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Every year, on the 10th of December, one piece is added to the history of science. This is the day when the Nobel Prizes are awarded to those scientists who "during the preceding year have conferred the greatest benefit on mankind". The Nobel Prize carries the highest prestige and fame of all distinctions in the world of science. There have been many speculations regarding the prize: What effect does it have on its recipients? Does it boost their research activities or does it kill them? Is it merely an after-the-fact recognition of important steps in the history of science, or does it also create history by changing the directions along which science develops? What role does it play in the sociology of science? Is it a prize for leaders of big research teams or is there a preference for the genius working completely on his own? Are there equal opportunities for men and women, for Swedes and Russians, for black and white? Where does one find the track that leads to Stockholm?

The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10 000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. Although the Heisenberg Uncertainty Principle often limits measurement accuracies, in many cases the validity of quantum mechanics makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: (1) Existence of discrete quantum states of energy. (2) Energy conservation in transitions between two states. (3) Electromagnetic radiation of frequency v is quantized with energy hv per quantum. (4) The identity principle. (5) The Heisenberg Uncertainty Principle. (6) Addition of probability amplitudes (not probabilities). (7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its affect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems. These effects are discussed and illustrated.

An introduction to the Standard Electroweak Model is given. The three sectors of the Model are briefly reviewed. Some of the topics discussed are symmetries, the number of families, top quark, Higgs boson, CP violation and baryon asymmetry of the universe. I also give a list of some open questions in physics.

A brief survey is given of studies of parity non-conserving phenomena in atomic physics and of the search for permanent atomic electric dipole moments (edm's). The latter can only occur if there is simultaneous violation of both parity and time-reversal invariance. The role of such experiments in testing the Standard Model is discussed. "P only" experiments are in quantitative agreement with the Standard Model. While the Model predicts edm's well below the present level of sensitivity, and none has yet been observed, the hope is for surprises.

Precise measurements of various physical quantities are being made with a much improved precision in experiments with trapped charged particles, many of which are reported in this Nobel symposium. In the present paper, these and other precise measurements are placed in the wider context of the successively more accurate determination of the fundamental physical constants which has taken place during the last decades. The role of systems of units of measurement, based on physical constants and the most accurate measurements, is recalled in providing a coherent framework in which the results of experiments made on different occasions and in different fields of physics may be related to one another.

Some nuclear processes related to astrophysical problems are discussed. Primordial nucleosynthesis, the cold and hot CNO cycles, the αp and rp processes as well as the synthesis of elements heavier than iron are treated. Special emphasis is put on experiments where radioactive nuclear beams are used.

Ions are ubiquitous in astrophysical environments. Knowledge of the cross sections and rates for the atomic and molecular processes which create ions and which destroy them is an important part of any detailed model of an astronomical object. Ions and ionic collisions in two very different environments, the early Universe and planetary nebulae, are explored in this paper. Electron-ion recombination leading to the eventual formation of primordial molecules is described. Collisions of ions with electrons and atoms, central to the interpretation of emission lines in astrophysical plasmas, are discussed. Recent work in predicting element abundances in planetary nebulae is highlighted.

This paper gives a short introduction in the history of the determination of atomic masses. Their differences can often be found with high precision from measurements of nuclear and reaction energies. But here, emphasis is given to features determining the precision with which the masses themselves can be determined with mass spectrometers.

A short history of the development of the ion storage technique for precision experiments is given. This is by no means meant to be a complete review of the field, but the intend is to use a few specific examples to describe how the persistence, ingenuity, and experimental skill of a few people has generated the core of a field which is now growing at an ever faster pace, spreading into new areas, developing sub fields, and allowing a view at nature, using very modest experimental equipment, which by far rivals even the most ambitious dreams of high energy physics.

In this article an introduction and overview of heavy ion storage rings is given. The different cooling schemes for ion beams, i.e. electron, laser, and stochastic cooling as well as beam heating mechanisms are described. Connected to this are collective effects in cold stored ion beams which lead to a form of crystallization. The potential of cooler rings in atomic and molecular physics experiments with stored and cooled ion beams is discussed. This will be exemplified with results from atomic lifetime measurements and the interaction of atomic and molecular ions with electrons and photons utilizing the electron cooler.

