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Birkeland Currents in Cosmic Plasma
Abstract
An electromotive force ϕ = ∫ v × B⋅ dl giving rise to electrical currents in conducting media is produced wherever a relative perpendicular motion of plasma and magnetic field lines exist (Sect. 3.5.2). An example of this is the sunward convective motion of the magnetospheric plasma that cuts the earth’s dipole field lines through the equatorial plane, thereby producing a Lorentz force that drives currents within the auroral circuit. The tendency for charged particles to follow magnetic lines of force and therefore produce field-aligned currents has resulted in the widespread use of the term “Birkeland Currents” in space plasma physics.
... The hypothesis here is that the means of transporting the cosmic spermata could be through the moving of sheathed and internally structured plasmoids within gigantic Birkeland Currents on a cosmic scale (Peratt, 1992). They would be hurtled through vast distances at nearly relativistic speeds between star systems and even between galaxies. ...
We review the main lines of evidence (molecular, cellular and whole organism) published since the 1970s demonstrating Lamarckian Inheritance in animals, plants and microorganisms viz. the transgenerational inheritance of environmentally-induced acquired characteristics. The studies in animals demonstrate the genetic permeability of the soma-germline Weismann Barrier. The widespread nature of environmentally-directed inheritance phenomena reviewed here contradicts a key pillar of neo-Darwinism which affirms the rigidity of the Weismann Barrier. These developments suggest that neo-Darwinian evolutionary theory is in need of significant revision. We argue that Lamarckian inheritance strategies involving environmentally-induced rapid directional genetic adaptations make biological sense in the context of cosmic Panspermia allowing the efficient spread of living systems and genetic innovation throughout the Universe. The Hoyle-Wickramasinghe Panspermia paradigm also developed since the 1970s, unlike strictly geocentric neo-Darwinism provides a cogent biological rationale for the actual widespread existence of Lamarckian modes of inheritance - it provides its raison d'être. Under a terrestrially confined neo-Darwinian viewpoint such an association may have been thought spurious in the past. Our aim is to outline the conceptual links between rapid Lamarckian-based evolutionary hypermutation processes dependent on reverse transcription-coupled mechanisms among others and the effective cosmic spread of living systems. For example, a viable, or cryo-preserved, living system travelling through space in a protective matrix will need of necessity to rapidly adapt and proliferate on landing in a new cosmic niche. Lamarckian mechanisms thus come to the fore and supersede the slow (blind and random) genetic processes expected under a traditional neo-Darwinian evolutionary paradigm.
... The interfacial pattern observed, which extends out to 0.6 mm beyond the membrane, is reminiscent of the Birkeland currents (field-aligned currents) [7] in a cold discharge plasma, i.e., a plasma discharge before breakdown into glow discharge or arcing. These currents tend to form helical twisted pairs of filaments similar in appearance to the pairs of particle streamers visible here. ...
Exclusion zone (EZ) formation at water-membrane interfaces was studied via bright- and dark-field microscopy. Various aqueous colloids including suspensions of charged microspheres, silicon dioxide particles, and raw whole milk were studied with Nafion® hydrophilic membranes. Interfacial formations observed included EZs and more complex patterns including striations, double layers, banding, dendritic aggregates of particles, and double-stranded structures resembling Birkeland current filaments in cold plasmas. A complex three-dimensional dynamic structure and continuous flow patterns persist in and around EZs, maintaining movement of the colloidal particles even after EZs are fully formed, for which a schematic is proposed. Since radiant energy is critical for EZ formation, we hypothesize that these interfacial phenomena are non-equilibrium dissipative structures that self-organize and self-maintain due to ongoing dynamic processes that may involve hydrodynamic interactions. Another experimental approach undertaken involved the construction of a microscope flow cell to measure the kinetics of EZ formation using sequential microphotography analyzed with macro-programmed ImageJ software to investigate effects of different types of conditioned water. No significant difference was found between spring water and the same water treated by a magnetic vortexer. A significant difference was found for municipal tap water compared to electrolyzed alkaline tap water from the same source.
The extent to which two selection effects, visual bias and random
accidents, enter into the perception of filaments in the CfA catalog is
investigated. The minimal spanning tree (MST) algorithm is used to
identify the filaments, and a data-permuting technique is used to
determine their statistical significance. The suitability of the MST for
this purpose is demonstrated. It is found that the filaments are not
accidental alignments or illusions; they disappear when the
small-amplitude correlations at large scale lengths are removed. This is
the first objective, statistical evidence for the physical existence of
the filaments.
