Relativistic Charged Particle Beam Research Articles

Thermal wave model for nonlinear longitudinal dynamics of a relativistic charged particle bunch in cold plasmas

We study the longitudinal dynamics of a relativistic charged particle bunch through a cold, unmagnetized plasma, within the framework of the recently proposed thermal wave model for relativistic charged particle beam propagation. We show that, under the action of both a purely electrostatic plasma wave potential well and the plasma wake potential (self-interaction), the longitudinal bunch dynamics is governed by a nonlinear Schrödinger 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, allows us to study synchrotron-like oscillations in the plasma wave potential well as well as to obtain a longitudinal envelope equation which includes the self-interaction. Furthermore, we show that a soliton solution for the bunch density is possible and it results to be the natural asymptotic evolution of a modulational instability occurring when the bunch propagates in the plasma under the action of the self-force only.

Luminosity enhancement by a self-ionized plasma ine+e−collisions

We employ a two-dimensional particle-in-cell code to investigate the focusing of relativistic charged-particle beams in plasmas. The intense electric fields generated by electron and positron beams in high-energy physics experiments can ionize a gas into a plasma which will then focus the beams. This self-ionization mechanism will enhance the luminosity in ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ collisions by implementing a plasma lens in the interaction region. We investigate the dependences of the luminosity enhancement on the plasma lens thickness and plasma density. The application of plasma lens focusing to the Stanford Linear Collider is discussed.

Thermal wave model for nonlinear longitudinal dynamics in particle accelerators

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 Schrödinger 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.

BEAM TEMPERATURES AND THE ENERGY BROADENING OF A RELATIVISTIC CHARGED-PARTICLE BEAM IN AXIALLY SYMMETRIC ELECTRIC- AND MAGNETIC-FIELDS

Starting from the relativistic motion equation of a single particle,the motion constants were obtained. And then by using these motion constants a distribution function of the beam particles was constructed which satisfies the Vlasov equation. The beam temperatures and the energy broadening of a relativistic charged-particle beam in axially symmetric electric- and magnetic-fields have been calculated by using the distribution function,and the weakly and strongly relativistic approximations have also been discussed respectively.

Self-consistent interaction between the plasma wake field and the driving relativistic electron beam.

It is shown that the self-consistent interaction between wake fields and the driving electron bunch in a collisionless, unmagnetized, overdense (${\mathit{n}}_{\mathit{p}}$\ensuremath{\gg}${\mathit{n}}_{\mathit{b}}$) plasma is governed by three coupled equations. In the long-beam limit, they reduce to a pair consisting of an appropriate nonlinear Schr\odinger equation for the a/Ibeam wave function \ensuremath{\Psi}, and an equation for the wake-field potential that is driven by the transverse profile of the beam density, which is proportional to \ensuremath{\Vert}\ensuremath{\Psi}${\mathrm{\ensuremath{\Vert}}}^{2}$. The pair of equations are suitable for studying the beam self-focusing (self-pinching equilibrium) for the case in which the beam-spot size is larger (smaller) than the wavelength of the wake fields. It is demonstrated that our self-consistent theory, which is based on the recently proposed thermal wave model for relativistic charged-particle beam propagation, is capable of reproducing the main results for the beam-filamentation threshold and the self-pinching equilibrium condition that are already known in the conventional theory of the beam self-interaction in collisionless plasmas.

Focusing properties of a plane wiggler magnetic field

We have considered the focusing properties of an inhomogeneous magnetic field. General analytic formulae for the horizontal and vertical properties are deduced. The focusing of a relativistic charged particle beam in a wiggler is analyzed, and the effect of the superconducting wiggler upon the betatron tunes in the SIBERIA-2 storage ring is computed.

Fluid models for relativistic electron beams: An independent derivation

A generalized fluid model is proposed for a relativistic charged particle beam. The model is constructed by starting with the covariant Vlasov equation, taking the moments, and closing via a suitable ‘‘constitutive law’’ for the third-order moment. The ‘‘constitutive law’’ is uniquely specified by requiring consistency with a supplementary conservation law representing entropy balance. The derivation presented here is independent and also different from a previous one utilizing results obtained within the framework of relativistic extended thermodynamics.