The talk touches upon the following subjects: Goethe's Faust, the magic of Democritus' "ατoμoν", magnetism of the neutron, a neutral particle, the crucial problem of physics, crucial experiments, seeing an atom with my eyes, bringing an electron to rest, measuring electron magnetism, proton magnetism, electron radius from its magnetism, speculating on Salam's sub-sub-...-quarks and the cosmon, the simplest thing that ever was.

The potential of electromagnetic traps and storage rings for precision measurements in atomic and nuclear physics is greatly enhanced by combining the features of both, particularly when external sources of exotic ions can also be used. Such applications require the transfer of collections of ions between these devices. The basic engineering principles for designing such transfer are presented in terms of projections of the 6-dimensional phase space volume of charged particle collections into momentum-displacement action planes. The significance of such projections is discussed as well as some of the general features of computational methods to obtain such projections from numerical simulations of charged particle motions within and between the devices. Some examples of the use of the design methods are presented.

In many experiments utilizing ion traps, the ions must be cooled in order to increase the precision and accuracy of the measurements. Laser cooling is very effective when it can be applied, but it can only be used with a few kinds of ions, since it depends critically on the details of the electronic level structure. Other methods, such as resistive cooling, active-feedback cooling, collisional cooling, radiofrequency side-band cooling, or sympathetic laser cooling, can be applied to many kinds of ions. Progress in cooling of trapped ions has made possible improved measurements of mass ratios and atomic spectra and the observation of new phenomena, such as the formation of ordered Coulomb "crystals" of ions.

The use of electron cooling for experiments in atomic physics is reviewed. We discuss the benefits of cooling stored ion beams and the effects on the beam relevant to experiments. The properties of the cooler when it is used as an electron target for recombination experiments are described. In particular we point out the influence of the electron temperature on the shape of recombination spectra and how the temperature affects energy resolution and count rates for different types of atomic and molecular processes.

Concepts in nonlinear dynamics and chaos are discussed on an introductory level. Chaos is shown to play a major role in the physics of the Paul trap and the dynamic Kingdon trap.

Traps for neutral atoms are briefly surveyed and compared with ion traps. Motivations for trapping atoms and ions are discussed. Fundamental restrictions on atom trap design and ways to circumvent them are presented. Methods for cooling trapped atoms and ions are compared and contrasted and differences in their low-temperature collective and collisional behaviors are noted.

The Penning trap mass spectrometer at the University of Washington is described along with the relevant detection mechanisms and the systematic shifts associated with the finite energies in the normal modes of the trapped particle. The cyclotron frequency for the particle-of-interest is compared with the corresponding frequency of a single trapped carbon ion (usually C⁶⁺). Upon correcting for lost electrons and their binding energies, the relative mass ratio then becomes the atomic mass for the particle-of-interest. As a recent example, the value of the electron's "atomic mass" has been measured to be M_e = 0.000 548 579 911 7(17) u and the corresponding proton–electron mass ratio becomes m_p/m_e = 1836.152 664 6 (58).

We report measurements of mass ratios of 20 pairs of molecular ions with a single ion Penning trap mass spectrometer having an accuracy exceeding one part in 10¹⁰. The dominant source of error is random magnetic field fluctuations which cause a 2.6 × 10⁻¹⁰ rms scatter in measurements of the cyclotron frequency. Robust statistical analysis of the data ensures that nongaussian outliers are weighted less heavily in a smooth and consistent manner. Systematic errors are estimated to be 2 × 10⁻¹¹ or below for doublet mass comparisons. The ratios form an overdetermined set, such that the atomic masses of nine isotopes can be derived from at least two independent groups of ion mass ratios, providing many consistency checks for systematic errors at the 10⁻¹⁰ level. At this level of precision, certain mass measurements have important implications in fundamental metrology. Results presented here are essential for defining a practical atomic standard of mass, for calibrating γ-ray wavelengths and for determining the molar Planck constant and the fine structure constant.

