Crystalline beam ground state

Conference · Fri Jan 01 00:00:00 EST 1993

DOI:https://doi.org/10.2172/10171427· OSTI ID:7368544

Wei, Jie ^[1]; Li, Xiao-Ping; Sessler, A M ^[2]

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1. Brookhaven National Lab., Upton, NY (United States)
2. Lawrence Berkeley Lab., CA (United States)

In order to employ Molecular Dynamics method, commonly used in condensed matter physics, we have derived the equations of motion for a beam of charged particles in the rotating rest frame of the reference particle. We include in the formalism that the particles are confined by the guiding and focusing magnetic fields, and that they are confined in a conducting vacuum pipe while interacting with each other via a Coulomb force. Numerical simulations has been performed to obtain the equilibrium structure. The effects of the shearing force, centrifugal force, and azimuthal variation of the focusing strength are investigated. It is found that a constant gradient storage ring can not give a crystalline beam, but that an alternating-gradient (AG) structure can. In such a machine the ground state is, except for one-dimensional (1-D) crystals, time-dependent. The ground state is a zero entropy state, despite the time-dependent, periodic variation of the focusing force. The nature of the ground state, similar to that found by Rahman and Schiffer, depends upon the density and the relative focusing strengths in the transverse directions. At low density, the crystal is 1-D. As the density increases, it transforms into various kinds of 2-D and 3-D crystals. If the energy of the beam is higher than the transition energy of the machine, the crystalline structure can not be formed for lack of radial focusing.

• Research Organization: Brookhaven National Lab., Upton, NY (United States)
• Sponsoring Organization: USDOE; National Science Foundation (NSF); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: AC02-76CH00016; AC03-76SF00098
• OSTI ID: 7368544
• Report Number(s): BNL-48385; CONF-930511-63; ON: DE93014331; CNN: DMR-91-15342
• Resource Relation: Conference: International particle accelerator conference, Washington, DC (United States), 17-20 May 1993
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ION BEAMS
CRYSTALLIZATION
COMPUTERIZED SIMULATION
DYNAMICS
EQUATIONS OF MOTION
GROUND STATES
HAMILTONIANS
MAGNETIC FIELDS
SHEAR
STORAGE RINGS
BEAMS
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE TRANSFORMATIONS
QUANTUM OPERATORS
SIMULATION
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics