Damping of geomagnetic pulsations by the ionosphere

A significant sink of geomagnetic pulsation energy is due to Joule dissipation in the ionosphere. To investigate this we have computed the damping experienced by standing Alfvén waves in a dipole magnetic field. Both the uncoupled poloidal and toroidal modes are considered with Joule dissipation being introduced through a boundary condition which relates the electric and magnetic field strengths at the ionosphere, viz: $\text{4πΣ}{}_{\mathrm{p}}\text{E}\text{c}\text{= b,}\text{where}\text{Σ}{}_{\mathrm{p}}$ is the height integrated Pederson conductivity. The damping rates are strongly dependent on the ionospheric conductivity and we find that typically the normalized damping rate, $\text{γ}\text{ω}\text{,}\text{is}\text{～0.1}$ for nightside values of conductivity and ～0.01 for the dayside. This would account for the observed scale of bandwidths in pulsation signals. Away from regions of extreme damping we find γ ∝ L^?1Σ_p^?1.     

Ionospheric Joule dissipation as a damping mechanism for high latitude ULF pulsations: Observational evidence

On 9 January 1979 an SI-excited pulsation event was observed by the Scandinavian Magnetometer Array. The pulsation period shows a clear variation with latitude which suggests decoupled oscillations of individual magnetic field shells. The pulsation amplitudes exhibit an e-fold decay with the damping rate γ varying both in longitudinal and latitudinal directions. Assuming Joule heating in the ionosphere as the dominant damping mechanism (and thus γ ～ Σ^?1_p) approximate height-integrated Pedersen conductivity profiles were calculated which fit well with previously observed Σ_p distributions. This is interpreted as observational evidence for ionosopheric Joule dissipation as the major damping mechanism for high-latitude ULF-pulsations.     

Transient ULF pulsation decay rates observed by ground based magnetometers: The contribution of spatial integration

Theoretical studies suggest that Joule dissipation in the ionosphere is the major source of damping for resonant ULF pulsations. The decay rates of transient pulsations (i.e. short-lived pulsations with latitude dependent periods) observed by ground based magnetometers are however generally larger than those predicted, and also larger than those observed in the magnetosphere. We have modelled the integration effects of ground based magnetometers on transient pulsations by considering empirical models of the associated ionospheric currents. The simulated ground magnetometer data show a smearing of the amplitude and period variations, which is more pronounced for smaller scale (specifically latitudinal) variations. The period increase with latitude is reduced, and may even be eliminated over appreciable latitude ranges. For all spatial scales the observed decay rates are typically 2–3 times larger than the true values, due to the additional decay resulting from spatial integration of the incoherent transient pulsations. Estimates of the ionospheric Pedersen conductance based on ground magnetometer observations of decay rates are correspondingly too small, and spurious gradients may be introduced. The present calculations reconcile observed decay rates on the ground with those predicted using the assumption that Joule dissipation is the dominant damping mechanism for toroidal mode resonant oscillations.     

ULF pulsation mode coupling in the ionosphere and magnetosphere

The effect of realistic ionospheric Hall conductances on axisymmetric toroidal mode hydromagnetic wave resonances is investigated. The toroidal modes couple to evanescent poloidal modes near the ionospheres such that the composite modes resonate at the constant frequencies of the corresponding single-field-shell resonances for zero Hall conductance. A model for these composite modes is developed which has narrow but finite latitudinal resonance widths such as to make the modes valid solutions of the hydromagnetic equations. The modes also suggest that “shell” solutions can realistically describe such properties of real pulsations as frequency, damping, phase variation along the field-line and node-antinode behaviour at the ionospheres. Estimates of ionospheric coupling strength are obtained and compared with magnetospheric coupling strength. It is found that magnetospheric coupling dominates ionospheric coupling for any single non-axisymmetric mode. However, ionospherically coupled axisymmetric modes should be necessary components of the Fourier sum of modes required to model any real pulsation of low to moderate apparent azimuthal wave number.Estimates of the range of magnetospheric coupling strength are obtained for pulsations under a variety of conditions.     