Eulerian formalism of linear beam-wave interactions.

A detailed account of a formal mathematical description of the interaction of relativistic charged particle beams with electromagnetic waves, within the frame of classical electrodynamics, is presented. The standard system of eight equations (Maxwell and Lorentz gauge conditions and fluid dynamics) in the four-vector potential ${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$ and the four-vector current density ${\mathit{j}}_{\mathrm{\ensuremath{\mu}}}$ is reduced, after linearization, to a canonical system of four coupled partial differential equations in the electromagnetic field perturbation \ensuremath{\delta}${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$. Both electromagnetic and dynamical quantities are treated as fields, according to the Eulerian formalism. This new system is very general, and different beam-wave interactions are characterized by different fluid equilibria and boundary conditions for \ensuremath{\delta}${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$ and its derivatives. Finally, the equations are used, as an example, to study the dispersive characteristics of space-charge waves propagating in a cylindrical waveguide, along a relativistic electron beam confined by an axial magnetic field. The problem is treated in a fully relativistic way, for arbitrary values of the axial guide field and any degree of azimuthal symmetry.

First-order covariant treatment of the influence of space charge and external fields on finite-emittance relativistic beams of charged particles in generalized curvilinear coordinates

A first-order covariant treatment of space-charge effects on relativistic beams of charged particles under the influence of applied fields of arbitrary forms is presented. The beams and fields are assumed to fulfill no particular symmetry conditions, and curvilinear orthogonal coordinates are used. Relative to a given distribution function, a suitable choice of both metric tensor and optical axis allows for the selection of appropriate coordinates, reducing the overall transverse motion of a charged particle to a pair of independent motions along the principal axes of a tensor that is related to both geometry and field. Detailed formulas applying to a microcanonical distribution in an eight-dimensional phase space are worked out, and the envelope equations for a monokinetic beam are carried out explicitly. The distribution function is shown to separate into the product of a stationary distribution in transverse-coordinate space and momentum space by using factors carrying the relativistic corrections. As a result, the envelope equations are formally identical to the customary equations describing the envelope of a nonrelativistic beam under the influence of merely transverse forces. A few numerical applications are finally presented; the behavior of beams moving through a magnetic prism and through a cycloidal analyzer is displayed graphically.

Fluid models for relativistic electron beams

A system of equations is provided that may be used in the study of relativistic charged particle beams. The equations are based upon the equations of the kinetic theory for first, second and third order moments and the system is closed by letting the third order moment depend on the lower order ones. The form of that dependence is formally equal to the explicit constitutive function given by extended thermodynamics. However, here the contributions to the third order moment can be classed as being different in order of magnitude, because there is a smallness parameter characterizing the small dispersion of the particle beam. The resulting system of equations is quite specific, it is fully covariant and it is equivalent to a symmetric hyperbolic system thus ensuring existence and uniqueness of solutions.

Larroche and Pellat reply.

The Comment by Beskin, Gurevich, and Istomin about our calculation of the radiative instability of a relativistic beam of charged particles is twofold; we wish to reply to those two points.

Cooling and focusing of a relativistic charged particle beam in crossed laser field

A new method to focus a relativistic charged particle beam is suggested and studied. This idea is based on the use of the ponderomotive force which arises when a periodic electromagnetic field is created, as in the case of two crossed laser beams.

Curvature instability of relativistic particle beams.

We investigate the instability of curvature radiation of a relativistic beam of charged particles in a very strong curved magnetic field, which is of interest as a pulsar radiation mechanism. The conditions for growth are a fairly steep boundary at the outer edge of the beam and high frequencies meeting a non-WKB requirement. High growth rates are found.

Initial Beam Test Results from a Silicon-Strip Detector with VLSI Readout

Silicon detectors with 256 strips, having a pitch of 25 μ m, and connected to two 128 channel NMOS VLSI chips each (Microplex), have been tested in relativistic charged particle beams at CERN and at the Stanford Linear Accelerator Center. The readout chips have an input channel pitch of 47.5 μ m and a single multiplexed output which provides voltages proportional to the integrated charge from each strip. The most probable signal height from minimum ionizing tracks was 15 times the rms noise in any single channel. Two-track traversals with a separation of 100 μ m were cleanly resolved.