A dispersion relation which includes finite axial wavevectors, k, is derived in the rest frame of the beam where the instability is assumed to be electrostatic. The dispersion relation is obtained in the lab frame by a Lorentz transformation. The instability is found to have a finite k bandwidth with the most unstable mode occurring at k≠0. The growth rate for the most unstable mode is found to be reduced by approximately 1/γ2 from the nonrelativistic result while the real frequency of this mode remains virtually unchanged. The effects of finite v z shear, which are left out of the analysis, are estimated and discussed.
This paper gives a linearized theory for the breakup of magnetically focused hollow beams of electrons. A zero-thickness developed beam is assumed. Growing waves are found to be possible both at zero frequency and at finite frequencies. When there are electrodes close to the beam inside and out, the waves grow more rapidly as the electrodes are moved further from the beam. If the current is increased and the magnetic field is increased just enough to keep the beam together, the rate of growth is increased. The theory predicts a greater rate of growth for a higher number n of cycles of variation around the circumference of the beam, but for actual beams of finite thickness the theory is inaccurate for large values of n. In a simple case, frequency becomes important only when the wavelength of waves along the beam becomes comparable with the wavelength measured around the circumference of the beam. Increasing waves are also found in a zero-thickness beam in crossed electric and magnetic fields, as in a magnetron amplifier or carcinotron, but not at zero frequency.
Certain satellite and terrestrial observations of transient magnetic fluctuations show a high degree of localization, while other observations are of a definite worldwide character. The worldwide fluctuations in the magnetic field are probably well explained in terms of hydromagnetic waves propagating through the magnetosphere in modes with the wave polarization current flowing perpendicular to the geomagnetic field. However, for the localized fluctuations such an interpretation is inconsistent with present theory of hydromagnetic wave propagation in the magnetosphere. We suggest that the observations of localized magnetic fluctuations might be better interpreted in terms of field-aligned currents in the magnetosphere.
Electron beams of tW/cm2 (~0.4 MeV) which are split into
filaments are produced by an inductive generator which transfers field
energy to beam particles in 1-10-ns pulses. Target-damage analysis
reveals the composite internal structure of each filament as a sequence
of concentric circles with a discontinuous pattern. The nonuniform
distribution of collectively accelerated positive ions within a filament
contributes to resolve the filament structure which propagates at a
speed ~3c4 and can cross unaffected a 103-G magnetic field.
A theoretical analysis of the magnetic fields surrounding field-aligned
current sheets confirms that stable spirallike distortions (or, in some
cases, folds) should occur at the free end. It is demonstrated that a
Birkeland current sheet is completely analogous to a fluid shear layer,
with the magnetic field and the current playing the roles of fluid
streamlines and of vorticity, respectively. The rotational sense of the
distortions indicates the direction of current. Spirals observed in the
aurora imply upward current in all cases where this mechanism applies.
The calculated threshold current density for distortion of an auroral
arc is 0.0000025 A/m.
Hydrodynamical conditions are obtained for the stability of an ideal cylindrical gaseous conductor in an external magnetic field.
A general analysis of the electromagnetic wakefields for an axisymmetric charge distribution moving through a cold uniform plasma is presented. Particular attention is given to the electromagnetic and relativistic effects influencing the waves. It is shown that the plasma provides shielding of the transverse wakefields on a scale length of a few electromagnetic skin depths (c/..omega../sub p/). The implications for plasma wakefield accelerators are that driving beams with radii of a few skin depths will experience severe pinching, whereas larger beams will be subject to filamentation instabilities. These conclusions are supported by self-consistent particle-in-cell simulations. The deleterious effects of transverse wakefields will severely limit the accelerating gradients that can be obtained even if a magnetic field is used to guide the driving beam.
The diocotron (or slipping stream) instability of low density (ωp « ωc) electron beams in crossed fields is considered for a cylindrical geometry. For a simple density distribution, the normal modes of the electron beam correspond to a continuum of eigenvalues, plus two discrete eigenvalues. Work due to Case and Dikii appears to show that the continuous spectrum is not important in stability studies of this type. The condition for stability considering the discrete modes only is derived; under suitable geometrical and electrical conditions, it is shown that these modes can be stable. The analogy between the electromagnetic problem considered here and the problem of the stability of an ideal rotating fluid is discussed. It is shown that stability conditions derived for the latter problem depend on the possibility of axial perturbations; what this implies for the electron beam problem is briefly discussed.
