Relativistic Electron Layers Research Articles

Instability in a relativistic electron layer with a strong azimuthal magnetic field

A thin relativistic electron layer immersed in a strong azimuthal magnetic field between two concentric cylindrical conductors is shown to be unstable. The instability is caused by the curvature of the walls, which modifies the interaction between particles in such a way that the inductive (attractive) forces are greater than the electrostatic (repulsive) forces. The growth rate of the instability peaks at long axial wavelengths.

Stabilization of the Negative Mass Instability in a Rotating Relativistic Electron Beam

It is shown that the negative mass instability in a rotating relativistic electron layer may be stabilized by a radial dc electric field of a suitable magnitude. The stabilization mechanism is independent of the beam velocity spread, and is insensitive to the beam current, the container geometry, or the azimuthal mode number. A simple stability criterion is given.

Theory of a low magnetic field gyrotron (gyromagnetron)

The stability of a relativistic electron layer inside a magnetron waveguide is examined. The dispersion relationship for the cyclotron maser/negative mass instability in this "gyromagnetron" device is derived, using a Pierce type analysis. The coupling constant e between the electron beam and the waveguide circuit is computed. Based on a study of ~, we design a proof-ofprinciple experiment for a gyromagnetron amplifier which operates at the sixth cyclotron harmonic, thereby reducing the magnetic field requirement by a factor of six. The operating beam voltage is relatively low. The problem of mode competition is examined, but is found to be not serious. The design procedure is described.

Simple macroscopic theory of cyclotron maser instabilities

The stability of an annular layer of relativistic electrons, guided by a uniform magnetic field inside a circular waveguide, is analyzed using a fluid dynamical treatment. The simple theory presented here is aimed at providing some perspective of the cyclotron maser instability which traditionally has required an analysis in phase space. The same dispersion relationship is recovered from the macroscopic fluid model. Thus in addition to the usual interpretation in terms of phase bunching in the electronic motions, the cyclotron maser instability may also be regarded simply as a growing space-charge wave in a relativistic beam which is in sychronism with the surrounding structure, or as due to current bunching, or even as an instability of the shear flow of a rotating relativistic electron fluid. Such a variety of interpretations emerges because the cyclotron maser instability is recently identified as the negative mass instability in rotating relativistic beams. The ac space-charge effects are completely accounted for in the present study. The theory presented here follows closely the treatment of classical electron tubes, and is valid even for nonsynchronous interactions. The threshold beam voltage required for the onset of cyclotron maser instability may also be derived using the fluid dynamical approach. The effects of axial bunching are analyzed. This macroscopic theory may be applied to various geometrical configurations.

Where do charged particles enter in and exit from the magnetosphere? Some HEOS-2 measurements

The review concentrates on HEOS-2 spacecraft results in two main areas: 1. (1) Solar protons penetrating the magnetosphere: The picture emerging from earlier spacecraft and groundbased measurements is summarized in the light of proton trajectory computations and the theories of direct and diffusive proton entry to the polar caps. The direct in situ measurements made available through the unique positioning of HEOS-2 in the polar magnetosphere are described. 2. (2) The magnetopause electron layer: The HEOS-2 spacecraft has discovered an essentially permanent layer of energetic and relativistic electrons at the polar magnetopause. The properties of this layer and its response to geomagnetic and interplanetary conditions are described.

Energetic and relativistic electrons near the polar magnetopause

More than 2 years of Geos 2 observations in the high-latitude outer magnetosphere and magnetosheath have confirmed the presence of a layer of energetic and relativistic electrons near the polar tail magnetopause. This layer, appearing as 'electron spike' on almost every magnetopause crossing, contains electrons over a wide range of energies up to relativistic energies of >2MeV. Their differential energy spectrum, if fitted by a power law, an average spectral index between 3 and 4.5. The spikes are typically 1--2R/sub E/ wide extending more into the mangetosheath than into magnetosphere. The electron intensity in the magnetopause layer decreases with distance along the tail, away from the polar cusp, and increase with K/sub P/ values. It tends to be higher when the magnetosheath field is parallel or antiparallel to the tail magnetic field. In many cases the magnetopause spikes in the magnetosheath which often follow closely the fluctuations of the magnetosheath field direction and/or intensity. A map of the average electron distribution in the polar magnetosphere and magnetosheath is presented.

