Ebook: Physics with Many Positrons

In the year of the 2009 “Enrico Fermi” Course on Physics with Many Positrons, the field of low-energy positron science, excluding positron emission tomography (PET), produced about 500 journal articles per year covering 1) studies of positron and positronium scattering from atoms and molecules and emission from surfaces, 2) measurements of voids and other defects in numerous types of materials, 3) studies of the electronic and magnetic structure of bulk solids and surfaces, 4) experiments on plasmas, and 5) various types of positronium spectroscopy. This modest output compared with more accessible fields such as photoemission (1400/year), vacancies (2600/year), electron scattering (4000/year), electron plasmas (4800/year) and PET (4500/year) cannot be ascribed to the fact that the positron is a strong probe, because the state of present day theory and computational expertise is sufficient to extract detailed information about the properties of many systems even though the positron distorts their electronic structure, may form an impurity atom (positronium), and often annihilates the very electron it seeks to probe. Rather it is because experimentation with antimatter 1) requires a significant investment in learning the techniques of turning a source of relativistic positrons into a useful probe and 2) the scale-up to facilities analogous to synchrotron light sources or neutron sources is still under way.

The basic science of positrons was the focus of the 1981 “Enrico Fermi” School on Positron Solid State Physics directed by Werner Brandt and Alfredo Dupasquier

Positron Solid-State Physics, Proceedings of the International School of Physics “Enrico Fermi”, Course LXXXIII, edited by W. Brandt and A. Dupasquier (North-Holland) 1983.

What happens when positronium atoms are created at a high density and are able to interact with each other? This is a question that may now be addressed experimentally with the advent of high-intensity low-energy positron pulses derived from a Surko trap. By creating bursts of positrons with spatiotemporal densities up to 10²⁰ cm⁻² s⁻¹ and implanting them into suitable materials, it is possible to observe “many positron” processes, such as Ps-Ps scattering and Ps₂ molecule formation. Here I shall describe various experiments we have conducted using high intensity and high density positron pulses, and outline our plans for future work.

These notes contain speculations about interesting situations that might occur when two or more low-energy positrons interact with each other and/or with various forms of ordinary matter. Topics include many positrons compressed to high density at a field emission tip, a long-lived metastable cold neutral electron positron plasma in a box, dipositronium and other multipositron molecules, the positronium Bose-Einstein condensate, precision measurements on positronium cooled by a pulsed laser method, stimulated emission of annihilation radiation, head-on collisions of two positronium annihilation gamma-ray laser pulses, and possible uses for gamma-ray lasers.

Sustained advances in the trapping of positrons and antiprotons led to the recent creation of cold antihydrogen in vacuum under controlled conditions. This was achieved at the unique Antiproton Decelerator facility located at CERN, Geneva. The collection, manipulation and mixing of clouds of the antiparticles necessary to promote antihydrogen formation are described herein, including some of the more practical aspects of positron accumulation. This discussion is prefaced by a treatment of basic Penning trap and plasma physics of relevance to antihydrogen formation. The detection of the nascent antihydrogen atoms, both via their annihilation on Penning trap electrodes and following field ionization of weakly bound pairs, is reviewed. We present a brief description of aspects of the physics output of the antihydrogen experiments in terms of the nature of the states which are formed and implications of measurements of the spatial distribution of antihydrogen annihilation events. Theoretical simulations of antihydrogen formation have been useful in providing guidance in interpreting experimental data, and aspects of this work are reviewed. Trapping of neutral systems using a magnetic-field minimum device is described and the new ALPHA antihydrogen trapping experiment is introduced. We conclude with a look to the future of the new field of antihydrogen physics.

In this lecture I show how the ATHENA data samples on the anti-hydrogen () formation may be used to provide useful information on the two different possible formation mechanisms: the 3-body reaction (+e⁺+e⁺→+e⁺) and the 2-body reaction (+e⁺→+hν).

Future spectroscopy of antihydrogen has the potential to test the fundamental symmetry between matter and antimatter at unprecedented levels of experimental precision. We review spectroscopy of ordinary hydrogen and describe recent proposals and advances towards antihydrogen spectroscopy.

Many advanced experiments require efficient production of positronium at low kinetic energy. Progress in this field calls for a careful design of the material used to convert positrons into positronium, with regards not only to the chemistry but also to the morphology of the converter. The aim of the present paper is to set ground for future advancements by presenting the current framework of knowledge regarding positronium formation and cooling. The first section addresses positronium formation in bulk solids and at surfaces, with information on yields, energy spectra and angular distributions. The second section discusses the basic principles of collisional cooling in porous solids or in powders and presents a choice of relevant results.

