocity distributions. We find the potential profile near the plasma–sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to “practical infinity.” While within limits of “very low” and “relatively high” ion source temperatures, the potential is proportional to the space coordinate powered by rational numbers α=1/2 and α=2/3, with medium ion source temperatures. We found α between these values being a non-rational number strongly dependent on the ion source temperature. The range of the non-rational power-law turns out to be a very narrow one, at the expense of the extension of α=2/3 region towards unexpectedly low ion source temperatures.

A new method of solution for one-dimensional quasi-neutral bounded plasmas

AbstractA new method is proposed for calculating the potential distribution Φ(z) in a one-dimensional quasi-neutral bounded plasma; Φ(z) is assumed to satisfy a quasi-neutrality condition (plasma equation) of the form ni{Φ(z)} = ne(Φ), where the electron density ne is a given function of Φ and the ion density ni is expressed in terms of trajectory integrals of the ion kinetic equation. While previous methods relied on formally solving a global integral equation (Riemann, Phys. Plasmas, vol. 13, 2006, paper no. 013503; Kos et al., Phys. Plasmas, vol. 16, 2009, paper no. 093503), the present method is characterized by piecewise analytic solution of the plasma equation in reasonably small intervals of z. As a first concrete application, Φ(z) is found analytically through order z4 near the center of a collisionless Tonks–Langmuir discharge with a cold-ion source.

The ionization length in plasmas with finite temperature ion sources

The ionization length is an important quantity which up to now has been precisely determined only in plasmas which assume that the ions are born at rest, i.e., in discharges known as “cold ion-source” plasmas. Presented here are the results of our calculations of the ionization lengths in plasmas with an arbitrary ion source temperature. Harrison and Thompson (H&T) [Proc. Phys. Soc. 74, 145 (1959)] found the values of this quantity for the cases of several ion strength potential profiles in the well-known Tonks–Langmuir [Phys. Rev. 34, 876 (1929)] discharge, which is characterized by “cold” ion temperature. This scenario is also known as the “singular” ion-source discharge. The H&T analytic result covers cases of ion sources proportional to exp(βΦ) with Φ the normalized plasma potential and β=0,1,2 values, which correspond to particular physical scenarios. Many years following H&T’s work, Bissell and Johnson (B&J) [Phys. Fluids 30, 779 (1987)] developed a model with the so-called “warm” ion-source temperature, i.e., “regular” ion source, under B&J’s particular assumption that the ionization strength is proportional to the local electron density. However, it appears that B&J were not interested in determining the ionization length at all. The importance of this quantity to theoretical modeling was recognized by Riemann, who recently answered all the questions of the most advanced up-to-date plasma-sheath boundary theory with cold ions [K.-U. Riemann, Phys. Plasmas 13, 063508 (2006)] but still without the stiff warm ion-source case solution, which is highly resistant to solution via any available analytic method. The present article is an extension of H&T’s results obtained for a single point only with ion source temperature Tn=0 to arbitrary finite ion source temperatures. The approach applied in this work is based on the method recently developed by Kos et al. [Phys. Plasmas 16, 093503 (2009)].

Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas

This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B&J) [Phys. Fluids 30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B&J model is a generalization of the well-known Tonks–Langmuir (T&L) [Phys. Rev. 34, 876 (1929)] discharge model characterized by a “cold” ion source. Unlike the T&L model, which can be readily solved analytically, attempts to solve the B&J model with a “warm” ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B&J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B&J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc. 74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures.

Fluid and kinetic parameters near the plasma-sheath boundary for finite Debye lengths

