Theory of electron beam tracking in reduced-density channels
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Abstract:
A theory is presented for the guiding of relativistic electron beams by rarefied gaseous channels. The analysis is based on analytic computations of the transverse force felt by a rigid‐rod beam propagating off axis from a channel of reduced gas density. The density gradients produce an attractive channel force that can be surprisingly robust, even though it develops from relatively subtle gas chemistry properties. Static numerical calculations support the analytic work. Longitudinal beam coupling and effects that degrade channel guidance are discussed as well.Keywords:
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A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the Particle-In-Cell code OSIRIS.
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The numerical computation of Kolmogorov entropy is used to study the dynamical stability of a free-electron laser with a planar wiggler. Axial magnetic field and ion-channel guiding are examined as two different types of focusing mechanism for confinement of the electron beam against its self-fields. It was found that the dynamical stability of electron trajectories decreases profoundly near the resonance region. Self-fields increase the dynamical stability in group I orbits and decrease it in group II orbits. These orbits are defined according to their axial magnetic field or ion-channel density.
Wiggler
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The space–charge effect in high density electron beams (beam current ∠2 μA) focused by a uniform magnetic field is studied computationally. On an approximation of averaged space– charge force, a theory of trajectory displacements of beam electrons is developed. The theory shows that the effect of the averaged space–charge force appears as a focal length stretch. The theory is confirmed not only qualitatively but also quantitatively by simulations. Empirical formulas for the trajectory displacement and the energy spread are presented. A comparison between the empirical formulas and some theoretical formulas is made, leading to a severe criticism on the theories of energy spreads.
Field theory (psychology)
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The head of a relativistic electron beam propagating into un-ionized or weakly ionized gas is not self-pinched and expands freely, causing the beam to take on a ’’trumpet’’ shape. The region where the beam pinches, referred to as the ’’pinch point’’, moves steadily back into the beam because of the reduced ionization rate at the expanding beam head and energy loss to the induced electric field. This beam head ’’erosion’’ is modeled by assuming that the axial beam profile is stationary in a reference frame moving with the pinch point. This assumption allows the beam equations to be written in time-independent form, and radial averaging then yields a set of one-dimensional ordinary differential equations for the beam radius and energy, the mean pinch force, and the background conductivity. Solution of these equations with appropriate boundary conditions gives both the erosion rate and the beam axial structure. The results of extensive numerical calculations are presented, along with analytic estimates of the erosion rate, degree of current neutralization, and axial scale lengths.
M squared
Relativistic electron beam
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In this report the basic configuration of and the motivation for the triaxial geometry for intense electron beam focusing is reviewed. The theory that has been used to guide and to aid in the interpretation of the experiments is based primarily on the calculated motion of idealized, energetic line currents which move in the magnetic fields induced by these currents in their interaction with the walls of cylindrical drift channels. A computer program was used both to search for the beam injection conditions and channel geometries which would lead to the best transport and focusing and to predict the experimental results when the measured beam injection conditions were used in the calculations. The experiments will be discussed in a second report under the same title, but as ''Part II--The Experiments.''
Relativistic electron beam
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Relativistic electron beam
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This paper describes an experimental and theoretical study of a charge-neutralized, hollow, rotating relativistic electron beam propagating inside a metal tube in the absence of an external magnetic guide field. A model has been developed in which the radial equilibrium is derived from the force balance on the beam interacting with its self-field, and the velocity of propagation of the beam is derived from the power balance. The experimental results show close agreement with the predictions of the model.
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Interim
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Relativistic electron beam
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Electron acceleration by ultrahigh intensity lasers is studied by means of two-dimensional planar particle-in-cell simulations. It is shown that the full divergence of the fast electron beam is defined by two complementary physical effects: the regular radial beam deviation depending on the electron radial position and the angular dispersion. If the scale length of the preplasma surrounding the solid target is sufficiently low, the radial deviation is determined by the transverse component of the laser ponderomotive force. The random angular dispersion is due to the small scale magnetic fields excited near the critical density due to the collisionless Weibel instability. When a preplasma is present, the radial beam deviation increases due to the electron acceleration in larger volumes and can become comparable to the local angular dispersion. This effect has been neglected so far in most of the fast electron transport calculations, overestimating significantly the beam collimation by resistive magnetic fields. Simulations with a two-dimensional cylindrically-symmetric hybrid code accounting for the electron radial velocity demonstrate a substantially reduced strength and a shorter penetration of the azimuthal magnetic field in solid targets.
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Ponderomotive force
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Citations (96)