The study of instabilities driven by azimuthal shear (diocotron) and axial shear is extended to annular relativistic beams. The analysis is done nonrelativistically in the beam frame where the instability is assumed to be electrostatic, and the dispersion relation is then transformed back to the laboratory frame where magnetic perturbations are non-negligible. This requires keeping finite axial wavenumber kz in the analysis. The axial and azimuthal shears are related through the self-consistent equilibrium, assuming emission from an equipotential cathode. Axial shear destabilizes the diocotron modes at higher azimuthal wavenumbers l. It also produces a set of modes including l=1 modes, that are unstable as the result of wave–particle interactions. The annular configuration introduces an important second pole in the differential equation.
Streams of fast electrons which can accumulate positive ions in sufficient quantity to have a linear density of positives about equal to the linear density of electrons, along the stream, become magnetically self-focussing when the current exceeds a value which can be calculated from the initial stream conditions. Focussing conditions obtain when breakdown occurs in cold emission. The characteristic features of breakdown are explained by the theory. Failure of high voltage tubes is also discussed.
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Transverse magnetic disturbances are regularly observed at 1100-km altitude in the auroral region with the magnetically oriented satellite 1963 38C. For the dayside period 1000-1400 LT the lower-latitude boundary of the disturbance region has an average invariant latitude Ab of 76 ø during mgnetic quiet (K 40) and shifts southward to Ab -- 68 ø dur- ing periods of magnetic activity (Kp _ 4o). For 2300-0100 LT, this latitude is 67 ø when K 4o and is 63 ø when K _ 4o. The magnetic amplitudes range from about 30 y (the mini- mum here detectable) to 380 % or about 1% of the local geomagnetic field. Such variations are absent between A -- 31 ø (the minimum sampled) and the Aappropriate to the local time and K. The quiet-time location and diurnal variation of the magnetic disturbance region correspond to those for the auroral oval and the trapping cutoff electrons _ 40 key; all three phenomena have a nightside po.sition comparable to the trapping cutoff for electrons _ 280 key and _ 1.2 Mev, whose dayside displacement is also toward higher latitudes but with a small diurnal shift, 2 ø. The location and diurnal variation of the region containing most of these geophysical properties are reflected in the surface values of magnetic intensity recorded at the Baker Lake (A -- 75 ø) and Fort Churchill (A -- 70 ø) observatories; around local noon the Baker Lake values exceed those for Fort Churchill, while the reverse is true at local midnight.
The characteristics of field-aligned currents at an altitude of 800 km in the dayside high-latitude region over the northern hemisphere were determined from the Triad satellite magnetometer data recorded at College, Alaska, from January 1973 to October 1974. The field-aligned currents discussed here are located poleward of the large-scale field-aligned currents reported earlier and referred to as 'region 1 field-aligned currents' by the authors (Iijima and Potemra, 1976). These high-latitude field-aligned currents are most often observed in the dayside sector between 0930 and 1430 MLT and are statistically distributed between 78° and 80° invariant latitude during weakly disturbed conditions as indicated by westward electrojet activity (abs. value of AL < 100..gamma..). Although these high-latitude field-aligned currents show complicated variations, they generally flow away from the ionosphere in the forenoon hours (0930--1200 MLT) and into the ionosphere in the afternoon hours (1200--1430 MLT). These flow directions are opposite to the quasi-permanent region 1 field-aligned currents related to the S/sub q//sup p/ currents previously discussed by the authors. The directions and spatial distribution of these field-aligned currents are consistent with the antisolarward equivalent ionospheric current near 1200 MLT deduced from simultaneous ground-based magnetograms at approx.81° invariant latitude. The intensity of these high-latitude field-aligned currents increases as the interplanetary magnetic field increases in the southward direction. These field-aligned currents are located within the region associated with the dayside magnetospheric cusp, and their relationship to geomagnetic activity, especially interplanetary magnetic field variations, suggests that they may play an important role in the coupling between the interplanetary medium and the magnetosphere. (AIP)
