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IEEE Advanced Accelerator Concepts Workshop (AAC)

On the physical limitations to the lowest emittance (toward colliding electron-positron crystalline beams)

A. A. Mikhailichenko

Published Jan 1, 1997• 9 citations
Publisher

Abstract

In this paper we explore the conditions under which a relativistic beam of electrons or positrons, treated as a Fermi gas, becomes degenerate. The quantum effects give an absolute limit to the emittance of the beam. We discuss here some methods for preparing this ultra-cold electron-positron gas in a framework of colliding beams at high energy.

DOI
10.1063/1.53056

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In this paper we explore the conditions under which a relativistic beam of electrons or positrons, treated as a Fermi gas, becomes degenerate. The quantum effects give an absolute limit to the emittance of the beam. We discuss here some methods for preparing this ultra-cold electron-positron gas in a framework of colliding beams at high energy.
Background : The theory of a Fermi gas constitutes a useful physical model with multiple applications from solid state to stellar physics. The theory of a non-relativistic Fermi gas is relatively simple when compared with the one for a relativistic Fermi gas. Therefore, it would be useful if a rigorous theory of a relativistic Fermi gas could be constructed like the theory of a non-relativistic Fermi gas. Methods : Such a theory, for T > 0 K, is presented here. It is based on using a recently reported formula for the energies of a relativistic spin-0 particle in a three-dimensional infinite well. The Pauli exclusion principle is used for taking care of the fermion nature of the particles forming a Fermi gas. Results : A unified description of a Fermi gas at low temperatures is presented. This description is valid from the non-relativistic to the ultra-relativistic limits. Moreover, it is simple. The theory follows the relatively simple approach often used for constructing the theory of a non-relativistic Fermi gas. Conclusions : The ultra-relativistic results reported here are often obtained using a different approach than the one used in this work. These results are not new, but they corroborate the correctness of the presented approach. In addition, the relative simplicity of the approach presented in this work allows for teaching the theory of a relativistic Fermi gas in introductory quantum mechanics courses.
Ultra-cold plasmas with electron temperatures of ~10 K can be created by photo-ionization just above threshold of a cloud of laser-cooled atoms. Recently it was shown 7 by GPT particle tracking simulations that an ultra-cold plasma has an enormous potential as a pulsed bright electron source. Here we discuss these results in the framework of normalized 6D brightness, which allows us to make a proper comparison both with the performance of pulsed, radio-frequency photo-emission sources and with the performance of continuous, needle-like field-emission sources. In addition we speculate on the possibility of using ultra-cold plasmas to realize quantum degenerate electron beams, constituting the ultimate limit in electron beam brightness.
The low intensity and poor resolution of conventional slow positron beams is limiting the study of atomic and molecular collisions and prohibits more ambitious fundamental studies. The application of trapping promises huge enhancement in instantaneous beam intensity; ideal for studying short lived positron bound states. Cooling of trapped positrons gives vast improvement in energy and spatial resolution and gives access to a new low energy regime. This new technology is proving to be both challenging and exciting; the relative merits of several different trapping schemes will be discussed and recent progress presented.
An overview is presented of recent studies of the interaction of low-energy positrons with atoms and molecules using a trap-based positron beam. The beam is tunable from ~100 meV to many electron volts, with a typical energy resolution of 25 meV (FWHM). A variety of scattering processes are investigated using the properties of positron orbits in a spatially varying magnetic field. Recent scattering measurements are reviewed, and new data for electronic excitation, ionization, and positronium formation in noble gases are presented. In a separate set of experiments, positron annihilation below the threshold for positronium formation is studied in molecules as a function of positron energy. The data show large Feshbach resonances in the range of energies of the molecular vibrations. Within the framework of this model, these results provide the first experimental evidence that positrons bind to hydrocarbon molecules.
Summary form only given. Cold, dense gases of fermions offer exciting new opportunities for fundamental studies of quantum degeneracy, collective behavior, and superfluidity. Fermionic /sup 6/Li has been the subject of numerous theoretical treatments. This is due in part to its anomalously large and negative triplet scattering length, a/sub T/=-2160 a/sub O/, which arises from a near zero energy resonance. The large scattering length leads to two-state mixtures which are predicted to undergo a transition to a superfluid state at a relatively high temperature. To increase our well depth, we retroreflect the CO/sub 2/ beam which forms our optical trap, nearly doubling the intensity of the trapping field and thus the well depth. We will discuss this technique and its effect on evaporative cooling, and report our progress towards producing a degenerate gas of /sup 6/Li.
Cosmic rays are deemed to be generated by a process known as "Fermi acceleration" in which charged particles scatter against magnetic fluctuations in astrophysical plasmas. The process itself is, however, universal, has both classical and quantum formulations, and is at the basis of dynamical systems with interesting mathematical properties, such as the celebrated Fermi-Ulam model. Despite its effectiveness in accelerating particles, Fermi acceleration has so far eluded unambiguous verifications in laboratory settings. Here, we realize a fully controllable Fermi accelerator by colliding ultracold atoms against engineered movable potential barriers. We demonstrate that our Fermi accelerator, which is only 100 μm in size, can produce ultracold atomic jets with velocities above 0.5 m/s. Adding dissipation, we also experimentally test Bell's general argument for the ensuing energy spectra, which is at the basis of any model of cosmic ray acceleration. On the one hand, our Letter effectively opens the window to the use of cold atoms to study phenomena relevant for high energy astrophysics. On the other, the performance of our Fermi accelerator is competitive with those of best-in-class accelerating methods used in quantum technology and quantum colliders, but with substantially simpler implementation no fundamental physics limit.