Hollow Relativistic Electron Beam Research Articles

The influence of a background plasma on the diocotron instability of a relativistic hollow electron beam

The influence of a background plasma on the diocotron instability of a relativistic hollow electron beam is investigated within the framework of a cold fluid model. The background plasma is taken to have a uniform density except at the mean radius of the electron beam where the density is assumed to be discontinuous. Of the charged species comprising the plasma, only the electrons influence the dynamics of the beam-plasma system; the effect of the ions is negligible because of their small plasma frequency. A dispersion relation for the eigenfrequencies of the system is derived and employed to examine instabilities. It is found that the fundamental (l = 1) mode, which is unconditionally stable for a hollow electron beam in a vacuum, is now unstable for certain parameter regimes. The appearance or growth of instabilities with increases in the plasma density discontinuity is observed, while increases in the relativistic factor γb are seen to exert a stabilizing influence. It is also found that thin beams are generally more unstable than thick ones.

Diocotron instability in asymmetric beams

A hollow relativistic electron beam propagating in a cylindrical drift tube is subject to the diocotron instability. It is shown that if the beam is not azimuthally symmetric, then the diocotron effect can disrupt the beam in a substantially shorter time than in the symmetric case.

Theory of free electron laser instability in a relativistic annular electron beam

A self-consistent theory of the free electron laser instability is developed for a hollow electron beam propagating through an undulator (multiple mirror) magnetic field. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that the beam is thin, with radial thickness much smaller than the mean beam radius, and that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the characteristic energy of the electron beam. The dispersion relation describing the free electron laser instability in a hollow relativistic electron beam is obtained for an equilibrium distribution function in which all electrons have the same value of transverse energy and the same value of canonical angular momentum, and a Lorentzian distribution in axial momentum. It is shown that the influence of finite radial geometry plays a critical role in determining the detailed stability behavior. Moreover, the growth rate and bandwidth of the instability can be expressed in terms of Budker’s parameter ν, instead of the plasma frequency as in the case of a uniform density beam. Furthermore, it is found that free electron laser stability properties exhibit a sensitive dependence on axial momentum spread.

Diocotron instability of a relativistic hollow electron beam

The diocotron stability properties of a relativistic hollow electron beam are investigated within the framework of the macroscopic, cold fluid model, in which the electron motion is assumed to be laminar. The stability analysis is carried out for the case of a sharp boundary density profile, including the important influence of relativistic effects and fractional charge neutralization on the stability behavior. It is found that the growth rate of instability is proportional to 1/γb2, thereby being reduced considerably by increasing the electron energy γbmc2. Moreover, the fractional charge neutralization plays a significant role in the stability behavior, particularly for the relativistic electron beam.

Electron Beams Generated in Foilless Diodes

The operation of a foilless diode to generate a hollow relativistic electron beam has been performed on the FX-25, a Van de Graaff charged 3 MV device. The diode consists of a cylinder of carbon (graphite) supporting either a cathode tip of larger diameter or a right circular cylinder of equal diameter and a coaxial anode guide wall having either an abrupt discontinuity in wall diameter or a smooth wall. Six configurations were employed to explore the emitted electron behavior in the crossed electric and magnetic fields. Finite gyroradius effects limit the transmitted current at low applied axial magnetic field strengths. The transmitted current increases with increasing field strength until a critical field is reached, when further increase in field strength results in a decrease to a plateau in transmitted current. This critical field produces an electron gyroradius equal to the gap between cathode guide wall (anode) and is found to satisfy ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> > 2 ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> where ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is the electron gyro-frequency and ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> is the beam plasma frequency. At high applied field strengths a very thin beam is transmitted and bounded by the space charge limited current. These features agree qualitatively with recent computer simulations of Jones and Thode.

Theory of foil-less diode generation of intense relativistic electron beams

A study is made of the generation of intense hollow relativistic electron beams in a foil-less diode. A strong magnetic field is assumed so that the electron motion is one dimensional. Also, the electron motion is considered to be ultra-relativistic. The problem of the self-consistent space charge in the diode is reduced to a singular integral equation. This integral equation is solved and the nature of the solutions is discussed. The beam density increases at the beam edges and has a minimum in the beam interior. The diode impedance as a function of the beam thickness and geometry is discussed.