A narrow, closed high-latitude region exists where large geophysical disturbances occur at all longitudes simultaneously along what is being called the auroral oval [Akasofu, 1966] because of its oval shape (centered roughly at the dipole pole) and association with the spatial distribution of visual aurora [Feldstein, 1963, 1966; Akasofu and Chapman, 1963; Piddington, 1965; Akasofu, 1966]. The auroral oval corresponds on the section around local midnight to the frequently discussed auroral zone for visual aurora, but on the dayside it extends to latitudes considerably above those extrapolated from the nightside auroral zone. The auroral oval also marks the magnetic shells near or coincident with those containing the following phenomena often treated in terms of a diurnal variation: the polar electro jet [Akasofu et al., 1965; Feldstein, 1966], the outer boundary of trapped electrons [O'Brien, 1963; McDiarmid and Burrows, 1964; Frank et al., 1964; Williams and Palmer, 1965; Williams and Mead, 1965], the maximum electron precipitation [O'Brien, 1962; McDiarmid and Burrows, 1964; Frank et al., 1964], the region with the radio aurora, also shown to match that of the visual aurora [Bates, 1966; Bates et al., 1966], and large, transverse magnetic disturbances at 1100-km altitude [Zmuda et al., 1966]. Theoretical models potentially applicable to the currents and fields in the oval have recently been reviewed by Boström [1966].
CONTENTS
1. Introduction 163
2. Formulation of problem and initial equations 164
3. Limiting currents in uncompensated electron beams 165
4. Critical currents in compensated unbounded electron beams 168
5. Influence of finite longitudinal dimensions of the system on the critical currents in electron beams 170
6. Interaction of unbounded relativistic electron beams with a plasma 172
7. Stability of bounded electron beams in a plasma 174
8. Critical currents of relativistic electron beams in a plasma 175
9. Comparison of theory with experiment 176
Cited literature 178
A plasma gun has been developed which projects ionized matter (metallic and deuterium ions) at speeds up to 2×107 cm per second. There is some evidence to support the hypothesis that the plasma projected by this gun comes off in an expanding torus which is shaped by its own magnetic field. When the plasma gun is fired into a dc magnetic field, the plasma forms a compact geometrical configuration (a plasma-magnetic entity called a plasmoid) which proceeds across the magnetic field. Plasmoids appear to be plasma cylinders elongated in the direction of the magnetic field. Plasmoids possess a measurable magnetic moment, a measurable translational speed, a transverse electric field, and a measurable size. Plasmoids can interact with each other, seemingly by reflecting off one another. Their orbits can also be made to curve toward one another. Plasmoids can be made to spiral to a stop if projected into a gas at about 10-3 mm Hg pressure. Plasmoids can also be made to smash each other into fragments. There is some scant evidence to support the hypothesis that they undergo fission and possess spin.
Recent research on magneto-hydrodynamics has indicated the existence of a great number of situations where a magnetic field stabilizes the state of motion of an electrically conducting liquid. Examples have been given by Hartmann & Lazarus (1937), Murgatroyd (1953 a,b ), Shercliff (1953), and Stuart (1954) for viscous flow between parallel planes and in pipes, by Chandrasekhar (1953) and Lehnert (1952 a ) for viscous flow between rotating cylinders, by Chandrasekhar & Fermi (1953) for problems of gravitational stability and by Chandrasekhar (1952) and Nakagawa (1955) for the inhibition of convection in a fluid layer.
Renewed interest in colliding plasmas is due primarily to two device oriented research applications - fast plasma shutters for high-power glass lasers and radiation source emission from colliding exploding-wire plasmas in high-power pulseline generators. The present paper deals with three-dimensional electromagnetic computer simulations which demonstrate the evolution of colliding columnar plasmas. The interaction leads to a spiral configuration from which radiation is emitted.
BS>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. (auth);
Experimental observations of the propagation of an intense, unneutralized, annular, relativistic electron beam along a homogeneous magnetic guide field show that it is unstable. The instability is accompanied by a loss of beam particles and intense microwave emission.
