The quest for crystalline ion beams

Abstract

The phase transition of an ion beam into its crystalline state has long been expected to dramatically influence beam dynamics beyond the limitations of standard accelerator physics. Yet, although considerable improvement in beam cooling techniques has been made, strong heating mechanisms inherent to existing high-energy storage rings have prohibited the formation of the crystalline state in these machines up to now. Only recently, laser cooling of low-energy beams in the table-top rf quadrupole storage ring PAaul Laser cooLing Acceleration System (PALLAS) has lead to the experimental realization of crystalline beams. In this article, the quest for crystalline beams as well as their unique properties as experienced in PALLAS will be reviewed.

Spatial Compression of Bunched Crystalline Ion Beams

“…The closed orbit of PALLAS is surrounded by 16 drift tubes for the manipulation of the longitudinal position of stationary ions, but also for the modulation of the velocity of an ion beam for diagnostic [4,5] or bunching purposes [14], as described later in the text. Their voltage penetration to the closed orbit amounts to 0.5% [15].…”

“…Over the last year, the rf quadrupole storage ring PALLAS has served as a model system for the investigation of the dynamics of laser-cooled low-energy ion beams. In particular, the crystallization [1,2,3] of a coasting Mg þ ion beam into a string of ions could be realized experimentally at a beam energy of around 1 eV [4,5], and the focusing requirements for the attainment of crystalline beams of more complex structure have been mapped [6]. In such a crystalline beam, the constituent ions arrange themselves to a periodic long-range order due to their mutual Coulomb-repulsion, provided that their thermal energy is sufficiently reduced.…”

“…In the following two sections, the low-energy rf quadrupole storage ring PALLAS will be introduced. As details about its construction [15,16,17], its operation as a linear ion trap [18,4], its relation to high-energy storage rings [16,17,19], and especially about its usual mode of operation with coasting ion beams [4,5,6,7] are published in the given references, we only describe those points relevant for the bunching of ion beams [14].…”

Uncertainty in energy of a high-energy particle

“…This may be supported by the constant interparticle spacing in all the structures 4 and the observation that the particles are located on well-ordered lattice positions in the crystalline beam. 3 The close range attraction force may be attributed to the spin pairing between the particles. The situation may be comparable to the one in which electrons in filled atomic orbitals are spin-paired.…”

“…These crystalline beams are obtained by cooling the ordinary warm ion beams with the application of intense cooling techniques, namely electron or laser cooling. [2][3][4] Due to cooling, an ordered state of the particles is formed. So while measuring the momentum of such a bunch of particles, one obtains a momentum spread (or a momentum spectrum) consisting of an ordered state of the momentum of the particles of the bunch.…”