Yosuke Yuri

Efficiency Enhancement of Indirect Transverse Laser Cooling with Synchro-Betatron Resonant Coupling by Suppression of Beam Intensity

The efficiency of indirect transverse laser cooling with synchro-betatron resonance coupling has been improved with the reduction in beam intensity by scraping the tail part of the beam. In order to measure the beam size at a low beam intensity, a new scheme to measure the beam profile by observation of the survival ratio with changing the scraper position has been established. With 104 particles, the transverse cooling time was reduced to 1.2 s, and the cooled horizontal and vertical beam sizes were 0.19 and 0.61 mm, corresponding to temperatures of 20 and 29 K, respectively, which is largely improved compared with that in our previous experiment [Nakao et al.: Phys. Rev. ST Accel. Beam 15 (2012) 110102].

Effect of a longitudinal radio-frequency field on crystalline beams

Applying a strong dissipative force to energetic charged particles in a storage ring, we can eventually reach a crystalline ground state. Once a beam is crystallized, the repelling Coulomb force just balances the external focusing force provided by magnets. Seen in the laboratory frame, the whole ordered structure circulates around the machine at great speed. According to past theoretical work, a variety of crystal configurations such as one-dimensional (1D) strings, 2D zigzag and 3D shell structures can be formed, depending on the line density of the beam. Physically, beam crystallization is equivalent to the Coulomb ordering that has been experimentally demonstrated in radio-frequency (rf) ion traps. Nevertheless, nobody has succeeded so far in producing a crystalline beam; several factors peculiar to storage rings have made beam crystallization practically difficult to achieve. One of the most essential difference between storage rings and ion traps is the existence of dipole guiding fields in the former systems. Any circular accelerator needs dipole magnets in order for the design beam orbit to be closed. As a result, momentum dispersion is induced inevitably. In this short note, we show that the momentum dispersion can seriously affect even 1D and 2D crystalline structures whenever an rf bunching field is excited. The ring dispersion naturally generates a correlation between the horizontal and longitudinal motions of stored particles. This particular nature enables us to extend a powerful longitudinal laser cooling force to the other two degrees of freedom, which is one major advantage brought by dipole magnets. However, the dispersion also yields unfavorable effects. For instance, we must give a greater average velocity to a radially outer particle in order to stabilize a crystalline structure with a finite horizontal extent; in other words, we are forced to taper the cooling force. If too powerful an untapered laser is applied, multidimensional crystalline structures can be easily destroyed because such a conventional laser simply equalizes the longitudinal velocities of all particles. The destructive dispersive effect is avoidable only when all particles are confined onto the vertical plane including the design beam line. Consider a coasting crystalline beam. If the spatial configuration is a string or a vertical zigzag, the beam clearly has no horizontal dimension. Then, we do not have to care about any dispersive effects as discussed above. An important question now is whether this is still true for bunched crystalline beams. In recent laser cooling experiments, bunched beams have been actually employed quite often because of some practical reasons. Once an rf field is turned on, the energies of individual ions can never be identical but depend on the longitudinal relative positions. For the phase stability, the synchronous ion located at the center of the beam must pass through the resonator exactly when the rf electric field switches from decelerating phase to accelerating phase; the ions after the synchronous one gain some energies while the rest half are decelerated. Any bunched crystalline beam thus has a finite energy spread, which suggests that even an ideal string can no longer stay on the design orbit. In order to verify the above expectation, multi-particle simulations were carried out. In the present simulations, we not only incorporate the direct Coulomb interactions among individual ions but also take into account the characteristics of actual storage rings like bending and straight sections, and alternating gradient focusing. With respect to cooling, however, a simple linear friction model is adopted to save the computing time; i.e. the kinetic momentum of each ion is reduced once in a turn by a particular amount at the cooling devise. Among a wide range of choices, we here consider 1MeV 24Mgþ beams circulating in the Test Accumulation Ring for Numatron Project (TARN II). The circumference of TARN II is 77.7m, and the lattice has a six-fold symmetry. We adjust both of the horizontal and vertical betatron tunes to 2.1, so that the so-called maintenance condition is satisfied. In order to bunch the beam, we introduce an rf field whose harmonic number is 1000. Figure 1 displays the real-space configuration of a string crystalline beam observed at a certain location of the ring. It consists of 35 24Mgþ ions. Although the ions form a straight line, they are not on the design closed orbit. The whole string oscillates about the beam line horizontally, keeping its linear configuration. Since the tune is 2.1 and there is no adequate horizontal self-force against the external focusing force, each ion crosses the beam line four times in every turn. The threshold number of ions at which a string converts into a zigzag configuration is plotted in Fig. 2 as a function of the synchrotron tune s. The critical value naturally decreases at a higher s because the beam is more strongly compressed in the longitudinal direction. The s-dependence of average inter-particle spacing is also indicated in Fig. 2. It is evident that the critical line density c depends on the cooling power. Note that c is considerably lower than the value theoretically predicted for static, continuous Coulomb crystals. The theory by Hasse and Schiffer gives c