Stability, emission of radiation, and some problems of evolution for pinch systems are considered on the basis of the theory of equilibrium of a plasma with a high current. The analysis of small oscillations in the approximation of two-fluid hydrodynamics of ideal charged liquids shows that the most dangerous instability is the one resulting in the filamentation of a diffuse equilibrium state of the current into separate jets. The criterion of stability for a pinch systems is established. According to this criterion the plasma compressed up to the electron degeneration is stable. The theory of emission of radiation by pinch systems shows a very important role of stimulated synchrotron radiation in the process of evolution of a high-current channel. The experimental properties of high-current pinches find a natural explanation in the theory. Aside from evident practical applications, the electromagnetic selfcompression of plasma in high-current devices provides the unique possibility to create and investigate ultradense matter, huge electric and magnetic fields, and ultrahigh pressures in the Earth laboratory experiments.
Image converter photographs of various interfaces between a magnetic field and an accelerated plasma show clearly the production of plasma vortex filaments in pairs. These vortex filaments fall into two classes: those parallel to B0 (the background magnetic field) and those perpendicular to B0.
Auroral spirals of 20- to 1300-km diameter are a common part of the active auroral display. They appear most frequently in the evening and midnight sectors, where they appear to be produced as a consequence of magnetic field line distortion caused by field-aligned currents. More quiescent spiral forms exhibiting somewhat different characteristics occur during quiet times in the polar cap near the dawn portion of the auroral oval. (AIP)
An experimental demonstration has been given of the initiation of a
vortex-forming instability in sheets of charge by perturbations in the
shape of the sheet. The net motion of charge along the sheet wherever
the sheet is bent is shown to be related to displacement of the
potential minimum in the sheet. These results suggest the existence of
an instability in current sheets which also produces vortex forms. There
is evidence that both of these instabilities result in the formation of
vortexes in the aurora.
Three-dimensional, electromagnetic computer simulation experiments are presented showing the evolution of plasma columns subjected to external electric and magnetic fields. The results of two experiments are presented here. In the first, self-confinement is achieved; in the second, an instability arises which drives the plasma into a helical configuration.
The detection of faint, supercluster-scale radio emission at 326 MHz that extends between the Coma cluster of galaxies and the Abell 1367 cluster and which is apparently not associated with any individual galaxy system in the complex is described. The radiation's synchrotron origin implies the existence of a large-scale intercluster magnetic field with an estimated strength of 0.3-0.6 microgauss, which is remarkably strong. The synchrotron-emitting relativistic electrons cannot be older than a few times 10 to the 8th yr. It is speculated that the magnetic field is the fossil of a pregalactic primeval field which was amplified in the course of the formation of intergalactic voids and superclusters.
Theoretical self-consistent relativistic electron beam models are developed which allow the propagation of relativistic electron fluxes in excess of the Alfve´n–Lawson critical-current limit for a fully neutralized beam. Development of a simple, fully relativistic, self-consistent equilibrium is described which can carry arbitrarily large currents at or near complete electrostatic neutralization. A discussion of a model for magnetic neutralization is presented wherein it is shown that large numbers of electrons from a background plasma are counterstreaming slowly within the beam so that the net current density in the system, and therefore, the magnetic field, is nearly zero. A solution of an initial-value problem for a beam–plasma system is given which indicates that magnetic neutralization can be expected to occur for plasma densities that are large compared with beam densities. It is found that the application of a strong axial magnetic field to a uniform beam allows propagation regardless of the magnitude of the beam current. Some comparisons are made with recent experimental data.
The stability of an infinitely long, inviscid, incompressible fluid
cylinder of finite electrical conductivity in the presence of an axial current. a
longitudinal magnetic field, and an infinitely long coaxial conducting sheath
placed at some distance from the fluid cylinder is investigated. The axial
current is assumed to be maintained constant by external sources. The effect of
surface tension is included. In the case when the fluid is mercury and the axial
current and the longitudinal magnetic field are of the order of a few hundred
amperes and a few hundred gauss respectively, it is shown that there exists a
critical product of axial current and longitudinal magnetic field which
determines whether the m = 0 mode or the m = 1 mode will be manifested first in
the instabilities. The results of this theory are compared with those obtained
of the same geometry but with the assumption of infinite electrical conductivity
for the fluid. (auth)
Areas of interest for charged-particle beams are mentioned, and the classical beam concepts due to Alfvén, Lawson, and Bennett are described. From the equation of plasma mass transport the virial theorem of plasma physics is derived and evaluated for rotationally symmetric configurations so as to apply to long particle beams of nonrelativistic plasma character. A general global equation for such a beam expansion or compression is obtained and discussed. New aspects are given on the classical concepts, and the Alfvén-Lawson limiting current is slightly modified. With respect to certain important electron-beam properties observed in fusion research, special consideration is given to beam internal magnetic field generation and beam transverse mass rotation, and an important conversion mechanism is described.