Comments on ’’Simple models of solid and hollow relativistic electron beams with arbitrarily high current’’

Comments on ’’Simple models of solid and hollow relativistic electron beams with arbitrarily high current’’

Observations of Collective Ion Acceleration by a Relativistic Electron Beam in a Magnetic Cusp

VOLUME PHYSICAL REVIEW LETTERS $6, NUMBER 24 For a discussion of one-photon coherent effects, see, for example, L. Allen and J. H. Eberly, OPtical Reso- nance and Taboo-Leve/ Atoms (Wiley, New York, 1975). References to earlier NMR work can be found in A. Ab- ragam, The Principle of Nuclear Magnetism (Oxford Univ. Press, Oxford, England, 1961). 'S. R. Hartman, IEEE J. Quantum Electron. 4, 802 E. M. Belenov and I. A. Poluektov, Zh. Eksp. Teor. Fiz. 56, 1407 (1969) ISov. Phys. JETP 29, 754 (1969)]. M. Takatsuji, Phys. Rev. A ll, 619 (1975). R. G. Brewer and E. L. Hahn, Phys. Rev. A ll, 1614 D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975). 7R. L. Shoemaker and R. G. Brewer, Phys. Rev. Lett. N. Tan-no, K. Yokoto, and H. Inaba, Phys. Rev. Observations 14 JvNz 1976 Lett. 29, 1211 (1972). M. Matsuoka, H. Nakatsuka, and J. Okada, Phys. Bev. A 12, 1062 (1975). P. F. Liao and J. E. Bjorkholm, Phys. Rev. Lett. L. S. Vasilenko, V. P. Chebotaev, and A. V. Shisha- ev, Pis'ma Zh. Eksp. Teor. Fiz. 12, 161 (1970) [JETP Lett. 12, 113 (1970)j. W. K. Bischel, P. J. Kelly, and C. K. Rhodes, Phys. Rev. A 18, 1829 (1976). ~3F. Shimizu, J. Chem. Phys. 52, 8572 (1970). A. Gondhalekar, E. Holzhauer, and N. R. Hecken- berg, Phys. Lett. 46A, 229 (1979). Very useful infor- mation on the single-mode operation of the TEA laser has also been provided by R. L. Aggarwal, N. Lee, and C. Chase (private communication). D. Grischkowsky and M. M. T. Loy, Phys. Rev. A of Collective Ion Acceleration by a Relativistic Electron Beam in a Magnetic Cusp* C. W. Roberson, and N. Rostoker University of California, Irvine, California 9271 7 (Received 2 March 1976) S. Eckhouse, A. Fisher, S. Robertson, Physics Department, We have observed ion pulses of 10~3 protons by passing hollow relativistic electron beams through a magnetic cusp. Ion pulses are observed with drift-chamber fill pres- sures from 75 to 600 mTorr of H2. Magnetic fields of 0. 8 kG suppress the mechanism responsible for acceleration without magnetic field. A different mechanism appears to turn on and peaks as the cusp threshold is approached. More than 10~~ protons with en- ergies greater than 2 MeV are observed. In conventional particle accelerators, the elec- and magnetic fields at the particle are pro- duced externally and are subject to limitations imposed by V&B = 0 and V' ~ E = 0 in addition to the usual technical limitations of electrical break- down. In a collective accelerator the electromag- netic fieMs that accelerate a particle are internal and produced by many charged particles. The magnitude of the internal field is determined mainly by the beam density that can be achieved. The first observations of collectively acceler- ated ions with intense electron beams were in the experiment of Graybill and Uglum. ' They injected a 1. 6-MeV, 40-kA beam into a drift chamber filled with 200 mTorr of hydrogen and observed 100 A pf 5-MeV protons. The electric field was about 100 MV/m which is a factor of 10 greater than iri conventional accelerators. However, the acceleration took place over a distance of only 5 cm. In conventional accelerators the design and control of the fields at the particle is a highly developed science. In co11ective accelerators, tric since the fields are internal and created by many particles, the problem of design and control is still at a very early stage and involves much more complicated physics. One of the few meth- ods available for design and control of the elec- tron beam is the application of an externally pro- duced magentic field. In previous experiments this suppressed the co1lective acceleration. ' We report new experiments where collective accel- eration is enhanced by an external magnetic cusp. Collectively accelerated ions have been ob- served in a number of experiments' '0 when an intense beam is propagated through a low-pres- sure gas without an external magentic field. There has been considerable theoretica1 effort in The ex- conjunction with these experiments. perimental results are usually interpreted in terms of the acceleration of the space-charge we11 at the head of the beam as it breaks down the neutral gas or in terms of a localized pinch. Figure 1 is a sketch of the apparatus. The electron-beam generator produced a 1. 3-MeV,