Calculation of high power relativistic beams with consideration of collision effects

Numerical calculation of relativistic charged particle beams moving in axisymmetric systems in which the presence of a residual neutral gas is possible is considered. In this content it is essential to consider phenomena related to collisions between charged particles and neutrals (for example, ionization and charge transfer). Algorithms are constructed for numerical modeling of ionization processes within the framework of the ERA program complex [1]. Solutions of model and practical problems are presented as examples. Such problems were studied previously in [2, 3] where ionization processes were considered by a more complex method requiring a greater volume of calculations but valid at lower pressures.

Second-order treatment of the influence of space charge and external fields on rotationally symmetric finite-emittance relativistic beams of charged particles

The present paper reports a relativistic treatment of space-charge effects on rotationally symmetric beams of charged particles under the influence of an external electromagnetic field. The general form of a stationary distribution describing a homogeneous, monokinetic beam is suggested, and the details of a suitable generalization of the Kapchinskij–Vladimirskij distribution are fully developed. It is shown that if second-order terms, which mainly affect the longitudinal motion, are retained, the given distribution actually provides a parabolic charge density throughout a beam cross section while the longitudinal current density remains uniform, as is usually assumed. The relativistic version of the envelope equation, including the magnetic field, is also calculated and its classical limit is compared with an available equation applicable to a beam under the influence of merely an electric field. Emittance-dependent discrepancies, related to the longitudinal effects of the space charge, are detected. The standard geometry of a rotationally symmetric Pierce gun is finally revised to allow for the addition of an external magnetic field.

The interaction of relativistic charged-particle beams with interstellar clouds

view Abstract Citations (27) References (44) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The interaction of relativistic charged-particle beams with interstellar clouds Rose, W. K. ; Guillory, J. ; Beall, J. H. ; Kainer, S. Abstract Collimated beams of relativistic particles are known to be emitted from radio-bright active galaxies and quasars. Recent observations suggest that similar phenomena may occur in the nuclear regions of Seyfert galaxies. Some of the consequences that result from the interaction of a beam of relativistic particles with interstellar clouds have been calculated for a plausible range of physical parameters. Resonant plasma waves, nonresonant plasma waves, and ion acoustic waves are excit as a relativistic electron, electron-positron, or electron-proton beam traverses an interstellar cloud. The wave energy levels are characterized by either oscillatory or (quasi) steady state solutions. Nonresonant plasma waves may add power law tails to the distribution function of the background plasma electrons. The presence of electron tails can lead to enhanced optical and UV line radiation. The beam loses energy primarily as a result of the collisionless excitation of plasma waves, inverse Compton radiation, and resistive heating. The calculations made are described and some of their implications for observations of active galactic nuclei are discussed. Publication: The Astrophysical Journal Pub Date: May 1984 DOI: 10.1086/162025 Bibcode: 1984ApJ...280..550R Keywords: Galactic Nuclei; Interstellar Gas; Molecular Clouds; Particle Beams; Plasma-Particle Interactions; Relativistic Particles; Active Galactic Nuclei; Active Galaxies; Beam Interactions; Charged Particles; Magnetohydrodynamic Stability; Quasars; Seyfert Galaxies; Astrophysics full text sources ADS |

Symmetric, relativistic charged particle beam equilibria

The macroscopic equilibrium of relativistic charged particle beams is studied for configurations which are azimuthally symmetric and free of radial divergence. It is proved that in the limit of negligible internal energy all such equilibria are necessarily axially independent. Special radially dependent equilibria are derived.

Calculation of the motion of relativistic beams of charged particles in electromagnetic fields

In calculating high-current relativistic beams of charged particles moving in electromagnetic fields, it is necessary to take account of the effect of the electric and magnetic self-fields products by the beams themselves. This effect has been modeled on a computer [1, 2]. The present paper describes numerical algorithms contained in the KSI-BESM compiling system [3] which permit the inclusion of a broad class of relativistic problems, taking account of the magnetic field of currents flowing in the metal parts of the device being calculated, and also problems with virtual cathodes.

Radiation cooling of charged beams

It is shown that cooling (collimation) of relativistic charged particle beams can be realized by letting the particles pass through monocrystal under channeling conditions.