An ion of mass-to-charge ratio, m/q, moving under the combined influence of a static magnetic field, B, and an axial quadrupolar electrostatic potential field undergo three "natural" ("normal mode") motions: cyclotron rotation at frequency ω₊, magnetron rotation at frequency ω₋, and an axial "trapping" oscillation at frequency ω_T. Ordinarily, magnetron motion is unobserved, and considered to be undesirable, because ion-neutral collisions result in radial diffusive loss of ions as they roll "downhill" on the magnetron potential surface. However, azimuthal quadrupolar excitation at the ion cyclotron frequency, ω_c = qB/m, converts magnetron motion into cyclotron motion, and (for heavy ions) ion-neutral collisions then shrink the cyclotron orbit, leaving a compact ion packet at or near the center of the ICR ion trap. In this paper, we describe briefly the formal basis for such ion axialization, visualization of magnetron motion, the effect of quadrupolar rf excitation amplitude and duration, and how to achieve ion axialization over a wide range of ion m/q values. Applications of the axialization process include ion remeasurement with high (up to 99%) efficiency; prolonged and efficient ion trapping at high collision gas pressure for cooling of electronically, vibrationally, and/or rotationally "hot" ions; enhanced mass resolving power and peak height-to-noise ratio; and enhanced parent ion selectivity (first stage of MS/MS) and enhanced product ion S/N ratio and mass resolving power (second stage of MS/MS). Moreover, because ions may now be axialized, they need not be formed or injected on-axis, thereby making possible continuous injection of externally formed ions, and/or separation between ion and optical axes for photoionization, photodissociation, photodetachment, and optical spectroscopy of trapped ions.

Mass determination of radioactive isotopes is performed with the tandem Penning trap mass spectrometer ISOLTRAP at the on-line mass separator ISOLDE at CERN/Geneva. The design of the spectrometer matches the particular requirements for on-line mass measurements on short-lived isotopes with T_1/2 > 1 s. With the ISOLTRAP spectrometer masses of more than 70 radiactive nuclei have so far been determined with resolving powers exceeding one million and an accuracy of typically 10^-7.

The application of Schottky beam diagnosis for measurements of nuclear masses was proposed nearly 10 years ago when injection and electron cooling of radioactive beams in the Experimental Storage Ring ESR came into consideration. Experimental tests of this novel method have been performed recently using electron cooled beams of nuclear fragments produced in the ring itself by the interaction between different primary beams and the internal gas jet target. Both the relative accuracy and the resolution of mass differences in Schottky spectra proved to be in the low, 1 × 10^-6 range, allowing even the resolution of isomeric from ground state masses in some cases. Because of the required cooling time the spectrometry is applicable, so far, to nuclei with life times of at least a few seconds.

The procedure for calculating combined relativistic many-body-QED effects for heavy, highly charged ions is reviewed. Numerical results are presented for some helium- and lithium-like ions and compared with experiments.

A 200-keV super electron beam ion trap is being used to study the few electron ions of heavy elements. This device can produce and trap any highly charged ion at rest in the laboratory, including bare U⁹²⁺ ions. Measurements of the ground state binding energies of hydrogenlike and heliumlike ions, and the 2s-2p transition energies in lithiumlike through fluorinelike ions are being used to determine the QED energies in high-Z ions. The ionization cross sections for hydrogenlike and heliumlike high-Z ions are being directly measured for the first time. There are future opportunities for several new kinds of experiments.

A brief description of the LLNL Electron Beam Ion Trap (EBIT) facility and a summary of the experimental program in highly-charged heavy ion physics conducted at EBIT are presented. The heavy-ion research, involving ions up to fully stripped U⁺⁹², includes precision x-ray spectroscopy and lifetime studies, electron impact ionization, excitation cross section measurements, and investigation of ion-surface interactions and experiments with cold high-Z ions.

The SMILETRAP experimental set-up, a Penning trap mass spectrometer for highly charged ions, is described. Capture and observation of cyclotron frequencies of externally produced highly charged ions, rapid interchange of investigated and reference ions and measurements of the rotational kinetic energies are demonstrated. Mass measurements utilizing different charge states and species to verify the consistency of the measurements are presented. A relative uncertainty of about 10⁻⁹ is attained in comparisons between highly charged carbon, nitrogen, oxygen, neon and the singly charged hydrogen molecule.

The measurement of the g_j factor of the bound electron is a sensitive test of bound state QED. The theoretical relevance and some experimental aspects of the measurement of the g_j factor of hydrogenic ions are discussed.

