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Progress of Theoretical and Experimental Physics

Parameter optimization for Doppler laser cooling of a low-energy heavy ion beam at the storage ring S-LSR

Kazuya Osaki, H. Okamoto

Published May 14, 2014• 0 citations

Abstract

S-LSR is a compact ion storage ring constructed at Kyoto University several years ago. The ring is equipped with a Doppler laser cooling system aimed at beam crystallization. Bearing in mind hardware limitations in S-LSR, we try to find an optimum set of primary experimental parameters for the production of an ultracold heavy ion beam. Systematic molecular dynamics simulations are carried out for this purpose. It is concluded that the detuning and spot size of the cooling laser should be chosen around |$-$|42 MHz and 1.5 mm, respectively, for the most efficient cooling of 40 keV |$^{24}$|Mg|$^+$| beams in S-LSR. Under the optimum conditions, the use of the resonant coupling method followed by radio-frequency field ramping enables us to reach an extremely low beam temperature on the order of 0.1 K in the transverse degrees of freedom. The longitudinal degree of freedom can be cooled to close to the Doppler limit; i.e., to the mK range. We also numerically demonstrate that it is possible to establish a stable, long one-dimensionally ordered state of ions.

DOI: 10.1093/ptep/ptu059

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Japanese Journal of Applied Physics•Apr 1, 2007•5 citations

S-LSR is a compact ion storage ring constructed at Kyoto University several years ago. The ring is equipped with a Doppler laser cooling system aimed at beam crystallization. Bearing in mind hardware limitations in S-LSR, we try to find an optimum set of primary experimental parameters for the production of an ultracold heavy ion beam. Systematic molecular dynamics simulations are carried out for this purpose. It is concluded that the detuning and spot size of the cooling laser should be chosen around |

-

|42 MHz and 1.5 mm, respectively, for the most efficient cooling of 40 keV |

^{24}

|Mg|

^+

| beams in S-LSR. Under the optimum conditions, the use of the resonant coupling method followed by radio-frequency field ramping enables us to reach an extremely low beam temperature on the order of 0.1 K in the transverse degrees of freedom. The longitudinal degree of freedom can be cooled to close to the Doppler limit; i.e., to the mK range. We also numerically demonstrate that it is possible to establish a stable, long one-dimensionally ordered state of ions.

Utilizing S-LSR which has a super-periodicity of 6 and is designed to be tough against resonant perturbation to the circulating beam, we have tried to approach as low as possible temperature with laser cooled 40 keV 24Mg+ ion beam. With the use of theoretically proposed Synchro-Betatron Resonance Coupling scheme, we have experimentally demonstrated the capability of active indirect transverse laser cooling. At first, the achieved transverse cooling efficiency was limited due to heating caused by intra-beam scattering (IBS). For the purpose of reduction of IBS heating, we have established a scheme tocontrol the circulating ion beam intensity down to ~104 by scraping the outskirt of the beam with the use of a horizontally moving scraper, which enabled us to cool down the transverse beam temperatures down to 20 K and 29 K for horizontal and vertical directions, respectively for the operation tune without H-V coupling. They were modified to be 40 K and 11 K by the horizontal and vertical coupling with the difference resonance with an excitation of a solenoid of 22.5 G, which were further improved to 7.0 K and 2.1 K adding deceleration by an induction accelerator of 6 mV/m using a -26 MHz detuned laser.

A longitudinal laser cooling of ion beams at about 5% of the velocity of light has been performed at the Heidelberg Test Storage Ring with various cooling schemes employing the spontaneous force. For a 7.29-MeV

^{9}\mathrm{Be}^{+}

beam with an initial longitudinal temperature of 2700 K, the main characteristics of laser cooling in a storage ring are discussed. When undamped, the transverse betatron oscillations of the coasting ions limit the longitudinal temperature after laser cooling to typically 1 K. After damping the transverse motion by precooling the ions with an electron cooler, longitudinal temperatures of below 30 mK have been obtained in the subsequent laser cooling. In this case, the longitudinal ion-beam temperature can be understood as an equilibrium of the laser cooling rate with the heating rate due to intrabeam scattering. Moreover, single binary Coulomb collisions between the (still transversely hot) ions can cause such longitudinal velocity changes that ions are lost out of the critical capture range of the laser cooling force. In these two ways, intrabeam scattering imposes a substantial limit on the temperature or number of laser cooled ions in a storage ring. In our experiments, this process presently limits the ratio between the density-dependent Coulomb energy and the longitudinal thermal energy spread to a value on the order of 1, where liquid rather than gaseous behavior of the ion beam is expected to set in.

Experimental plan at S-LSR to realize ordered state with ultra-low temperature by application of laser cooling for 24Mg+ ions with kinetic energy of 35 keV has been surveyed. By normal mode with finite dispersion, 1 dimensional ordering and 2 dimensional zigzag structure of crystalline beam are expected if strong enough laser cooling force is applied with resonant coupling method. Three dimensional crystal is expected to be attained by the dispersion free mode with coupling cavity although limited at 1 layer level. With “tapered cooling ” utilizing Wien Filter, multi-layer 3 dimensional crystal state is expected to be realized.

At S-LSR, abrupt reduction of momentum spread of 7 MeV proton beam to ~2 times 10-6at proton number of -2000 has been observed, which indicates phase transition to 1 dimensional ordered state. Attained proton temperatures after transition are 26 mueV and 1 meV for longitudinal and transverse directions, respectively, which compared with the corresponding values of 20 mueV and 34 meV for electron beam, indicates the magnetization of electron. Laser cooling of24Mg+has also been started and momentum spread of ~108ions is reduced to 2 times 10-4, saturated with the momentum transfer from transverse degree of freedom by intra-beam scattering.

Doppler cooling of a single 40 Ca + ion in a spherical Paul trap is systematically investigated. Temperatures comparable to the Doppler limit are achieved by optimizing the cooling parameters. These parameters include the laser detunings, the intensities of the cooling beams, and the magnitude of the applied magnetic fields. The temperature of the Doppler-cooled ion is estimated to be 570 µK from the asymmetry of the vibrational sidebands on the quadrupole transition, which is close to the Doppler limit of 540 µK.