Time-dependent magnetospheric electric fields have been computed, including the effects of Birkeland currents from the inner edge of a sheet of ions that moves under the influence of the computed electric fields. Ionospheric currents are also taken self-consistently into account with the use of a time-independent model of ionospheric conductivity that includes day-night asymmetry and auroral enhancements but neglects electric fields parallel to the magnetic field. Ion precipitation and neutral winds are also neglected. The behavior and effects of the ion sheet are studied in a series of model calculations, with the following results. (1) In agreement with the conclusions of E. T. Karlson, L. P. Block, V. M. Vasyliunas, and D. W. Swift, Birkeland currents from the Alfven layer (inner edge of the ion sheet) are found to reduce the electric field earthward of the Alfven layer to a small value by the time a steady state is reached; however, different parts of the electric field earthward of the Alfven layer are eliminated at different rates; one component of the nightside field relaxes to near its low asymptotic value in a few minutes, whereas the dayside field takes hours to relax. (2) If the ion sheet is brought in from the tail by a large cross-tail electric field that stays large, the inner edge of the sheet generally touches the magnetopause boundary layer; however, a decrease in the cross-tail field can cause the Alfven layer to contract and form a complete ring. (3) For the parameters used, a cross-tail potential of 134 kv will bring a sheet of ring current protons in to about L = 4; the results of the model calculations support the idea that convection electric fields bring low-energy ions in from the tail to form the storm time ring current; the minimum geocentric distance to which convection fields can bring the ions is found to be roughly proportional to (ημ/Φ0σρ)1/3, where η is the number of ions per unit magnetic flux, μ is the ion magnetic moment, Φ0 is the cross-tail potential, and σρ is an average height-integrated Pedersen conductivity on the dayside. (4) The nightside Alfven layer naturally produces a dividing line near local midnight, such that particles arriving west of the line drift to the west, whereas those arriving east of the line drift east; this characteristic is often observed in motions of barium clouds and auroral arcs.

Self‐consistent calculation of the motion of a sheet of ions in the magnetosphere

The electron–cyclotron maser is a process that generates coherent radiation from plasma. In the last two decades, it has gained increasing attention as a dominant mechanism of producing high-power radiation in natural high-temperature magnetized plasmas. Originally proposed as a somewhat exotic idea and subsequently applied to include non-relativistic plasmas, the electron–cyclotron maser was considered as an alternative to turbulent though coherent wave–wave interaction which results in radio emission. However, when it was recognized that weak relativistic corrections had to be taken into account in the radiation process, the importance of the electron–cyclotron maser rose to the recognition it deserves. Here we review the theory and application of the electron–cyclotron maser to the directly accessible plasmas in our immediate terrestrial and planetary environments. In situ access to the radiating plasmas has turned out to be crucial in identifying the conditions under which the electron–cyclotron maser mechanism is working. Under extreme astrophysical conditions, radiation from plasmas may provide a major energy loss; however, for generating the powerful radiation in which the electron–cyclotron maser mechanism is capable, the plasma must be in a state where release of susceptible amounts of energy in the form of radiation is favorable. Such conditions are realized when the plasma is unable to digest the available free energy that is imposed from outside and stored in its particle distribution. The lack of dissipative processes is a common property of collisionless plasmas. When, in addition, the plasma density becomes so low that the amount of free energy per particle is large, direct emission becomes favorable. This can be expressed as negative absorption of the plasma which, like in conventional masers, leads to coherent emission even though no quantum correlations are involved. The physical basis of this formal analogy between a quantum maser and the electron–cyclotron maser is that in the electron–cyclotron maser the free-space radiation modes can be amplified directly. Several models have been proposed for such a process. The most famous one is the so-called loss-cone maser. However, as argued in this review, the loss-cone maser is rather inefficient. Available in situ measurements indicate that the loss-cone maser plays only a minor role. Instead, the main source for any strong electron–cyclotron maser is found in the presence of a magnetic-field-aligned electric potential drop which has several effects: (1) it dilutes the local plasma to such an extent that the plasma enters the regime in which the electron–cyclotron maser becomes effective; (2) it generates energetic relativistic electron beams and field-aligned currents; (3) it deforms, together with the magnetic mirror force, the electron distribution function, thereby mimicking a high energy level sufficiently far above the Maxwellian ground state of an equilibrium plasma; (4) it favors emission in the free-space RX mode in a direction roughly perpendicular to the ambient magnetic field; (5) this emission is the most intense, since it implies the coherent resonant contribution of a maximum number of electrons in the distribution function to the radiation (i.e., to the generation of negative absorption); (6) it generates a large number of electron holes via the two-stream instability, and ion holes via the current-driven ion-acoustic instability which manifest themselves as subtle fine structures moving across the radiation spectrum and being typical for the electron–cyclotron maser emission process. These fine structures can thus be taken as the ultimate identifier of the electron–cyclotron maser. The auroral kilometric radiation of Earth is taken here as the paradigm for other manifestations of intense radio emissions such as the radiation from other planets in the solar system, from exoplanets, the Sun and other astrophysical objects.