Positively charged antihydrogen ions can be efficiently cooled to cryogenic temperature. After removing the extra positron from the ion using a laser beam, direct measurement of the gravitational acceleration will be possible by observing the free fall of the neutral atom. To create the antimatter ions, antiprotons should be injected into a sufficiently dense ortho-positronium (o-Ps) cloud. To achieve the o-Ps density needed, thin mesoporous silica films are suggested as efficient converter systems which produce low-energy o-Ps with high efficiency upon irradiation with positrons at keV energy. The optimization of the growth parameters and the characterization of the films are discussed using 3 gamma annihilation franction, ortho-positronium lifetime and time-of-flight spectroscopy. A method for the determination of the precise vacuum ortho-positron escape yield, based on the correct measurement of the full o-Ps lifetime distribution, is presented. A positron source, presently under construction at CEA Saclay (France), is described. It is based on a dedicated linear electron accelerator and can serve as a test device for a future generation of self-containing, high-intensity positron sources that are free from radioactive isotopes.

We present the physics and the antihydrogen production strategy of the AEGIS experiment at CERN. This strategy is based on a series of steps in which positronium (Ps), produced by e⁺ impinging on a porous target, is laser excited to high-n (Rydberg) levels and then made to interact with ultracold antiprotons (around 100 mK). An antihydrogen beam is then formed by Stark acceleration to be sent through a Moire' deflectometer to measure g for antimatter. The efficiency of the antihydrogen production process depends critically on the positronium excitation process which will be described in detail in the paper. The Ps cloud is produced within a relatively strong magnetic field at 1 T, with a consequent deep modification of Rydberg levels structure. A two-step laser light excitation is proposed, and the physics of the problem is discussed. We derive simple expressions giving the Ps excitation probability with feasible laser pulses suitably tailored in power and spectral bandwidth.

We summarize here in a pedagogical manner our present knowledge of compounds that consist of both antimatter and ordinary (or koino) matter, specifically, compounds of positrons and discrete electronic systems (i.e., atoms and molecules). A few dozen such compounds are known to exist, most from quantum calculations and others from laboratory observations. In the past two decades, direct laboratory measurements of binding energies have begun to appear, and we expect that the present modest interplay between theory and experiment will soon become more robust and informative. Of recent and increasing interest are compounds containing more than one positron, in particular Ps₂ and Ps₂O.

In the last decades, a large variety of low-energy positron beams has been built based on β⁺ sources. However, the available maximum intensity of laboratory beams is limited to about 10⁷ moderated positrons per second. For this reason, several setups have been developed at large-scale facilities such as electron accelerators and research reactors in order to generate high-intensity positron beams using the conversion of high-energy γ radiation into positron-electron pairs. Within this contribution, first the experimental constraints and the physical basics, how positrons can be produced and how positron sources are realized, are reviewed. In the second section the moderation of positrons is briefly described. This leads to the principal scheme of the positron beam setup in the laboratory scale and to an overview of existing and possible future large-scale positron beam facilities. Finally, the NEutron-induced POsitron source MUniCh NEPOMUC with its instrumentation is presented.

Pulsed low-energy positron beams of variable energy are powerful tools for defect profiling in materials. In this lecture we will at first describe two pulsed-beam systems developed over the last two decades: The Pulsed Low Energy Positron System (PLEPS) for depth-resolved defect profiling and the Scanning Positron Microscope (SPM), which in addition offers lateral resolution. We then consider some examples of applications of those pulsed beams to condensed matter problems. Next, the limits of those systems are discussed. Finally, we will give an outlook how pulsing with many positrons may be achieved and used for the purposes of materials sciences by combining existing experimental equipment with a strong positron source.

Two different positron beam projects in the United States are outlined here. The North Carolina State University (NCSU) slow-positron beam is built on a 1 MW PULSTAR reactor and can sustain a stable beam of 6×10⁸ slow positrons per second over a 3 cm diameter. The Argonne National Laboratory Slow-Positron source (APosS), based on a 12–20 MeV electron linac accelerator, can create a beam of 3×10⁷ slow positrons per second over a few mm diameter. Both the NCSU beam and the APosS rates can plausibly be increased by more than an order of magnitude with planned improvements.