Spatial and temporal structure of a high-latitude transient ULF pulsation

Auroral radar observations of transient ULF pulsations with latitudinally varying period have recently been reported. An event of this type is analysed using data from the Scandinavian Magnetometer Array, the STARE radar, and the GEOS-2 satellite. The magnetometers show long-period (～450 s) oscillations consistent with the pulsations observed in the ionosphere using STARE, and confirm that the geomagnetic field shells are resonating in the toroidal mode. There is also a localised, small-amplitude component with 250-s period South of the STARE pulsations. Electric field measurements at GEOS-2 show only an impulsively stimulated pulsation of 250-s period. The wave fields at GEOS-2 imply that the satellite was earthward of a localised toroidal standing-wave resonance, which mapped to the ionosphere at least one degree South of the expected position. A radial profile of equatorial plasma mass density is inferred from the GEOS-2 and STARE results. This shows a radially increasing density near GEOS-2, and a radially decreasing density outside the satellite position.An interpretation of the event is given in which a tailward propagating hydromagnetic impulse directly stimulates field shells outside 7 R_E to oscillate at their eigenperiods. In the region of increasing density near GEOS-2, a relatively highly-damped surface wave is excited. This feeds energy rapidly into a narrow monochromatic toroidal field-line resonance, which subsequently decays more slowly through ionospheric dissipation.     

Pc3-4 geomagnetic pulsations at very low latitude in Brazil

In order to investigate Pc3-4 geomagnetic pulsations at very low and equatorial latitudes, L=1.0 to 1.2, we analyzed simultaneous geomagnetic data from Brazilian stations for 26 days during October-November 1994. The multitaper spectral method based on Fourier transform and singular value decomposition was used to obtain pulsation power spectra, polarization parameters and phase. Eighty-one (81) simultaneous highly polarized Pc3-4 events occurring mainly during daytime were selected for the study. The diurnal events showed enhancement in the polarized power density of about 3.2 times for pulsations observed at stations close to the magnetic equator in comparison to the more distant ones. The phase of pulsation observed at stations near the magnetic equator showed a delay of 48-62° in relation to the most distant one. The peculiarities shown by these Pc3-4 pulsations close to the dip equator are attributed to the increase of the ionospheric conductivity and the intensification of the equatorial electrojet during daytime that regulates the propagation of compressional waves generated in the foreshock region and transmitted to the magnetosphere and ionosphere at low latitudes. The source mechanism of these compressional Pc3-4 modes may be the compressional global mode or the trapped fast mode in the plasmasphere driving forced field line oscillations at very low and equatorial latitudes.     

A study of the relationship between geo-magnetic storms and ionospheric disturbances at mid-latitudes

The problem of the ionospheric disturbances associated with geomagnetic storms is examined with the goal of searching for a relationship between the time-developments of the two phenomena. Faraday rotation measurements of total electron content (N_T) are used to monitor the ionospheric F-region at a mid-latitude site, while a variety of geomagnetic parameters are examined as possible ways of following the geomagnetic variations. The ionospheric and geomagnetic data taken during 28 individual storms from 1967 to 1969 are used to search for a predictive scheme which can be tested using data from 17 storms in 1970. The specific aim is to find the geomagnetic parameter whose time-development can best forecast whether or not the ionospheric response will include an initial positive phase prior to the normally extended period of F-region depletions. Correlations between N_T and the geomagnetic indices K_p, and equatorial Dst(H) prove to be wholly inadequate. The local times of main-phase-onset (MPO) determined from the equatorial Dst(H) indices as well as from local horizontal component data, also prove to be unsatisfactory. The best correlations are obtained using local measurements of the total geomagnetic field (F). These results show that a storm commencement (SC) will produce an enhancement in n_t during the afternoon period following the SC unless there is an intervening post-midnight period with a strong depression of the geomagnetic field. Operationally this is taken to be a depression in F of at least 100γ near 03:00 LT     

Source induced vertical components in geomagnetic pulsation signals

We show how large vertical components may be induced in geomagnetic pulsation signals because of the localised nature of the source. The effect is greatest when the signal varies on a horizontal scale length which is shorter than the skin depth of the signal in the Earth. However, the horizontal scale length is also constrained to be equal or larger than the height of the ionospheric E-region (～ 120 km) as signals varying on a shorter scale are severely attenuated. Such conditions are best met by high latitude pulsations and some recent high latitude observations are explained by our results. We find that the vertical component is best correlated with the horizontal component in the direction in which the signal varies most rapidly.     