Computer simulation of pulse trapping and pulse stacking of relativistic electron layers in astron

During the past two years computer simulation has been used extensively to obtain a detailed description of pulse trapping and pulse stacking of relativistic E layers in astron. Resistors are essential to good trapping, in agreement with experiment. In the code, pulse trapping can easily be arranged to be 100% efficient—in marked contrast to the experiment. Details of pulse stacking are dependent on resistor configuration, degree of charge neutralization, and external well shape, but the field reversal increase invariably runs into a saturation due to axial expansion of the layer. This process can be described as a phase space exclusion or, alternatively, as nonadiabatic axial heating. The pulse-stacking process involves a tearing and bunching, and it is also nonadiabatic in the radial motion; as a consequence, radial expansion always occurs, and this can also act as a limitation to field reversal unless the resistor locations allow considerable radial room. Very tightly focused (axially) pulses can result from vacuum pulse trapping if system conditions are optimized correctly. This in turn lessens the axial expansion problem for vacuum layers. In contrast, the radial expansion problem is much more severe for vacuum layers, and this effect causes radial loss at some layer strength well short of field reversal. Large-current (2500 A) nuetralized pulses result in field reversal with one pulse.

Effects of Cold Plasma on the Negative Mass Instability of a Relativistic Electron Layer

The stability of a cylindrical layer of gyrating relativistic electrons (E layer), both in vacuum and in a cold plasma, is examined. The beam model assumes concentric particle orbits and allows for a finite thickness of the E layer. It is shown that the background plasma can stabilize the lower azimuthal modes (modes with their frequency less than the cold cyclotron frequency, or azimuthal wavenumber l less than the relativistic mass factor γ). The mechanism of stabilization can be interpreted in terms of an inductive impedance at the beam edge due to the cold plasma. The interaction of the beam with the plasma at the upper hybrid frequency is discussed briefly.

Negative-mass instability in a cylindrical layer of relativistic electrons

Negative-mass instability in a cylindrical layer of relativistic electrons

Negative-mass instability in a cylindrical layer of relativistic electrons

The purpose of this work is to examine the stability of a cylindrical layer of relativistic particles in a geometrical configuration that approximates the Astron machine. The model is that of a long thin cylindrical shell of relativistic electrons that gyrate in an axial magnetic field and are enclosed in cylindrical conducting walls. It is shown that a number of the lower azimuthal (`negative-mass') modes can be rendered stable even in the absence of any energy spread by the proximity of a highly conductive outer wall. This stabilization is a property of the cylindrical geometry, and is in marked contrast to the results for a toroidal tank geometry such as those used in particle accelerators. A calculation of the instability growth rates in the presence of the Astron resistor structure is also presented.

A computation for studying the formation of the relativistic electron layer in astron

In the controlled fusion experiment, Astron, relativistic electrons are injected at the end of a long cylindrical tank across an applied axial magnetic field. A rotating cylindrical sheath of electrons is formed. The self-consistent field problem is solved by integrating the time-dependent Vlasov-Maxwell equations numerically using finite-difference methods. The problem described is four dimensional and requires a large scale computing system for the solution of the difference equations.

Development of 36-Megawatt Modulators for the Astron 1000-Megawatt Electron Accelerator

A 1000-megawatt peak-power linear electron accelerator is required for the injection of electrons into a thermonuclear fusion experimental device, called the Astron, which is now under construction at the Lawrence Radiation Laboratory in Livermore, California. The Astron will determine the feasibility of an actual power-producing fusion reactor utilizing the principles of confinement and heating of a plasma by establishing a long rotating layer of relativistic electrons. The linear electron accelerator under construction is designed to produce a pulsed electron beam with an energy of 5 Mev ±0.5%, a pulse current of 200 amperes, with a pulse duration of 0.25 μsec and at 60 pulses per second. The accelerator will be of the induction type utilizing large magnetic cores. Approximately 400 cores will be used and each one will contribute a minimum acceleration of 12,000 volts. The details of the design and development of a line-type modulator used for pulsing cores and capable of an output peak power of 36 megawatts will be discussed in detail. A type 6587 and type 5949A thyratron were life-tested at 32 kv, 2000 amperes, and 60 pps. Useful life in excess of 1000 hours was obtained. In addition, it was necessary to develop corona-resistant connectors for this application. Life data and final design for a small connector suitable for operation at 16-kv, 0.4-μsec (70% amplitude points) pulses with 60-nanosecond rise time, and at 60 pps are presented.