Transformation of the Transverse Beam Intensity Distribution by Sextupole Focusing in a Transport Line

We investigate the transformation of the transverse intensity distribution of a charged-particle beam focused by one or two sextupole magnets in a beam transport line. It is expected, from the equation of transverse motion, that the beam is deflected toward one direction and thus deformed due to the second-order force of the sextupole magnet. Such a sextupole-induced deformation of the beam distribution has been studied analytically in detail. The beam centroid displacement and the change of the beam size are determined using the first-order and second-order moments of the intensity distribution function. In order to verify the theoretical consideration, numerical simulations and experiments were performed at the cyclotron facility of Japan Atomic Energy Agency. We experimentally demonstrate that an ion beam with a uniform transverse distribution can be formed using two sextupole magnets.

Three-dimensional ordering of cold ion beams in a storage ring: A molecular-dynamics simulation study

Three-dimensional (3D) ordering of a charged-particle beams circulating in a storage ring is systematically studied with a molecular-dynamics simulation code. An ion beam can exhibit a 3D ordered configuration at ultralow temperature as a result of powerful 3D laser cooling. Various unique characteristics of the ordered beams, different from those of crystalline beams, are revealed in detail, such as the single-particle motion in the transverse and longitudinal directions, and the dependence of the tune depression and the Coulomb coupling constant on the operating points.

Molecular Dynamics Simulation of the Three-Dimensional Ordered State in Laser-Cooled Heavy-Ion Beams

It is theoretically known that a Coulomb crystalline state of an ion beam circulating in a storage ring can be attained in the low-temperature limit [1]. Actually, the formation of one-dimensional (1D) and two-dimensional (2D) crystalline states of low-current bunched ion beams has been numerically predicted by three-dimensional (3D) laser cooling through synchro-betatron resonant coupling [2]. Recently, efficient 3D laser cooling of Mg ion beams has been experimentally accomplished in a cooler storage ring “S-LSR” at Kyoto University toward the formation of a crystalline ion beam [3].

Simulation Study of Emittance Growth from Coulomb Collisions in Low-Temperature Ion Beams

We systematically investigate the collisional heating process of space-charge-dominated coasting ion beams in a storage ring using the molecular dynamics simulation technique. To evaluate the heating rate over the whole temperature range, we start from an ultralow-emittance state where the beam is Coulomb crystallized, apply perturbation to it, and follow the emittance evolution until the beam comes to a regular high-temperature state. The dependence of the heating behavior on various machine and beam parameters, such as the line density, betatron tune, kinetic energy, mass number, and charge state of ions, is explored systematically. The parameter dependence of the heating behavior can be combined, in several cases, into the Coulomb coupling constant. An approximate formula is given for the magnitude of emittance at which the collisional heating is maximized.