Dynamo currents representing geomagnetic L variation demonstrated by a multi-layer ionospheric model

A multi-layer ionospheric model and lunar (2,2) tidal mode have been used to calculate dynamo current systems representing lunar geomagnetic semidiurnal variations. Since both the height variation of the ionospheric conductivities and latitudinal dependence of the height of the conductivity peaks have been taken into account, the dynamo current systems agree with equivalent ones (estimated from geomagnetic data) better than those for a thin shell model of the ionospheric conductivity, especially in the polar region.     

The role of the Hermanus Magnetic Observatory in geomagnetic field research

Geomagnetic field research carried out at the Hermanus Magnetic Observatory over the past decade is reviewed. An important aspect of this research has been the study of geomagnetic field variations, with particular emphasis on ULF geomagnetic pulsations. Features of geomagnetic pulsations which are unique to low latitude locations have been investigated, such as the cavity mode nature of low latitude Pi 2 pulsations and the role played by ionosphericO ⁺ ions in the field line resonances responsible for Pc 3 pulsations. A theoretical model has been developed which is able to account for the observed relationships between geomagnetic pulsations and oscillations in the frequency of HF radio waves traversing ionospheric paths. Other facets of the research have been geomagnetic field modelling, aimed at improving the accuracy and resolution of regional geomagnetic field models, and the development of improved geomagnetic activity indices.     

Time of flight calculations for high latitude geomagnetic pulsations

High latitude geomagnetic field lines differ significantly from a dipole geometry. Time of flight calculations using the Mead-Fairfield (1975) model of the geomagnetic field are presented for different tilt angles and K_p conditions. Typical standing wave periods of geomagnetic pulsations are estimated for three different magnetospheric cold plasma regions, corresponding to waves guided in (i) the plasmatrough, (ii) the extended plasmasphere and (iii) regions of enhanced proton density (detached plasma) within the plasmatrough.Pc4/5 pulsation studies at high latitudes are briefly reviewed and some new results from Tromso are given. Many of the observations reveal hydromagnetic waves whose location and period are consistent with ducting in a region of enhanced plasma density within the plasmatrough.     

Local time asymmetry in the characteristics of Pc5 magnetic pulsations

The wave characteristics of Pc5 magnetic pulsations are analyzed with data of OGO-5, ISEE-1 and -2 satellites. The toroidal modes (δB_D >δB_H) of Pc5 pulsations are observed at a higher magnetic latitude in the dawnside outer magnetosphere. The compressional and poloidal modes (δB_z.dfnc; ～ δB_H >δB_D) of Pc5 pulsations are mostly observed near the magnetic equator in the duskside outer magnetosphere. This L.T. asymmetry in the occurrence of dominant modes of Pc5's in space can be explained by the velocity shear instability (Yumoto and Saito, 1980) in the magnetospheric boundary layer, where Alfvénic signals in the IMF medium are assumed to penetrate into the magnetospheric boundary layer along the Archimedean spiral. The asymmetrical behaviour of Pc5 pulsation activity on the ground across the noon meridian can be also explained by the ionospheric screening effect on the compressional Pc5 magnetic pulsations. The compressional modes with a large horizontal wave number in the duskside magnetosphere are expected to be suppressed on the ground throughout the ionosphere and atmosphere.     

Pc1-2 Discrete regular daytime pulsation bursts at high latitudes

A family of related Pc1-2 (0.2–10 s) discrete daytime geomagnetic pulsations is presented using pulsation data obtained at Davis, Antarctica, a typical polar-cap station. The morphological properties of IPRP and Pclb pulsation regimes, which maximize in amplitude and frequency of occurrence under the projection of the polar cusp, are examined. Furthermore, two other variations of discrete pulsation bursts yet to be named are also presented, viz IPFP (Intervals of Pulsations with Falling Period) and IPAP (Intervals of Pulsations with Alternating Period) which are observed on rare occasions. It is also suggested that the Pc1b (0.2–5 s) should be extended to incorporate Pc2b (5–10 s) which from the results in this paper are physically the same phenomenon and could be collectively classified as IPCP (Intervals of Pulsations with Constant Period).     

