Radiation Damping and Quantum Excitation for Longitudinal Charged Particle Dynamics in the Thermal Wave Model

On the basis of the recently proposed {\it Thermal Wave Model (TWM) for particle beams}, we give a description of the longitudinal charge particle dynamics in circular accelerating machines by taking into account both radiation damping and quantum excitation (stochastic effect), in presence of a RF potential well. The longitudinal dynamics is governed by a 1-D Schr\"{o}dinger-like equation for a complex wave function whose squared modulus gives the longitudinal bunch density profile. In this framework, the appropriate {\it r.m.s. emittance} scaling law, due to the damping effect, is naturally recovered, and the asymptotic equilibrium condition for the bunch length, due to the competition between quantum excitation (QE) and radiation damping (RD), is found. This result opens the possibility to apply the TWM, already tested for protons, to electrons, for which QE and RD are very important.Comment: 10 pages, plain LaTeX; published in Phys. Lett. A194 (1994) 113-11

Full Phase-Space Analysis of Particle Beam Transport in the Thermal Wave Model

Within the Thermal Wave Model framework a comparison among Wigner function, Husimi function, and the phase-space distribution given by a particle tracking code is made for a particle beam travelling through a linear lens with small aberrations. The results show that the quantum-like approach seems to be very promising.Comment: 15 pages, plain LaTeX, + 3 uuencoded figures, to be published in Phys. Lett.

Classical and Quantum-like approaches to Charged-Particle Fluids in a Quadrupole

A classical description of the dynamics of a dissipative charged-particle fluid in a quadrupole-like device is developed. It is shown that the set of the classical fluid equations contains the same information as a complex function satisfying a Schrodinger-like equation in which Planck's constant is replaced by the time-varying emittance, which is related to the time-varying temperature of the fluid. The squared modulus and the gradient of the phase of this complex function are proportional to the fluid density and to the current velocity, respectively. Within this framework, the dynamics of an electron bunch in a storage ring in the presence of radiation damping and quantum-excitation is recovered. Furthermore, both standard and generalized (including dissipation) coherent states that may be associated with the classical particle fluids are fully described in terms of the above formalism.Comment: LaTex, to appear in Physica Script

Coherent instabilities of intense high-energy "white" charged-particle beams in the presence of nonlocal effects within the context of the Madelung fluid description

A hydrodynamical description of coherent instabilities that take place in the longitudinal dynamics of a charged-particle coasting beam in a high-energy accelerating machine is presented. This is done in the framework of the Madelung fluid picture provided by the Thermal Wave Model. The well known coherent instability charts in the complex plane of the longitudinal coupling impedance for monochromatic beams are recovered. The results are also interpreted in terms of the deterministic approach to modulational instability analysis usually given for monochromatic large amplitude wave train propagation governed by the nonlinear Schr\"odinger equation. The instability analysis is then extended to a non-monochromatic coasting beam with a given thermal equilibrium distribution, thought as a statistical ensemble of monochromatic incoherent coasting beams ("white" beam). In this hydrodynamical framework, the phenomenon of Landau damping is predicted without using any kinetic equation governing the phase space evolution of the system.Comment: 14 pages, 1 figur

Dynamics of the wakefield of a multi-petawatt, femtosecond laser pulse in a configuration with ultrarelativistic electrons

The wake field excitation in an unmagnetized plasma by a multi-petawatt, femtosecond, pancake-shaped laser pulse is described both analytically and numerically in the regime with ultrarelativistic electron jitter velocities, when the plasma electrons are almost expelled from the pulse region. This is done, for the first time, in fluid theory. A novel mathematical model is devised that does not break down for very intense pump strengths, in contrast to the standard approach that uses the laser field envelope and the ponderomotive guiding center averaging. This is accomplished by employing a three-timescale description, with the intermediate scale associated with the nonlinear phase of the electromagnetic wave and with the bending of its wave front. The evolution of the pulse and of its electrostatic wake are studied by the numerical solution in a two-dimensional geometry, with the spot diameter \geq 100 microns. It reveals that the optimum initial pulse length needs to be somewhat bigger than 1 micron (1-2 oscillations), as suggested by simple analytical local estimates, because the nonlocal plasma response tends to stretch very short pulses

Quantum corrected electron holes

The theory of electron holes is extended into the quantum regime. The Wigner--Poisson system is solved perturbatively based in lowest order on a weak, standing electron hole. Quantum corrections are shown to lower the potential amplitude and to increase the number of deeply trapped electrons. They, hence, tend to bring this extreme non--equilibrium state closer to thermodynamic equilibrium, an effect which can be attributed to the tunneling of particles in this mixed state system.Comment: 12 pages, 3 figure

Coherent States for Particle Beams in the Thermal Wave Model

In this paper, by using an analogy among {\it quantum mechanics}, {\it electromagnetic beam optics in optical fibers}, and {\it charge particle beam dynamics}, we introduce the concept of {\it coherent states} for charged particle beams in the framework of the {\it Thermal Wave Model} (TWM). We give a physical meaning of the Gaussian-like coherent structures of charged particle distribution that are both naturally and artificially produced in an accelerating machine in terms of the concept of coherent states widely used in quantum mechanics and in quantum optics. According to TWM, this can be done by using a Schr\"{o}dinger-like equation for a complex function, the so-called {\it beam wave function} (BWF), whose squared modulus is proportional to the transverse beam density profile, where Planck's constant and the time are replaced by the transverse beam emittance and by the propagation coordinate, respectively. The evolution of the particle beam, whose initial BWF is assumed to be the simplest coherent state (ground-like state) associated with the beam, in an infinite 1-D quadrupole-like device with small sextupole and octupole aberrations, is analytically and numerically investigated.Comment: 21 pages, Late

Quantum computation by quantum-like systems

Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and quantum gates to segments of the fiber providing an unitary transformation of the mode structure along a space direction. Simulation of nonlinear quantum effects is also discussed.Comment: 12 pages, Late

Nonlocal effects in high energy charged particle beams

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms of a nonlinear coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalised nonlinear Schroedinger equation including a nonlocal nonlinear term. The consequences of the resistive part on the propagation of particle bunches are examined using analytical as well as numerical methods.Comment: 6 pages, 6 figures, uses RevTeX