Heavy ion storage ring without linear dispersion

A possible method to realize a dispersion-free storage ring is described. The simultaneous use of a magnetic field $\mathbf{B}$ and an electric field $\mathbf{E}$ in bending regions, where the two fields are set perpendicular to each other, enables us to control the effect of momentum dispersion. When the relation $(1+1/{\gamma }_0^2)\mathbf{E}(\rho )=-{\mathbf{v}}_0\times \mathbf{B}$ is satisfied for a beam with the velocity $v_0$, the linear dispersion can be completely eliminated all around the ring. It is shown that the acceleration and deceleration induced by the electrostatic deflector counteracts the heating mechanism due to the shearing force from dipole magnets. The dispersion-free system is thus beneficial to producing ultracold beams. It looks probable that the technique will allow one to achieve three-dimensional crystalline beams. At ICR Kyoto University, an ion cooler storage ring S-LSR oriented for various beam physics purposes is now under construction. The application of the present idea to S-LSR is discussed and the actual design of the dispersionless bend is given.

Figure 1

The conceptual illustration of the shearing force. If all stored particles in a crystalline ground state have the same longitudinal velocity, the revolution frequency of a radially outer particle becomes longer than that of an inner particle. Consequently, the two particles are more and more distanced longitudinally every turn, which eventually leads to the melting of the crystalline state. The strength of the shearing force is closely related to the momentum dispersion, as shown in Sec. 3.

Figure 2

Example of a dispersion suppressor. A curved electrostatic deflector is installed in the gap of a dipole magnet. Note that the direction of the electric field is radially outward.

Figure 3

The lattice structure of S-LSR. The number of the superperiod is 6. An rf cavity is introduced for beam bunching. Especially, in the case of only a magnetic storage ring, the rf cavity is also used for 3D cooling. For the dispersion-free condition, in addition to the rf cavity, a coupling rf cavity is to be installed for 3D cooling. In the horizontal beam dynamics, the radial focusing effect of the deflection element is utilized for beam focusing. Thus, all quadrupole magnets have diverging effect horizontally and focusing effect vertically.

Figure 4

Deflection element for S-LSR. The deflection element is constructed by a dipole magnet which has no field gradient and a curved electrostatic deflector. The electrostatic deflector is installed in the gap of the dipole magnet. The electrostatic deflector can be moved out when the deflection element is used as a normal dipole magnet.

Figure 5

Cross section around the electrostatic deflector. The height of the electrostatic deflector is limited by the gap size of the dipole magnet and the vacuum vessel. The electrostatic deflector is constructed by a pair of main electrodes and four pairs of intermediate electrodes. The ideal field distribution is maintained by the intermediate electrodes. In addition to the electrodes, support plates and ceramic plates are introduced for the purpose of keeping the position of the electrodes.

Figure 6

The stable region of the betatron oscillation. The stable region is plotted on the focusing or defocusing quadrupole plane. The beta functions of the operating point $A1$ are given in Fig. 7.

Figure 7

Beta functions of the operating point $A1$ of Fig. 6. The tune values are $(1.49,3.49)$. The beta functions are drawn as a function of the position $s$. The positions of the deflectors and quadrupole magnets are shown in the above diagram. $D_x$ is the horizontal dispersion function.

Figure 8

Beta functions as a function of the position $s$. In this case deflection elements are used as conventional dipole magnets. The betatron tune values are $(1.44,1.44)$.