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The electron–cyclotron maser for astrophysical application

A model of auroral arcs is presented. It is assumed that the magnetic field lines into the auroral oval are loaded with kev electrons, that precipitating auroral electrons locally constitute a net field-aligned current, and that currents close in the outer magnetosphere by polarization currents. The model predicts that a flux tube convecting through the oval will undergo a highly nonlinear oscillation that produces standing waves, the auroral arcs. The conditions to be satisfied are (1) Ohm's law in the ionosphere, (2) electron number conservation in the ionosphere, (3) electric current continuity, (4) the tendency for electric fields to map between ionosphere and magnetosphere. The physics of condition 4 is not understood, but it is probable that arc-like solutions exist for several models. A specific model, including perfect mapping of electric fields, is studied. The solutions to this model closely resemble the arcs. Predicted in agreement with observation are arc thickness, inter-arc spacing, and the electric field behavior. The thickness and the spacing are functions of both the amplitude of the oscillation and the physical properties of the system. However, thickness times spacing is a function of the physical properties only, and the thickness divided by the spacing is a function of amplitude only. Presumably these and other quantitative relationships can be checked by observations.

Auroral arcs: Result of the interaction of a dynamic magnetosphere with the ionosphere

Data taken by incoherent scatter radar have been used to investigate ionospheric conductivities and electrical currents. During quiet days, the conductivities appear to vary in a way consistent with ionization arising from solar EUV radiation. In the evening hours, enhancements in the northward electric field are found to precede small increases in the conductivities. Strong enhancements of the Hall conductivity relative to the Pedersen conductivity occur during negative bays when the electric field is in a southwestward direction. The ionospheric currents calculated in the geomagnetic east-west direction are in good agreement with the H component measured by a nearby magnetometer; this result indicates that the current causing the ground level magnetic fluctuations is a broad horizontal sheet current. The north-south ionospheric current, however, consistently disagrees with the observed D component in a manner that cannot easily be explained unless currents parallel to the earth's magnetic field are present.

Incoherent scatter measurements of E region conductivities and currents in the auroral zone

On the motion of artificial ion clouds in the magnetosphere

In April 1967 five Nike-Apache rockets were launched from Kiruna, Sweden, carrying barium release and electron concentration experiments. The component of the electric field transverse to the magnetic lines of force is derived from the motion of the ion clouds. The electron concentration measurements provide ionospheric conductivities. The magnitudes of the electric fields varied between 2 and 20 v/km. Their directions were northwestward for evening conditions and southwestward for morning conditions. The magnetic perturbations on the ground that would result from ionospheric currents derived on the basis of the measured fields and conductivities closely resemble the actual ground magnetometer data. The electric fields vary appreciably with space and time; they can even reverse their directions over distances of the order of 60 km.

L. Haser

Papers

Preliminary results of electric field measurements in the auroral zone