No abstract

Molecular dynamics is employed to study the nature and magnitude of beam cooling that is required in order to achieve a crystalline beam. Analysis is presented of a number of cooling systems now in use, or whose use is contemplated, none of which has been shown to be able to achieve the crystalline state. However, for an adequately strong cooling system that produces on average a constant angular velocity among the particles, a crystalline state can be achieved. In this paper, we present numerical values for a particular example under typical experimental conditions; these values appear to be achievable in practice. [S0031-9007(98)05644-0] PACS numbers: 52.60. + h, 29.20.Dh, 52.65. -y, 61.50. -fFor the last decade there has been interest in and experimental effort to achieve crystalline beams. These beams are sufficiently cold in the beam rest frame, so that the particles making up the beam "lock into" a position where the repelling Coulomb force just balances the external focusing force. Seen from the laboratory, the whole ordered structure circulates at great speed. The interest, besides intrinsically on this new state of matter, is primarily on the possibility of studying the physics of completely space-charge dominated beams, the possibility of studying Wigner crystal, and the possibility of obtaining high luminosity in colliders.The ground state of a crystalline beam was proposed by Dikanskiȋ and Pestrikov [1] based on an experimental anomaly observed on an electron-cooled proton beam at the storage ring NAP-M, and was first studied using the molecular dynamics (MD) method by Schiffer and coworkers [2]. At the same time, experimental efforts have succeeded in achieving very low beam temperatures, but not yet a crystalline state [3].In a long series of papers we explored the conditions for a crystalline beam ground state in a real storage ring [4][5][6][7]. Despite the large amount of work and the many publications in this field, there has not previously been a careful study of the nature and magnitude of the cooling force required to reach a crystalline state (see the papers in Ref.[6]). We have undertaken such a study and report on the results in this Letter.Particle motion can be described by a Hamiltonian [4,6] in the rest frame ͑x, y, z, t͒ of a circulating reference particle in which the orientation of the axes is rotating so that the axes are constantly aligned to the radial (x), vertical ( y), and tangential (z) direction. Consider in general a system of multispecies of particles under Coulomb interaction and external fields. Define a reference par-ticle with electric charge Z 0 e and atomic mass M 0 , and define for the ith species of particles with charge Z i e and mass M i , Z i ϵ Z i ͞Z 0 , and m i ϵ M i ͞M 0 . Measure dimensions in units of the characteristic distance j with j 3 r 0 r 2 ͞b 2 g 2 , time in units of r͞bgc, and energy in units of b 2 g 2 Z 2 0 e 2 ͞j, where r 0 Z 2 0 e 2 ͞M 0 c 2 is the classical radius, bc and gM 0 c 2 are the velocity and energy of the reference particle, and r is...

We study halo formation from cylindrical beams propagating in a uniform focusing channel. Of particular interest here are the breathing-mode oscillations excited by an initial beam-size mismatch. We develop a one-dimensional space-charge code which is simple but powerful in exploring the halo properties of breathing beams. After giving a brief description of two particle-core models, we apply the developed code to three different types of nonlinear phase-space distributions. Based on a number of multiparticle simulation runs, we show several interesting results useful for the design considerations of high-power linear machines. In particular, the intensity of halo current as well as the maximum extent of halos are self-consistently evaluated with the different sizes of initial mismatch and beam density. We then find that the halo extent normalized with the initial root-mean-squared beam size is only weakly dependent on the tune depression and that the halo intensity appears to increase with the degree of mismatch. It is further demonstrated that the beam core in phase space is roughly stable and, thus, most halo particles remain outside the core boundary. We also see that it is, in principle, possible to scrape halos, e.g., by means of a multicollimator system.

An extensive experimental study is performed to confirm fundamental resonance bands of an intense hadron beam propagating through an alternating gradient linear transport channel. The present work focuses on the most common lattice geometry called "FODO" or "doublet" that consists of two quadrupoles of opposite polarities. The tabletop ion-trap system "S-POD" (Simulator of Particle Orbit Dynamics) developed at Hiroshima University is employed to clarify the parameter-dependence of coherent beam instability. S-POD can provide a non-neutral plasma physically equivalent to a chargedparticle beam in a periodic focusing potential. In contrast with conventional experimental approaches relying on large-scale machines, it is straightforward in S-POD to control the doublet geometry characterized by the quadrupole filling factor and drift-space ratio. We verify that the resonance feature does not essentially change depending on these geometric factors. A few clear stop bands of low-order resonances always appear in the same pattern as previously found with the sinusoidal focusing model. All stop bands become widened and shift to the higher-tune side as the beam density is increased. In the spacecharge-dominated regime, the most dangerous stop band is located at the bare betatron phase advance slightly above 90 degrees. Experimental data from S-POD suggest that this severe resonance is driven mainly by the linear self-field potential rather than by nonlinear external imperfections and, therefore, unavoidable at high beam density. The instability of the third-order coherent mode generates relatively weak but noticeable stop bands near the phase advances of 60 and 120 degrees. The latter sextupole stop band is considerably enhanced by lattice imperfections. In a strongly asymmetric focusing channel, extra attention may have to be paid to some coupling resonance lines induced by the Coulomb potential. Our interpretations of experimental data are supported by theoretical predictions and systematic multiparticle simulations.

This paper addresses the generalization of the single-particle betatron resonance condition derived by Courant and Snyder more than a half century ago. A two-dimensional resonance condition including the effect of space-charge interaction was recently conjectured from one-dimensional Vlasov predictions made by Sacherer, Okamoto, and Yokoya [K. Ito et al., Phys. Rev. Accel. Beams 20, 064201 (2017)]. The condition is remarkably simple which only contains a few measurable quantities and indicates the possibility that twice as many resonance stop bands as expected from the conventional incoherent picture may exist at high beam density. Self-consistent multiparticle simulations are performed systematically to locate low-order stop bands in the tune diagram. The proposed betatron resonance formula is shown to explain the basic feature of numerical observations, which suggests that no serious incoherent resonance is activated inside the phase-space core of a dense beam matched to the external linear focusing potential. It is confirmed that the coherent tune-shift factor of any collective mode is less than unity and practically considered as a constant over the whole tune space in a typical high-intensity storage ring. The procedure for finding the optimum operating point of the ring is discussed on the basis of the coherent picture instead of the commonly used picture relying on the concept of incoherent tune spread. Despite years of theoretical efforts by many researchers, the coherent resonance concept is still not being employed for the construction of a stability tune diagram. We here provide a simple prescription to draw the diagram quickly. The present study also indicates the possibility of complete suppression of emittance exchange on particular difference resonances by choosing a proper emittance ratio.