Paul and Penning ion traps have been used to determine hyperfine structures and g-factors of ionic ground states with great precision. These measurements can be used to perform tests of fundamental laws, to determine detailed structures of atomic nuclei or to improved determinations of atomic wavefunctions. The general method is the optical-microwave double resonance. Experiments on Ca⁺, Eu⁺ and Ba⁺ ions serve as recent examples of the present state as well as for possible extensions to radioactive ions and to metastable ionic states.

Starting with a look at the outstanding role of the hydrogen atom in modern physics, this work reviews aspects of an extension of precision spectroscopy to the ground-state hyperfine structure of highly charged hydrogenic ions. In this connection, the preferences of heavy-ion storage rings are outlined and illuminated by the laser-spectroscopic measurement (the first of that kind) of the 1s hyperfine splitting of ²⁰⁹Bi⁸²⁺, stored in the heavy-ion storage ring at GSI. The experimental results, including the mean lifetime of the upper 1s substate, are compared with the presently available theoretical calculations. The relevance of studying further hydrogenicc ions in the vicinity of the doubly magic ²⁰⁸Pb nucleus is emphasized. Final remarks briefly address the possibility of measuring the electron g-factor in a strong field and of realizing laser cooling of ions via M1 transitions.

For the last two decades, lifetimes of metastable levels with times ranging from hundreds of microseconds to many seconds have been measured on ions with low charge stored in Paul, Penning, and Kingdon ion traps. Recent developments in the capture of external ions into traps, use of the Electron Beam Ion Trap, and the employment of heavy ion storage rings now have greatly extended the range of charge states of stored ions which can be studied. There is also a continued demand for lifetime measurements on ions with low charge states, as tests for the development of many-electron theories and driven by astrophysical needs. Transition rates for intersystem lines of C⁺, precise lifetime measurements on the 2 ³S₁ level of helium-like C⁴⁺, N⁵⁺, and Ne⁸⁺, lifetimes of levels of several charge states of argon to Ar¹⁰⁺, and a measurement of a hyperfine structure level lifetime on hydrogenlike ²⁰⁹Bi⁸²⁺, all completed during the last two years, illustrate these current trends.

Weak-decay lifetimes of nuclei are influenced, sometimes dramatically, by the corresponding charge-state of the atom. In storage-cooler rings or in ion-traps weak-decay properties of highly charged ions can be measured for the first time, which has considerable impact for a better understanding of nucleosynthesis in hot stellar plasmas, where the mean atomic charge-state is high, too. As one striking example the first observation of bound-state beta decay is described in detail. Finally, future experiments which may shed light on fundamental questions of astrophysics will be discussed.

Accurate lifetime data for metastable, negative atomic or molecular ions are studied to test theoretical predictions for electron-electron correlation. Heavy-ion storage rings can now provide access to experimental studies of autodetachment lifetimes in the ∼10 μs–1 s time interval which is otherwise almost inaccessible by traditional beam techniques. The recent lifetime studies of the He⁻, Be⁻, Ca⁻, and He₂⁻ ions performed at the storage ring ASTRID are reviewed. Comparisons between the experimental lifetimes and available theoretical predictions exhibit significant deviations. New theoretical studies are needed.

An overview is given of experiments with stored metal cluster ions in a Penning trap system. The setup allows axial injection of clusters produced in an external source and a time-of-flight mass analysis of the reaction products after axial ejection. The system's options include the selection of stored ions, the manipulation of their orbits, addition of reactant and buffer gases and axial optical access for laser spectroscopic studies. As described by various examples, investigations have been made with respect to the development of trapping techniques and the characterization of metal clusters in terms of their physical and chemical properties.

Recent experiments involving fullerene ions in a storage ring are discussed. Storage times of the order of 2 to 10s set by collisional destruction in the background gas were observed. Short-lived components related to metastability of some of the ions were observed and are related to thermionic emission and unimolecular fragmentation. The long storage time may lead to "cold" cluster beams. An example (photodetachment) where this quality is utilized is also discussed.