In a recent paper by Kuhn et al. [Phys. Plasmas 13, 013503 (2006)], it has been demonstrated that in a plasma, the polytropic coefficient γ is a spatially varying quantity rather than a global constant as usually assumed in fluid theory. Assuming cold ion sources and using the asymptotic two-scale approximation (in which the ratio of the Debye length over the characteristic presheath length, ε, is set to zero), it was found that the γ profile exhibits a sharp peak (with values roughly between 6 and 8) at the plasma-sheath boundary. In the present paper, it is shown that in a finite ε approach, this sharp peak is smoothed to a regular maximum, which for increasing ε (e.g., decreasing plasma density) decreases and finally disappears. In any case, assumptions like γ=1 and/or γ=3, which are customarily encountered in the context of fluid approaches, are disproved. Although the present results were obtained for collisionless plasmas, it is reasonable to assume that the behavior uncovered holds qualitatively for any plasma with cold ion sources. In addition to calculating time-independent theoretical solutions by means of an analytic-numerical approach, we primarily employ particle-in-cell (PIC) computer simulations, which intrinsically represent a time-dependent approach. It is confirmed that, although extreme care is required to separate physical from numerical effects, the PIC simulation method is a highly suitable tool also for future investigations of more demanding physical scenarios assuming, e.g., warm ion sources and other more complex aspects that cannot be treated realistically by analytic-numerical means alone. In addition, the extension from time-independent analytic-numerical calculation to time-dependent simulation permits us also to investigate the effect of collective plasma oscillations on the ion velocity distribution function (VDF). Although the ion VDFs obtained in our PIC simulations visibly differ in some details from the time-independent theoretical ones, the related ion-temperature and γ profiles turn out to fit their theoretical counterparts very well over significant parameter ranges. Hence, the two methods may to some extent be applied as alternative ones in future investigations on the plasma-sheath transition.

Formation of Strongly Coupled Plasmas from MultiComponent Ions in a Penning Trap

This report reviews the production of strongly-coupled, multi-component, non-neutral, highly-charged ion plasmas in a cryogenic Penning trap. A unique ion source–Penning trap system has been developed and used an Electron Beam Ion Trap-Source (EBIT-S), able to produce ions up to U92+, has been combined with a cold-bore Penning ion trap. The developed experimental techniques such as the ion production, extraction, bunching, multi-ion species trapping and storage (ions up to Th80+), detection, cooling, and imaging are presented. The produced mixed plasmas, consisting of several ion species [e.g. Be+, Xeq+ (charge q = 34 ... 44)], are cooled to a temperature of about 1 degree Kelvin and below. These low temperatures were obtained by applying a sypathetic cooling scheme, using laser cooled Be+ ions. The determination of the temperature and the density from the laser resonance width and the fluorescence imaging of the Be+ clouds respectively, yield a Coulomb coupling parameter for the xenon ion plasma of over 1000, large enough for crystallization. Crystallization can be achieved at these relatively high temperatures since the Coulomb coupling parameter scales with q2.Ion species with different mass to charge ratios centrifugally separate at low temperatures in the trap, and the plasma consists of concentric spheroidal shells of single component plasmas. But even in this case excellent thermal coupling between ion species takes place due to the long range Coulomb interactions. This is demonstrated by molecular dynamics simulations of the ion mixtures, which show ordered structures, indicating evidence for crystallization of the highly charged xenon ions.During the investigation of highly charged ion Coulomb crystallization in mixed strongly coupled plasmas, several enabling techniques were developed that are applicable to various areas of physics research Analogous thermodynamics (Coulomb matter) of white dwarf astrophysical plasmas can experimentally be investigated, high precision laser spectroscopy is made possible due to reduced Doppler broadening effects, cold ion sources can be developed and coherent quantum control experiments can be further explored.

Production of very cold, highly charged ions by synchrotron radiation: Comparisons of the “scalpel” and “hammer” methods

Measurements of kinetic energies of highy charged argon ions produced by inner-shell photoionization and by ion-beam impact have been made using time-of-flight techniques. High-charge-state recoil ions produced by beams of ∼ 0.5−1 MeV/u Cl 5+ are found to have energies one to two orders of magnitude higher than ions of the same charge produced by vacancy cascades following inner-shell photoionization by synchrotron radiation. The results may have application to the development of a very cold ion source useful for angle-resolved atomic collision studies.

Functional tests of a cryo-cooled mass spectrometer ion source in a supersonic wind tunnel

A modified helium cooled ion source was operated in supersonic gas flows simulating some conditions of a rocket flight through the upper mesosphere and lower thermosphere. It is shown that the shock in front of this ion source is removed due to the low temperature of the ion source front part and that the mass spectrometer measures the composition of the undisturbed gas flow. Stability and angular dependence of the ion source signal are analyzed. The light emission from the cold ion source in an arc heated supersonic flow is discussed.