Renato Fedele

Thermal wave model for nonlinear longitudinal dynamics in particle accelerators

Abstract By using the recently proposed thermal wave model for relativistic charged particle beam propagation, a new approach for studying some nonlinear effects in accelerating machines is developed. By taking into account the interaction of a relativistic charged particle bunch with both RF and the self-induced wakes and neglecting the synchroton radiation emission, we show that the longitudinal dynamics is governed by a nonlinear Schrodinger equation for a complex wave function whose squared modulus is proportional to the longitudinal bunch density. This wave model, for which the diffraction parameter is represented here by the longitudinal emittance, is suitable to give a new description for the bunch instability and capable of reproducing the coherent instability conditions. Furthermore, we show that soliton-like solutions for the density profile are possible.

Kinetic theory of solitary waves on coasting beams in synchrotrons

A generalization of the Vlasov–Poisson system describing the collective dynamics of stored, high-energy hadron beams under the influence of a complex wall impedance is derived in the highly relativistic beam limit γ≫1. A coherent electric field structure Ez(r,z) is found to affect the beam dynamics in O(γ−2), giving rise to an updated feedback between line density (respectively, beam current) and self-fields. Propagating solitary wave solutions as special solutions of this system are obtained by the potential method known from plasma physics. Various parameter regimes are investigated and wave structures are found which are characterized by notches (respectively, humps) in the resonant part of the distribution function. These coherent waves typically travel with thermal velocities and below (kinetic solitary waves) but also structures moving with larger phase velocities (hydrodynamic solitons) are found. Dory’s conjecture about mass conjugation is approved a posteriori in the purely reactive case but is f...

Landau damping of partially incoherent Langmuir waves

Abstract It is shown that partial incoherence, in the form of stochastic phase noise, of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type damping. Starting from the Zakharov equations, which describe the nonlinear interaction between Langmuir and ion-acoustic waves, a kinetic equation is derived for the plasmons by introducing the Wigner–Moyal transform of the complex Langmuir wave field. This equation is then used to analyze the stability properties of small perturbations on a stationary solution consisting of a constant amplitude wave with stochastic phase noise. The concomitant dispersion relation exhibits the phenomenon of Landau-like damping. However, this damping differs from the classical Landau damping in which a Langmuir wave, interacting with the plasma electrons, loses energy. In the present process, the damping is non-dissipative and is caused by the resonant interaction between an instantaneously-produced disturbance, due to the parametric interactions, and a partially incoherent Langmuir wave, which can be considered as a quasi-particle composed of an ensemble of partially incoherent plasmons.

Wave-optics applications in charged-particle-beam transport

An overview of electron wave-optics applications to charged-particle-beam transport is presented in the context of the thermal wave model (TWM). The quantization of the electron optics is presented both in the configuration space and in the phase space. The former provides a description in terms of the Schrödinger-like equation for a complex function whose squared modulus is proportional to the transverse density profile. The latter provides a phase-space description in terms of a von Neumann-type equation for a sort of Wigner function. The main results concerning the Gaussian electron optics, including the theory of coherent states for charged-particlle beams and the beam transport through optical devices with multipole aberrations, such as sextupoles and octupoles, are reviewed within the above wave-like framework. In particular, some investigations concerning luminosity estimates in linear colliders as well as comparisons between the TWM results and the standard tracking simulations, recently discussed in the literature, are summarized. Finally, a fresh tomographic technique to study the beam transport in both the classical-like and quantum-like domains in terms of a marginal distribution, fully similar to the one used in quantum optics, is reviewed. In particular, a comparison between the beam Wigner function and the beam marginal distribution is presented.

The plasma undulator

On the basis of the theory of magnetic undulator for free electron laser (FEL) we analyze the use of a large amplitude plasma wave as an electrostatic undulator. We review the original idea of the plasma undulator and consider some particular plasma undulator configurations. By using low energy electron beams we show the possibility to generate very small wavelength electromagnetic radiation. The fluid theory for the FEL with a plasma undulator, in complete analogy with the ordinary ones, is presented and the thresholds for the FEL action are discussed. An analysis for the intrinsic efficiency, with respect to the emittance and the plasma wake field effects, is presented and applied to some new configurations.

An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap

Abstract We demonstrate that a tight transverse trap with the local frequency, ω ⊥ , gradually varying in the longitudinal direction ( x ) induces an effective potential for one-dimensional solitons in a self-attractive Bose–Einstein condensate. An analytical approximation for this potential is derived by means of a variational method. In the lowest approximation, the potential is N ( S + 1 ) ω ⊥ ( x ) , with N the solitons norm (number of atoms), and S its intrinsic vorticity (if any). The results can be used to devise nonuniform traps helping to control the longitudinal dynamics of the solitons. Numerical verification of the analytical predictions will be presented elsewhere.

Modulational instabilities within the thermal wave model description of high energy charged particle beam dynamics

Abstract Within the thermal wave model (TWM) description, an investigation was made of the longitudinal instability properties of a coasting high energy charged particle beam, where the interaction between the beam and its surroundings is characterized in terms of a complex impedance. The analysis is shown to correctly reproduce the characteristic features of the coherent instability as obtained previously by conventional techniques based on the Vlasov equation for the beam distribution. The results further validate the TWM approach as a consistent alternative description for analyzing the dynamics of high energy charged particle beams.

Wave theories of non-laminar charged particle beams: From quantum to thermal regime

The standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A 45 , 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics , Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D 13 , 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas 19 , 102106; Fedele, R. et al. 2012b AIP Conf. Proc. 1421 , 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrodinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherers equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci. NS-18 , 1105). Conversely, in the quantum regime and in Hartrees mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.

The slingshot effect: a possible new laser-driven high energy acceleration mechanism for electrons

We show that under appropriate conditions the impact of a very short and intense laser pulse onto a plasma causes the expulsion of surface electrons with high energy in the direction opposite to the one of the propagations of the pulse. This is due to the combined effects of the ponderomotive force and the huge longitudinal field arising from charge separation (“slingshot effect”). The effect should also be present with other states of matter, provided the pulse is sufficiently intense to locally cause complete ionization. An experimental test seems to be feasible and, if confirmed, would provide a new extraction and acceleration mechanism for electrons, alternative to traditional radio-frequency-based or laser-wake-field ones.

Self-modulation of a relativistic charged-particle beam as thermal matter wave envelope

The self-modulation, resulting from its interaction with the surrounding medium, of a relativistic charged-particle beam traveling through an overdense plasma, is investigated theoretically. The description of the transverse nonlinear and collective beam dynamics of an electron (or positron) beam in a plasma-based accelerator is provided in terms of a thermal matter wave envelope propagation. This is done using the quantum-like description provided by the thermal wave model. It is shown that the charged-particle beam dynamics is governed by a Zakharov-type system of equations, comprising a nonlinear Schrodinger equation that is governing the spatiotemporal evolution of the thermal matter wave envelope and a Poisson-like equation for the wake potential that is generated by the bunch itself.