Studies of gas-phase collisions of atomic particles have been driven largely by modelling and diagnostic needs of natural and laboratory plasmas and by a search for fundamental understanding. Ion traps of many varieties have been employed for a plethora of studies and have made possible investigations into some areas which are not accessible by other means. Various trapping schemes are mentioned and associated with the particular collisions areas where they are most effective. Collisions measurements in high-order electric multipole traps, in ion-storage rings, and in electron-beam ion trap/source (EBIT/EBIS) devices now occupy a prominent role in collisions work. They are discussed in the context of the spectrum of traps and studies done, but not in detail, since other papers in this issue are devoted specifically to them. Thus, after surveying the diversity of traps and collisions types for which they are used, the remainder of the paper is directed to an examination in more detail of the remaining trapping methods and collision measurements.

This contribution concentrates on the use of an ion trapping technique which has been developed for studying collision processes and chemical reactions at low temperatures and which utilizes inhomogeneous radio frequency fields. Special emphasis is put onto recent progress achieved with a cryo cooled 22-pole ion trap. Experimental results, measured at a nominal temperature of 10 K, are presented for radiative association of CH₃⁺ and C₂H₂⁺ with H₂. Another group of results discussed in this paper deals with the dynamics of the growth of hydrogen clusters starting from H₃⁺. In all cases, the influence of H₂ rotation was examined by utilizing p-H₂ and n-H₂. Also the process of isotope fractionation in the presence of HD and D₂ is briefly mentioned.

Results from recent experiments at the heavy-ion synchrotron storage ring CRYRING are described. These experiments include radiative recombination of deuterons using several separate techniques to investigate specific n-level capture, and dielectronic recombination of He⁺ and Ar¹³⁺. New methods applied to the argon dielectronic recombination experiment provided an energy resolution better than 30 meV FWHM and a determination of the peak positions to ±30 meV.

Dissociative recombination of molecular ions with electrons is a process which plays an important role in many astrophysical environments, such as the gas clouds in the interstellar medium, planetary atmospheres, and comets. It is also a process that has been very reluctant to reveal its secrets to those who attempt to study it, either by experimental or theoretical means. The advent of ion storage-cooler ring technology has provided the experimental atomic and molecular physics community with a very powerful instrument for studies of electron-ion collision processes. In the present paper, dissociative recombination is discussed, and it is shown how cross sections and rate coefficients for astrophysically important molecules like H₃⁺ and HeH⁺ are obtained. The experiments exploit the possibility to use ion storage as a mean to obtain vibrationally cool molecules. Recent theoretical work is also discussed and related to the new storage ring experiments.

A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering "bright" or the non-scattering "dark" state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.

Quantum mechanical effects which are manifested in measurements on trapped atomic ions are reviewed. Observation of these effects is facilitated by the long storage times of a fixed number of laser-cooled ions and by high detection sensitivities, primarily through the observation of scattered laser light. We discuss the observation of quantum jumps and the application of quantum jumps to measurement of atomic ion lifetimes and spectra, detection of antibunching of light, the quantum Zeno effect and quantum projection noise. Experiments which detect nonclassical features of fluorescent light from single or a few trapped ions are briefly reviewed. Finally, we discuss experiments which reveal quantum effects in the motion of trapped ions. We briefly describe possible future extensions for each of these topics.

A single ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described in terms of the Jaynes-Cummings Hamiltonian known in quantum optics. Similar to nonclassical states of light we propose to prepare nonclassical states of the ion motion in a harmonic trap. In particular, several schemes for the preparation of Fock states are presented, and techniques for the preparation of squeezed states and coherent states of the ion motion are indicated. For an observation of these nonclassical states we propose to measure quantum collapse and revival in the population inversion of a single trapped ion.

When measuring the g-factor of the electron to obtain information on its possible structure, an increase by factor 3 in resolution is about as important an improvement as a 3-fold increase in accelerator energy would be to high energy physicists looking for the Higgs particle. In this paper I review recent published work carried out with my colleagues at the University of Washington that has yielded a new spectroscopic technique capable of producing symmetric spin and cyclotron resonances only 1.1 Hz and 160 Hz wide, respectively as compared with the last Seattle geonium "S" work in which the resonances were highly asymmetric and the corresponding best widths were 3 Hz and 2000 Hz respectively. The new technique relies on the relativistic spin fine structure of the cyclotron resonance and the well known fact that in a synchro-cyclotron the frequency of the rf drive field must be swept down in order to keep up with the relativistic mass increase. Clearly an acceleration cycle can only succeed when the process does start at a frequency above a threshold value close to the zero energy cyclotron frequency v_c to be measured. This threshold frequency then provides a fair approximation of v_c, later calibrated relative to the 0 → 1 cyclotron transition.