An auroral arc undergoes various types of deformations, such as curls, folds and spirals. In this paper the formation mechanism of folds is examined by a plasma simulation method. It is suggested that folds, as well as curls, can arise from electrostatic shear-induced instabilities. The differences between the two forms are controlled by the presence of ambient ions that must be present to shield the electric field of the precipitating electron charge sheet. It is shown that curls form when the ion sheath thickness is large in comparison with the electron sheet. Folds form when the ion sheath is thin and lags slightly behind the electron guiding centers, setting up an additional electric field that controls the late stages of instability growth.
A PLASMA gun (or plasma source) has been developed which can project plasmoids1 (plasma-magnetic entities) across a magnetic field (in a vacuum) at speeds up to 107 cm./sec. A Taylor-instability jet2 produced in a plasma supported against gravity by magnetic field may thus be simulated and studied in the laboratory. The track left by the plasmoid in crossing a magnetic field is luminous1 because of the recombination light of the ions and electrons which have been left behind as ‘debris’. The track may thus be photographed.
Electrical quasi-neutrality is not a general property of a thermalized self-gravitating plasma. If the massive component of a two-component plasma consists of charged macroscopic solid grains for which the charge-to-mass ratio is of order then self-gravitation and thermalization lead to substantial large-scale charge separation. An alternative statement of the condition for substantial equilibrium charge separation is that the Jeans length and Debye length of the plasma are similar.
We consider a system of condensations in such a plasma and show that properties of the system are similar to observed properties of the system of galaxies.
A rearrangement of the geometry of cavity magnetron oscillators is proposed such that the magnetic field loops around the cathode, whereas waves and electrons travel along it. Application of various magnetron theories to the new geometry leads to the result that the device will oscillate under conditions similar to those for a conventional cavity magnetron. The required magnetic field can be generated by a heavy current passed axially through the cathode.
Macroscopic equilibria of relativistic electron beams in plasmas, with return current and with or without an external magnetic field parallel to the beam, are investigated in cylindrical geometry. Bennett-type identities and general solutions are derived, and special examples are considered, in particular low-net-current, quasineutral configurations. A general expression for the current screening factor is obtained. Because of screening, relaxed versions of the Alfven-Lawson conditions determine whether beam propagation is possible. These conditions are easily satisfied for low perpendicular temperatures and sufficiently diffuse density profiles of the beam; they do not limit the beam current. Only equilibria with zero total charge, nonzero total net current, and beam profiles without sharp boundary, can be obtained from the equations and boundary conditions used.
Two examples are given of non-laminar motion in an electrically conducting liquid in the presence of an external magnetic field.
A. Chapman-Ferraro's theory of magnetic storms is discussed. It is pointed out that the fundamental assumption about a non-magnetized beam is in conflict with cosmic ray evidence. It is further shown that there is a fundamental objection against any theory of the main phase based on a non-magnetized beam.B. The objections, which Cowling and Chapman have raised against the electric field theory, are discussed, and the discharge mechanism during a magnetic storm is analysed. When a magnetized beam enters the earth's magnetic field, it is heated due to the compression. In the hot plasma the earth will act as a “probe” so that it gets a negative charge in relation to the plasma. As a result of ambipolar diffusion to the earth, the ionosphere in the auroral zones will be bombarded by high energy protons and electrons.It is shown that a mechanism of this type is not subject to the objections which have been raised.
A generalized form of the Bennett pinch is studied in both cylindrical geometry and plane-parallel geometry. In this kind of pinch electromagnetic forces, kinetic pressure gradient forces, centrifugal forces, and gravitational forces may act. For each of the two geometries considered a generalized Bennett relation is derived. By means of these relations it is possible to describe among other things the pure Bennett pinch, Jean''s criterion in one and two dimensions, force-free magnetic fields, gravitationally balanced magnetic pressures, and continuous transitions between these states. The theory is applied to electric currents in the magnetosphere, in the solar atmosphere, and in the interstellar medium. It is pointed out that the currents in the solar atmosphere and in the interstellar medium may lead to pinches that are of vital importance to the phenomena of solar flares and star formation, respectively.
