Inhomogeneous cold beams undergo wave breaking as they move along the axis of a magnetic focusing system. All the remaining control parameters fixed, the earliest wave breaking is a sensitive function of the inhomogeneity parameter: the larger the inhomogeneity, the sooner the breaking. The present work analyzes the role of envelope size mismatches in the wave breaking process. The analysis reveals that the wave breaking time is also very susceptible to the mismatch; judiciously chosen mismatches can largely extend beam lifetimes. The work is extended to include recently discussed issues on the presences of fast and slow regimes of wave breaking, and the theory is shown to be accurate against simulations.
We investigate the role of the temperature in the onset of singularities and the consequent breakdown in a macroscopic fluid model for long-range interacting systems. In particular, we consider an adiabatic fluid description for the transport of intense inhomogeneous charged particle beams. We find that there exists a critical temperature below which the fluid model always develops a singularity and breaks down as the system evolves. As the critical temperature is approached, however, the time for the occurrence of the singularity diverges. Therefore, the critical temperature separates two distinct dynamical phases: a nonadiabatic transport at lower temperatures and a completely adiabatic evolution at higher temperatures. These findings are verified with the aid of self-consistent N-particle simulations. For long-range self-interacting systems, it is generally very difficult to obtain a fully kinetic description of the dynamics. This is the case in plasmas, charged particle beams, and self-gravitating systems among others, where the collision duration time diverges in the thermodynamic limit [1][2][3][4][5]. A largely used tool to overcome this difficulty is the employment of macroscopic fluid models. In contrast to the kinetic description that requires the knowledge of the evolution of the distribution function in the full phase space, the fluid description is simpler because it is based on local macroscopic variables obtained by averaging over the momentum space. Moreover, because the fluid variables consist of readily understood macroscopic quantities, the physical interpretation of the phenomena under investigation is generally more direct. Nevertheless, except for very specific cases, the fluid description leads to an infinite hierarchy of equations which, in practice, have to be truncated to be analyzed. The truncation is obtained by assuming a certain characteristic for the system dynamics which is expressed by an equation of state. Perhaps, the simplest used approximation is the cold fluid, which completely neglects thermal effects by assuming a vanishing temperature [6][7][8][9][10][11][12]. Other examples of largely used equations of state are isothermal [13][14][15][16][17] and adiabatic [18,19]. At any rate, the validity of the fluid description resides not only on the choice of equation of state but also on the fact that the infinite hierarchy has to be convergent; i.e., the macroscopic fluid variables may not present singularities. In the case of cold fluids, a wellknown cause of singularities is the onset of the so-called wave breaking where the fluid description looses its validity due to a divergence in the particles density at a certain position and time. This phenomenon is associated with a filamentation in the phase space and may have relevant consequences such as temperature increase, energy redistribution, and particle acceleration, depending on the system.In this Letter, we investigate the role of the temperature in the onset of singularities in the macroscopic quantities and the consequen...
Hyperchaos occurs in a dynamical system with more than one positive Lyapunov exponent. When the equations governing the time evolution of the dynamical system are known, the transition from chaos to hyperchaos can be readily obtained when the second largest Lyapunov exponent crosses zero. If the only information available on the system is a time series, however, such method is difficult to apply. We propose the use of recurrence quantification analysis of a time series to characterize the chaos-hyperchaos transition. We present results obtained from recurrence plots of coupled chaotic piecewise-linear maps and Chua-Matsumoto circuits, but the method can be applied as well to other systems, even when one does not know their dynamical equations.
Linac4, a 160 MeV normal-conducting H-linear accelerator, is the first step in the upgrade of the beam intensity available from the LHC proton injectors at CERN. The Linac4 Low Energy Beam Transport (LEBT) line from the pulsed 2 MHz RF driven ion source, to the 352 MHz RFQ has been built and installed at a test stand, and has been used to transport and match to the RFQ a pulsed 14 mA H-beam at 45 keV. A temporary slit-and-grid emittance measurement system has been put in place to characterize the beam delivered to the RFQ. In this paper a description of the LEBT and its beam diagnostics is given, and the results of beam emittance measurements and beam transmission measurements through the RFQ are compared with the expectation from simulations. Linac4, a 160 MeV normal-conducting H -linear accelerator, is the first step in the upgrade of the beam intensity available from the LHC proton injectors at CERN. The Linac4 Low Energy Beam Transport (LEBT) line from the pulsed 2 MHz RF driven ion source, to the 352 MHz RFQ has been built and installed at a test stand, and has been used to transport and match to the RFQ a pulsed 14 mA H -beam at 45 keV. A temporary slit-and-grid emittance measurement system has been put in place to characterize the beam delivered to the RFQ. In this paper a description of the LEBT and its beam diagnostics is given, and the results of beam emittance measurements and beam transmission measurements through the RFQ are compared with the expectation from simulations.
This work analyzes the dynamics of inhomogeneous, magnetically focused high intensity beams of charged particles. Initial inhomogeneities lead to density waves propagating transversely in the beam core, and the presence of transverse waves eventually results in particle scattering. Particle scattering off waves in the beam core ultimately generates a halo of particles with concomitant emittance growth. Emittance growth indicates a beam relaxing to its final stationary state, and the purpose of the present paper is to describe halo and emittance in terms of test particles moving under the action of the inhomogeneous beam. To this end an average Lagrangian approach for the beam is developed. This approach, aided by the use of conserved quantities, produces results in nice agreement with those obtained with full N-particle numerical simulations.
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