One-dimensional Beam Ordering of Protons at Ion Storage Ring, S-LSR

The ion storage ring, S-LSR has been constructed to study the beam cooling, especially for the physics of the extreme cold ion beam. The magnetic rigidity is 1 Tm and the circumference is 22.557 m. The lattice of the ring was designed to suppress the beam heating as small as possible. The construction was completed in the summer of 2005 and the beam commissioning using 7 MeV protons was started in October, 2005. The electron cooler at S-LSR has an effective cooling length of 0.44 m (2 % of the circumference). The 7 MeV proton beam was successfully cooled in November, 2005. After the improvements and the optimization of the electron cooler, the maximum cooling force of 0.12 eV/m is achieved with the electron energy of 3.8 keV and the electron current of 56 mA. The estimated electron temperature is 25 μeV. Since February, 2006, the one-dimensional ordering experiment of protons has been performed using the electron cooling. The first proton ordering was successfully confirmed in July, 2006. Abrupt drop in the momentum spread and the Schottky noise power have been observed at a proton number of ∼2000 with electron currents of 25 mA, 50 mA and 100 mA. The transition temperatures of the proton ordering are 0.17 meV and 1 meV in the longitudinal and transverse direction, respectively. The transverse proton temperature is much below the transverse electron temperature, which is the result of the magnetized electron cooling. Below the transition, the longitudinal proton temperature is cooled down to 26 μeV, which is close to the longitudinal electron temperature. The transition temperature of the proton ordering is much lower than those of the highly charged heavy ions at ESR because of the weak Coulomb interaction. Nevertheless, the particle reflection model agrees well with the experimental result of the proton ordering. The reflection probability of the proton at the transition is close to those of the heavy ions. It shows that the one-dimensional ordering of the proton occurs by the same mechanism as the highly charged heavy ions. The beam simulations using the molecular dynamics method also agree well with the experimental results.