A derivation of the physical conditions for magnetohydrodynamic equilibrium from first principles establishes a set of equations which differ slightly from the usual ones. The difference is only relevant in the special case when the current is parallel to the magnetic field. What is noteworthy is that these modified equations predict that the simplest magnetohydrodynamic equilibria can only exist in regions of field-aligned current sheets. This prediction is entirely consistent with the observed large-scale structures in the Earth's magnetosphere.
The advent of three-dimensional, electromagnetic, and fully relativistic particle simulations allows a detailed study of a magnetized, rotating plasma, galaxy model. When two such models are simulated, an interaction yielding results resembling observational data from double radio sources, including the emission of synchrotron radiation, are obtained. Simulation derived morphologies, radiation intensities, frequency spectra, and isophote patterns are directly compared to observations. The constituent plasma parameters associated with the source Cygnus A are found to ben
e
=1.810–3 cm–3,T=2.8 keV,B=20–30 gamma, with a small population of electrons accelerated to GeV energies by a rotation induced electric field. The results of these simulations, involving a computational resource of five CDC 7600 and five Cray-1 computers, strongly supports an inhomogeneous version of the Klein world model.
The stability of crossed‐field electron beams is treated for arbitrary values of the parameter q=ω p 2/ω c 2 = (plasma frequency/cyclotron frequency)2. The theory bridges a gap between existing theories applicable for q«1 and for q=1. For wavelengths longer than about five beam thicknesses an instability occurs with a growth rate not exceeding ∼¼qω c . It can be shorted out by conducting walls, or else one can prevent long wavelengths in closed (cylindrical or toroidal) beam geometries. For wavelengths shorter than roughly 6q beam thicknesses a cyclotron instability occurs with a growth rate ∼½qω c exp(-2/q). This becomes practically unimportant for q⪝0.2. Observations support these theoretical results.
The wave interaction underlying the diocotron effect is re‐examined and a physical model of the instability presented. A wave analysis is then given for circular, wall‐enclosed charge layers with finite length in the axial direction. Circular layers are of particular interest, since they apply to various plasma, discharge, and electron device geometries. Their instability behavior is found to be similar in many respects to the behavior of linear charge sheets, described in earlier work by R. W. Gould. In contrast to linear sheets, however, circular layers are unstable only when their thickness is sufficiently small. This effect is associated with the inability of charge perturbations to have a wavelength which exceeds the layer circumference. Data are presented for the magnitude of growth in various configurations and for the critical layer width at which growth terminates.
A time-dependent analysis of crossed-field interaction has been formulated for computer calculation. The computer program has achieved, for the first time, accurate and complete simulation of the magnetron oscillator, magnetron amplifier, and smooth-bore magnetron. We believe that crossed-field interaction of the distributed-emission type is finally predictable. The computer results are reliable enough to serve as design information. They also indicate that the nature of the interaction is turbulent in the sense that the operation of these devices borders between order and disorder under certain conditions.
The techniques used in this analysis are applicable to a wide range of problems dealing with other types of electron—wave interaction, and to plasmas.
A number of observations have been made of structure changes that occur in hollow and solid electron beams which are confined by a magnetic field. These structure changes occur in both the density of the beam and the transverse velocity components of the beam electrons. The velocity components have been measured by use of a pinhole camera.
Some of the results obtained are as follows. The density of electron paths in a beam may become non-uniform if there is a spread in the forward component of velocity of the electrons. This may occur either because of a spread in initial angle of the electrons or because of a potential depression in the beam.
In addition, changes in beam shape and transverse velocity components of the beam electrons can occur as a result of drifting of electrons in crossed electric and magnetic fields, the electric fields in this case being provided by the space charge of the electrons themselves. Thin beams have been found to be unstable and it has been observed that they divide into an array of vortex-like current filaments when the beam current is sufficiently high. A possible connection between this occurrence and phenomena in the aurora is suggested.
A thin strip or hollow electron beam drifting in a magnetic field directed parallel to the direction of motion is in an unstable condition. As a result of initial nonuniformities the beam breaks up into a series of ``spiral nebulae.'' This paper is written to describe some experimental observations which are of help in understanding the phenomenon, and to show that it can be applied to give useful amplification.