The measured ratio of charge-to-mass ratios for the antiproton and proton is 1.000 000 001 5 ± 0.000 000 001 1. This 1 part in 10⁹ comparison (1 ppb) is possible because a single or p is now directly observed while trapped in an open access Penning trap. The comparison is the most accurate mass spectrometry of particles with opposite charge and is the most sensitive test of CPT invariance for a baryon system. It is 40 times more accurate than our earlier comparison with many trapped antiprotons and protons, and is more than 45 000 times more accurate than earlier comparisons made with other techniques.

The beta-decay of the neutron, n → p + e⁻ + _e, either in its free or its bound state, is the most elementary of the semi-leptonic weak hadron decays, and, along with muon decay, is the prime source of experimental information underpinning the V–A description of weak interactions. We review its role in the context of the standard model of particle physics, and discuss the significance of both the neutron lifetime, and the various angular-polarization correlation coefficients which characterize the decay, in providing values for the polar and axial vector coupling constants, and relating these to the symmetry properties of the corresponding weak currents. We then describe a neutron decay detector, based on the use of a quasi-Penning trap to store and record recoil protons, which has been used to measure the neutron lifetime to better than 1% accuracy. A modified version of the same system is now being prepared to measure the proton spectrum, with a view to making an independent determination of the absolute coupling constant ratio, whose precise value is currently the subject of some debate.

The earliest trapped atom coherent resonance experiments were with material traps or bottles. In the atomic hydrogen maser the atoms are trapped inside a teflon-coated quartz bulb for about a second. Neutrons have been trapped for hundreds of seconds in suitably coated bottles or in superconducting magnetic traps. Results from experiments with trapped atoms and neutrons are given.

Even though positrons have been captured and stored in ion traps for precision measurements, the recent trapping and cooling of antiprotons may be considered as the beginning of a new era in antimatter research. For the first time all the ingredients to produce the first atom of the antimatter world, the antihydrogen atom, are at hand, and several groups have entered an active discussion on the feasibility of producing antihydrogen as well as on the possibility to perform precision tests on CPT and gravity. At the same time, the trapping of reasonable large numbers of antiprotons has opened up the way for a variety of exciting physics with ultra-low energy antiprotons, ranging from atomic physics issues to nuclear physics and medical applications. I will describe the current status of the work on trapping antiprotons and positrons, discuss possible physics applications of this technique, and describe the two most promising routes to produce antihydrogen for precision spectroscopy. Towards the end a few comments on storing the produced antihydrogen and on utilizing antihydrogen for gravity measurements and for CPT tests are given.

Many cold positrons in ultrahigh vacuum are required to produce cold antihydrogen, to cool highly stripped ions, and to study ultracold plasmas. Up to 3.5 × 10⁴ such positrons have now been accumulated into the ultrahigh vacuum of a 4.2 K Penning trap, at a rate exceeding 10³/hr. Both the accumulation rate (per high energy positron incident at the trap), and the number accumulated, are much larger than ever before realized at low temperatures in high vacuum. Cooling of high energy positrons (from ²²Na decay) in a tungsten crystal near the trap, together with purely electronic trapping and damping, are key to the efficient accumulation and to projected improvements.