Macroscopic Equilibrium Properties of Intense Hollow Relativistic Electron Beams

The equilibrium properties of intense hollow relativistic electron beams are investigated within the framework of a macroscopic cold-fluid model. The electron beam propagates parallel to a uniform magnetic guide field B0êz and is partially charge neutralized and partially current neutralized by a background plasma. In circumstances where the axial velocity profile of the beam is uniform (βz=const.) and the angular velocity profile ω(r) is a known function of r, it is shown that all other equilibrium properties (e.g., self-field profiles and beam density profile) can be calculated in closed form. Specific examples of diamagnetic and paramagnetic beam equilibria are discussed.

Self-consistent Vlasov equilibria for intense hollow relativistic electron beams

This paper discusses the procedure for constructing intense hollow relativistic electron beam equilibria within the framework of the steady-state (∂/∂t = 0) Vlasov–Maxwell equations. It is assumed that the electron beam propagates parallel to a uniform axial guide field Bext0 = B0 êz inside a grounded cylindrical conductor, and that the positive ions provide a partially neutralizing background with density n0i(r) = fn0e(r), where f = const. = fractional neutralization. The equilibrium properties are calculated for the specific choice of electron distribution function , where H, Pθ, and Pz are the energy, canonical angular momentum, and axialcanonical momentum, respectively, for an electron moving in the equilibrium fields, and , and P0 are constants. For this choice of distribution function, the mean axial velocity of the electron beam is equal to , and the beam density profile is hollow with inner and outer radii, R0 and R1, determined self-consistently from nonlinear boundary conditions that involve the equilibrium parameters Po, γb, γ0, etc., and the equilibrium self fields. Closed expressions for Ro and B1 are obtained for the case where the collisionless skin depth c/ωpe is large in comparison with the characteristic radius of the electron beam, and the beam density is sufficiently low that . The two cases, Po&gt;0 and Po&lt;0, are considered.

Implosion of an unneutralized drifting relativistic electron beam

A hollow relativistic electron beam, drifting in vacuum, can be made to implode radially when a grounded conductor is placed on the beam axis. The collapse is the result of the change in the direction of the electric field relative to that of a freely propagating beam. The entire energy content of the collapsed beam is dissipated in the conductor.

Simple models of solid and hollow relativistic electron beams with arbitrarily high current

A model of a neutralized electron beam in which the electrons make helical orbits about the axis is described. This differs from previous models in that there is no longitudinal field or azimuthal current. Three particular cases, corresponding to (1) uniform charge density in a solid beam, (2) uniform current density in a solid beam, and (3) uniform charge density in a hollow beam are analyzed. In none of these configurations is there a current limit, and all the electrons move in the forward direction.

Destructive Instabilities in Hollow Intense Relativistic Electron Beams

It is found that a 400-keV, 10-40-kA, 50-nsec duration hollow relativistic electron beam suffers from a severe instability when injected into neutral gas along a magnetic field. The dependence of beam distortion on beam thickness, magnetic field strength, beam current, and proximity of the surrounding conducting walls is experimentally studied. The experimental observations are consistent with the diocotron instability occurring during the first several nanoseconds of the beam pulse.