The heart of the radiation source ELBE at the Forschungszentrum Dresden-Rossendorf (FZD) is a 40 MeV LINAC with an average current of 1 mA. Due to its superconducting technology, the time structure is different from conventional LINACs. Electron bunches as short as 2 ps with a 26 MHz repetition rate can be used in continuous operation (cw) mode. This is an ideal host for an intense positron source. After organizing SLOPOS-9 in Rossendorf, it was decided to add EPOS (ELBE Positron Source) to the existing experiments at ELBE. EPOS consists of two LINAC-based setups, Gamma-induced Positron Spectroscopy (GiPS) and Mono-energetic Positron Spectroscopy (MePS). The GiPS setup, where positrons are produced inside the whole sample volume by pair production using a pulsed gamma beam, is unique so far. Here, bulky samples such as coarse powders, dispersions, but also liquids or whole devices of non-destructive testing can be investigated by all positron techniques important for materials science (lifetime spectroscopy, age-momentum correlation, and coincidence Doppler broadening spectroscopy). The same techniques will be applied at the MePS setup, where slow, mono-energetic positrons will be generated by moderation to study near-surface layers. This system is still under construction. The EPOS system will be completed by two conventional setups, a continuous slow positron beam and a positron lifetime/Doppler spectrometer, both operated by ²²Na sources.

The interest to explore many-positron systems requires new generations of more intense positron beams. A number of limitations preclude the use of long-lived beta-decaying sources for this purpose. Positron-electron pair creation from bremsstrahlung or short-lived radio-isotopes must be produced on-site. Powerful linear accelerators or nuclear reactors are prime choices but are in high demand and not available on an as-needed basis. The use of smaller laboratory-sized accelerators is presented. They can be a much needed step in developing new ideas. Driven by the needs of medical and industrial applications, these machines have become reliable and are relatively easy to operate even by small research groups such as the one at WSU. The current situation is briefly reviewed and experiences with one system in particular are discussed.

This paper describes a new positron source produced using ultra-intense short-pulse lasers. Although it has been studied in theory since as early as the 1970s, the use of lasers as a valuable new positron source was not demonstrated experimentally until recent years, when the petawatt-class short-pulse lasers were developed. In 2008 and 2009, in a series of experiments performed at Lawrence Livermore National Laboratory, a large number of positrons were observed after shooting a millimeter thick solid gold target. Up to 2×10¹⁰ positrons per steradian ejected out the back of ~ mm thick gold targets were detected. The targets were illuminated with short (~1 ps) ultra-intense (~1×10²⁰ W/cm²) laser pulses. These positrons are produced predominantly by the Bethe-Heitler process, and have an effective temperature of 2–4 MeV, with the distribution peaking at 4–7 MeV. The angular distribution of the positrons is anisotropic. These unique characteristics may enable this new positron source to contribute to the positron science community.

Methods are described to create, store, manipulate and characterize positron plasmas. Emphasis is placed on the so-called buffer-gas positron trapping scheme for positron accumulation that uses positron-molecule collisions to accumulate particles efficiently. Manipulation and storage techniques are described that exploit use of the Penning-Malmberg trap, namely a uniform magnetic field with electrostatic confining potentials along the direction of the field. The techniques described here rely heavily on single-component-plasma research, and relevant connections are discussed. The use of rotating electric fields to compress plasmas radially (the so-called “rotating wall” technique) is described; it has proven particularly useful in tailoring positron plasmas for a range of applications. The roles of plasma transport and available cooling mechanisms in determining the maximum achievable plasma density and the minimum achievable plasma temperature are discussed. Open questions for future research are briefly mentioned.

This paper describes recent research to create, manipulate and utilize positron, antimatter plasmas. One is the development of a method to extract cold beams with small transverse spatial extent from plasmas in a high-field Penning-Malmberg trap. Such beams can be created with energy spreads comparable to the temperature of the parent plasma and with transverse spatial diameters as small as four Debye screening lengths. Using tailored parent plasmas, this technique provides the ability to optimize the properties of the extracted positron beams. In another area, the design of a multicell positron trap is described that offers the possibility to accumulate and store orders of magnitude more positrons than is presently possible e.g., particle numbers >10¹². The device is scalable to even larger particle capacities. It would, for example, aid greatly in being able to multiplex the output of intense positron sources and in efforts to create and study electron-positron plasmas. This multicell trap is likely to also be an important step in the development of portable traps for antimatter. The third topic is a discussion of possible ways to create and study electron-positron plasmas. They have a number of unique properties. These so-called “pair” plasmas are interesting both from the point of view of fundamental plasma physics and for their relevance in astrophysics.

The design of a micro-trap capable of confining 10⁶ to 10⁸ positrons is described. By simulating the behavior of individual positron in the trap, key factors determining performance are identified. The unresolved issues and future research are also discussed.