This paper presents a brief overview of recent theory and experiment for plasmas with a single sign of charge. In principle these plasmas can be confined forever in a state of thermal equilibrium that is guaranteed to be stable and quiescent. In practice confinement times of hours are routinely obtained. The plasmas can be cooled to the cryogenic temperature range where liquid and crystal-like states are predicted and observed. The plasmas provide experimental access to the parameter regime of strong magnetization where a many particle adiabatic invariant constrains the collisional dynamics. Also, the plasmas can be used to model the 2D vortex dynamics and turbulence of an ideal (incompressible and inviscid) fluid

Experimental work which uses laser-cooled ions in Penning traps is reviewed. With laser-cooling the ions are strongly coupled and exhibit spatial correlations characteristic of a liquid or crystal. In plasmas with dimensions less than 10–15 interparticle spacings, the observed correlations are strongly affected by the finite size and shape of the trapping potential. Plasmas with greater than 60 interparticle spacings should exhibit correlations characteristic of an infinite one-component plasma. Radiation pressure from a laser is also used to apply a torque to the plasma and change the plasma density. This permits access to all possible thermal equilibria, including the maximum density state where the plasma undergoes Brillouin flow. If the size of the plasma is small compared to the trap dimensions, Penning traps produce plasmas with simple shapes whose normal modes can be calculated exactly. The modes provide a nondestructive diagnostic technique for obtaining information on the plasma density and shape.

In the paper experiments dealing with the formation of ordered ion structures in Paul traps are reviewed. The transition from an ion cloud to a crystal-like structure corresponds to a chaos-order transition. Furthermore recent experiments in polarization gradient cooling of ions in a quadrupole ring trap are described. The results show that it should be possible to cool the trapped ions into their vibrational ground state.

The first part of this paper discusses the nonlinear dynamics of ions stored in a Paul trap. Four topics are presented in detail: (i) The existence of a new deterministic melting region, (ii) crystallization in a secondary Mathieu stability region, (iii) the existence of hetero-charged ion crystals, and (iv) "cooling induced melting". In the second part, the dynamic Kingdon trap, a close relative of the Paul trap, is suggested as an alternative trap design for the study of nonlinear effects of trapped ions. The dynamic Kingdon trap shows a period doubling route to chaos as well as crystallization.

We review the evidence that the order-chaos transition of two ions in a Paul trap near the edge of the stability region is due to boundary crisis. A crucial element is that the transition is from stationary to transient chaos. Near the crisis the average lifetime T of chaotic transients scales with the dimensionless trap voltage q as T(q) ∝ (q_c−q)^−γ. The unstable, periodic orbits fundamental to a heteroclinic boundary crisis are identified and the intersection of their invariant manifolds in the four-dimensional phase space is located, yielding a prediction for q_c, the transition point between transient and stationary chaos, that agrees well with experiment. This provides a theoretical understanding of an order-chaos transition which previously has been a subject of controversy. With one additional assumption, the critical exponent γ can be calculated as well, yielding a completely deterministic description of the transient lifetime near criticality.

Identification and structural analysis of gas-phase ions is presently based on methods similar to those used in condensed-phase chemistry 75 years ago: namely, breaking the ion apart and weighing the fragments, and/or using chemical reactions to identify groups or reactive centers. For example, dissociation of mass-selected parent ions by (e.g.) collision-induced dissociation [CID], photodissociation, electron impact dissociation, surface-induced dissociation, etc., yields a product ion mass spectrum from which parent ion structure and bonding are indirectly inferred.

Optical spectroscopy, on the other hand, can reveal directly the structure of the absorbing species. Directly measured optical absorption spectra of ions have yielded structures of a few species, such as H₃⁺. Most such experiments have been carried out in a discharge tube although a few mass selected ion spectra have been obtained in a fast ion beam. Here, we propose to conduct optical absorption experiments on mass-selected ions in an ICR ion trap; such experiments require that both optical absorption sensitivity and the maximum number of trapped ions be improved by an order of magnitude. To increase absorption sensitivity, we have chosen a newly developed cavity ringdown method which has previously been demonstrated for visible spectra of neutrals. By use of quadrupolar excitation and collisional cooling to axialize and mass-select ions in a multi-chamber trap, we hope to trap as many as 10⁹ ions with an effective optical path length of 10 000 m, making it possible to detect ions of 10⁻¹⁶ cm² absorption cross-section.

This paper surveys the ongoing physics experiments at the Electron Beam Ion Trap (EBIT) facility at NIST, with particular attention paid to the underlying physical principles involved. In addition, some new data on the performance of our EBIT are presented, including results related to the determination of the trap width, ion temperature, and number of highly charged ions in the trap.

