The acceleration of charged particles in the magnetic current sheets downstream from magnetic neutral lines is discussed and related to the plasma populations expected to be formed in a simple open model magnetosphere. A simple model of plasma acceleration in the dayside current sheet is set up, and it is shown that magnetospheric particles may take up a considerable fraction of the electromagnetic energy dissipated in the sheet even though they may represent only a small fraction of the total particle influx. The process should result in energetic ring current and ionospheric particles being found in boundary layers on either side of the magnetopause, and accelerated ionospheric particles in the plasma mantle. Acceleration of magnetosheath plasma in the dayside current sheet should result in enhanced flow speeds in these boundary layers, but the process may amount to little more than a return to the sheath plasma of energy previously extracted from it during its inflow on the dayside and stored in the compressed sheath field, due to the appreciable energy take-up from the current sheet by magnetospheric particles. The energy separation between ionospheric plasma and magnetosheath plasma on cusp field lines is shown to result in a spatial separation of polar wind and plasma mantle populations in the tail, the polar wind ions usually reaching out to only a few tens of R
E down-tail such that they usually remain on closed field lines, forming a wedge-shaped region within the mantle shadow-zone. Polar wind ions are then convected back towards the Earth and thus their major sink is via the dayside current sheet rather than outflow into the tail. The major source for the plasmasheet depends upon the location of the neutral line, but mantle ions may usually be dominant. However, with a near-Earth neutral line during disturbed periods ionospheric plasma will be the sole ring-current source. Under usual conditions with a more distant neutral line the spatial separation of the two plasma sources in the tail may result in an energy separation in the inner ring current, with ionospheric particles dominant up to ∼2 to 20 keV and mantle ions dominant at higher energies. Formation of the plasmasheet is discussed, and it is shown that a layer of ions unidirectionally streaming towards the Earth should be formed on its outer boundary, due to current sheet acceleration of lobe particles and inward convection of the field lines. A similar process leads to earthward flows on the inner layer of the dayside cusp. Finally, the region tailward of the nightside neutral line is discussed and it is shown that a thin tailward flowing two-stream plasma band should be formed across the centre plane of the tail. The slow-speed stream corresponds to incoming lobe ions, the faster stream to the current sheet accelerated ions.

Plasma populations in a simple open model magnetosphere

The solar coronal magnetic field is anchored to a complex distribution of photospheric flux consisting of sunspots and magnetic elements. Coronal activity such as flares, eruptions and general heating is often attributed to the manner in which the coronal field responds to photospheric motions. A number of powerful techniques have been developed to characterize the response of the coronal field by describing its topology. According to such analyses, activity will be concentrated around topological features in the coronal field such as separatrices, null points or bald patches. Such topological properties are insensitive to the detailed geometry of the magnetic field and thereby create an analytic tool powerful and robust enough to be useful on complex observations with limited resolution. This article reviews those topological techniques, their developments and applications to observations.

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Topological Methods for the Analysis of Solar Magnetic Fields

Magnetic field enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic flux tubes, and coronal field lines often connect one flux tube to another, defining a pattern of inter-linkage. Using a model field, in which flux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal field were current-free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the flux linkage. This current forms singular layers (ribbons) flowing along topologically significant field lines called separators. Current ribbons store magnetic energy as internal stress in the field: the amount of energy stored is a function of the flux tube displacement. To explore this process we develop a model called the minimum-current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric flux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce flaring to rapidly change the flux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated flaring during the evolution of simple active regions, releasing anywhere from 1027–1029 ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to flaring (i.e., reconnection).

Topology and current ribbons: A model for current, reconnection and flaring in a complex, evolving corona

It was shown by Syrovatskii [Sov. Phys. JETP 33, 933 (1971)] that a perfectly conducting two‐dimensional magnetic field stressed externally develops a current sheet at an X point. A generalization of this analysis shows that a generic three‐dimensional magnetic field develops a closed ribbon of current along separators already existing in the field. A separator is a field line that begins and ends at different magnetic null points. A current ribbon will occur if there are two distinct separators beginning and ending at the same two nulls, thus forming a loop. The magnetic field containing the current ribbon is in force‐free equilibrium. An expression is found for the net current induced in the ribbon, and the magnetic energy stored by it, in terms of the amount of external stress. An electric field parallel to the current will facilitate reconnection and will dissipate the current and release the stored energy.

Current sheet formation along three‐dimensional magnetic separators

One year of magnetic field data from the geostationary spacecraft ATS 6 have been analysed for effects associated with the equatorial plane components of the interplanetary magnetic field (IMF). It is shown that perturbation fields in the Y (dawn to dusk) direction appear in association with the Y component of the IMF, in agreement with previous theoretical suggestions. On average a fraction 0.28 ± 0.02 of the IMF Y field appears at geostationary orbit, such that the average ATS 6 By field is 1.9 ± 0.4 nT larger when IMF By is positive than when it is negative. The perturbation field magnitudes are also found to depend strongly on local time, however, with largest effects appearing in the midnight and dawn quadrants, where the average perturbation fields are nearly half the simultaneous IMF Bv. field. At noon this fraction drops to one fifth, and no average effect occurs in the dusk quadrant. Both the daily mean perturbation fields and the diurnal modulation are also found to depend upon the level of magnetic disturbance as measured by KP, or equivalently upon IMF Bz, and upon season of the year. Overall stronger daily mean perturbation fields occur when KP is low or when IMF Bz is positive, than when KP is high or when IMF Bz is negative. This effect is not linear, however, and there is also a trend in the data towards increasing perturbation fields with IMF Bz negative and decreasing. On dividing the data according to season, increasingly strong daily mean effects are found in the order winter, summer and equinox for both quiet and disturbed magnetospheres. Diurnal modulations of the perturbation field magnitudes for low KP (IMF Bz > 0) take the form of large amplitude quasi-sinusoidal variations about mean values which are very marked in the equinox data, are present to a lesser degree during summer and are absent during winter conditions. When Kp is high (IMF Bz < 0) significant deviations from mean perturbation field values occur generally only during nightside hours and little seasonal dependence is evident. Finally, it is shown that the highest correlation between the IMF data and the ATS 6 perturbation fields occurs with zero time delay between the two data sets, showing that a prompt response to IMF conditions occurs at geostationary orbit within the 1 h time resolution available in this study. Although many details of the above ATS 6 response remain to be understood, these results overall demonstrate in a very direct manner the magnetically “open” nature of the Earth's magnetosphere.

Observation of an IMF sector effect in the Y magnetic field component at geostationary orbit

Field line reconnection on the day side magnetopause is assumed to take place along the separator of field line connectivity in the magnetic topology resulting from the interpermeation of a dipolar geomagnetic field and a uniform interplanetary field. The induced voltage is calculated to show its dependence on the magnitude and direction of the incident magnetic field.

Tyan Yeh

Papers

Day side reconnection between a dipolar geomagnetic field and a uniform interplanetary field