Quantization of the Coulomb Chain in an External Focusing Field

With the appropriate choice of parameters and sufficient cooling, charged particles in a circular accelerator are believed to undergo a transition to a highly-ordered crystalline state. The simplest possible crystalline configuration is a one-dimensional chain of particles. In this paper, we write down the quantized version of its dynamics. We show that in a low-density limit, the dynamics is that of a theory of interacting phonons. There is an infinite sequence of $n$-phonon interaction terms, of which we write down the first orders, which involve phonon scattering and decay processes. The quantum formulation developed here can serve as a first step towards a quantum-mechanical treatment of the system at finite temperatures.Comment: 9 Pages, 6 figure

Quantum Ground State and Minimum Emittance of a Fermionic Particle Beam in a Circular Accelerator

In the usual parameter regime of accelerator physics, particle ensembles can be treated as classical. If we approach a regime where $\epsilon_x\epsilon_y\epsilon_s \approx N_{particles}\lambda_{Compton}^3\$, however, the granular structure of quantum-mechanical phase space becomes a concern. In particular, we have to consider the Pauli exclusion principle, which will limit the minimum achievable emittance for a beam of fermions. We calculate these lowest emittances for the cases of bunched and coasting beams at zero temperature and their first-order change rate at finite temperature.Comment: 6 Pages, 1 figur

Numerical Calculation of Coherent Synchrotron Radiation Effects Using TraFiC4

Coherent synchrotron radiation (CSR) occurs when short bunches travel on strongly bent trajectories. Its effects on high-quality beams can be severe and are well understood qualitatively. For quantitative results, however, one has to rely on numerical methods. There exist several simulation codes utilizing different approaches. We describe in some detail the code TraFiC4 developed at DESY for design and analysis purposes, which approaches the problem from first principles and solves the equations of motion either perturbatively or self-consistently. We present some calculational results and comparison with experimental data. Also, we give examples of how the code can be used to design beamlines with minimal emittance growth due to CSR