Experiments on Ca⁺ ions, confined in a Paul trap, deal with the spatial distribution of the fluorescence intensity, from which information on the velocity distribution of an ion cloud can be derived. We obtained laser cooling of a large (about 10⁴) ion cloud. For a few or single trapped ions crystallization, "dark resonances" and quantum jumps have been observed.

The wavelength of the highly forbidden 5s^{2 1}S₀ → 5s5p³P₀ transition of the In⁺ ion, a promising candidate for an optical frequency standard, was measured in an optical-optical double resonance experiment using a single laser-cooled ion in a radiofrequency trap.

An RF mass spectrometer of the L. G. Smith type was built with 2 aims: to provide an experimental test of the CPT invariance (proton-antiproton mass comparison) and to measure the atomic masses of nuclei far from stability produced in the ISOLDE-PS Booster facility. As a priority was given to the first application, the features of the spectrometer are presented in this framework. Then, a discussion is made about the adaptation, currently under way, to the second application.

We give some general directions and methods on how to select nuclides of interest for mass measurements. We discuss also more specific cases, as for example the very high precision mass measurements available now from Penning Trap spectrometers.

A Penning-ion trap mass spectrometer which is designed to make sub ppb mass measurements on ions is described. The spectrometer incorporates an external ion source for the injection of ions to be "weighed" into the trap. Novel features include a nonmagnetic alloy from which the trap electrodes are machined, as well as an ion detection system based on a superconducting inductor and a very low-noise amplifier incorporating a gallium-arsenide field-effect transistor (GaAs FET). Also discussed is a technique to increase the axial resistive damping constant for trapped ions using a regenerative detection circuit.

Singly and doubly charged xenon ions have been generated by electron impact of xenon gas in the cylindrical cell of a Bruker CMS 47X Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. Subsequently, xenon ions with a particular mass and charge state have been selected by ejection of all other ions from the FT-ICR cell and allowed to react with neutral xenon atoms.

The rate coefficient for the charge transfer reaction (1)

¹³⁶Xe^+· + Xe → ¹³⁶Xe + Xe^+· (1)

has been determined to be 2.5 × 10⁻¹⁰ cm³ s⁻¹, which agrees very well with values reported in the literature. In the interactions between Xe²⁺ ions and neutral xenon atoms not only a single electron transfer [reaction (2a)], but also a double electron transfer [reaction (2b)] is observed.

¹³⁶Xe²⁺ + Xe → ¹³⁶Xe^+· + Xe^+· (2a)

¹³⁶Xe²⁺ + Xe → ¹³⁶Xe + Xe²⁺ (2b)

The overall rate coefficient for the charge transfer reaction [(2a) + (2b)] has been measured to be 2.7 × 10⁻¹⁰ cm³ s⁻¹. From this and the branching ratio of 0.8 between reactions (2a) and (2b) the rate coefficients for single and double electron transfer from Xe to Xe²⁺ have been calculated to be 1.2 × 10⁻¹⁰ cm³ s⁻¹ and 1.5 × 10⁻¹⁰ cm³ s⁻¹, respectively.

Estimates of operating parameters of a Paul trap suitable for synthesis and spectroscopy of anti-molecular hydrogen ions are presented. The trap may employ a 2-frequency trapping voltage. Transportable cryogenic Paul traps for the long-time storage of positrons and antiprotons may make such experiments possible in an average university lab in the not too distant future.

We give a brief introduction to the study of parity non-conserving effects in atoms. We describe the optical rotation experiments carried out in Oxford, and summarize recent results for bismuth and work in progress on samarium.

Keeping terms up to second order in the micro motion of two ions stored in a Paul trap we derive an improved two-ion pseudo potential which predicts crystal alignment effects that go beyond a standard pseudo-potential analysis and are supported by numerical evidence. The dynamical predictions can be checked experimentally with existing set-ups.

Through the use of detailed numerical simulations we predict the existence of a nontrivial region in the Paul trap parameter space (a, q) where stable, singly periodic orbits (crystals) do not exist. As ions are dragged into this region via an adiabatic change in control parameters, a deterministic melting transition is observed. A detailed map of this deterministic melting region is constructed for the 2 and 3 ion cases. As crystals are dragged into this region by an adiabatic change of control parameters, a melting transition will occur. This transition does not depend on external perturbations, such as laser noise or collisions with neutral atoms.