Plasmatrough ion mass densities determined from ULF pulsation eigenperiods

Auroral radar studies of ULF pulsations have proved useful in determining the spatial characteristics of resonant oscillations. A particular class of ringing or transient pulsations has been identified in the radar data as toroidal mode eigenoscillations. We have considered a total of 64 events of this type recorded by either the STARE radar in Scandinavia, or the Slope Point radar in New Zealand, giving a combined latitudinal coverage of approx. 12°. These events are interpreted as toroidal mode eigenoscillations; the periods for individual events and the mean periods increase with geomagnetic latitude. Use of hydromagnetic resonance theory allows the equatorial ion mass density to be determined. The densities obtained are appropriate to the plasmatrough and range from ～ 10 to 100 a.m.u. cm^?3 near geosynchronous orbit. The radial variation in the equatorial plane is typically R^?5 in the midnight-noon sector and R^?3 in the noon-midnight sector. To reconcile these pulsation periods with in situ electron density measurements implies that H⁺ ion densities in the range ～ 1–10 cm^?3 and ～50% O⁺ ions are required.     

Simultaneous geomagnetic and ionospheric oscillations caused by hydromagnetic waves

During magnetically quiet or slightly disturbed nights, closely correlated oscillations of the geomagnetic field and the F-layer were observed by means of magnetometers and a vertical-icidence continuous-wave Doppler sounder at 3.57 MHz. The magnetic oscillations were mostly Pi2 pulsations with periods from 0.5 to 2 min, and an amplitude of 10^?9 T corresponding to a Doppler shift of the order of 0.3 Hz. The observations cannot be explained by a dynamo-motor hypothesis assuming that the magnetic and ionospheric oscillations are caused by alternating E-layer currents, but they agree well with the theory of downgoing hydromagnetic waves. In particular, this theory explains the observed effects due to sporadic E-layer ionization and ion-neutral collisions. The results are found to differ substantially from those of other authors.     

On the diurnal period variation of midlatitude ULF pulsations

Magnetometer studies of the periods of mid-latitude ULF pulsations have produced conflicting results on the variation of the pulsation periods with both latitude and local time. Since the mid-latitude geomagnetic field is not expected to be significantly distorted by the solar wind, the observed diurnal period variations should be determined by changes in the ambient plasma density. We have applied a physically realistic plasmasphere model to the determination of pulsation eigenperiods over a 24-h interval at L=2.3 (appropriate to Wellington, New Zealand). The resulting model pulsation eigenperiods are largest during the day, with minimum and maximum values at 05.00 and 18.00 L.T. respectively. The model predicts a general increase in the eigenperiods during the replenishment of the protonosphere after a period of geomagnetic activity.     

Modelling of Pc5 pulsation structure in the magnetosphere

Magnetohydrodynamic resonance theory is used to model the structure of the magnetospheric and ionospheric electric and magnetic fields associated with Pc5 geomagnetic pulsations. In this paper the variation of the fields across the invariant latitude of the resonance are computed. The results are combined with calculations of the variation along a field line to map the fields down to the ionosphere. In one case the results are compared with measurements obtained by the STARE auroral radar and show good agreement. The relationship between the width of the resonance region and ionospheric height-integrated Pedersen conductivity is computed and it is shown how auroral radar measurements of Pc5 oscillations could be used to determine ionospheric height-integrated Pedersen conductivity. It is pointed out that from these calculations it would be possible to identify the field line on which a satellite was located by comparing a Pc5 pulsation observed by the satellite, and the same pulsation observed by STARE.     

A new theoretical approach to the modelling of toroidal Pc5 pulsations

A model is developed to represent a toroidal mode of Pc5 geomagnetic pulsations. It is shown that this model is consistent in its predictions, such as the latitude profiles of amplitude and phase and their dependence on the height integrated Pedersen conductivity, Σ_p, with those of Walker's (1980) theory. It is also shown that this theory is relatively easily capable of accommodating (i) a variety of field line plasma mass density distributions, (ii) a variety of external excitation schemes, (iii) unequal Σ_p's at each end of the field lines and (iv) non-dipolar geomagnetic fields. The theory yields the transient as well as the steady state response, an important feature permitting application to short-lived events or to those for which the generator is amplitude modulated. It is shown, for instance, that the amplitude-latitude profile varies during the transient. It is also shown that the steady state latitude profiles of amplitude and phase are the dual of those observed as a function of frequency when the excitation frequency is scanned through a resonance. A more realistic steady state energy flow from a generator along the field lines to the ionosphere is inherent in this theory compared with that from the mode to the ionosphere which is inherent in Walker's theory.     

Nonlinear pulsations of red supergiants

Excitation of radial oscillations in population I (X = 0.7, Z = 0.02) red supergiants is investigated using the solution of the equations of radiation hydrodynamics and turbulent convection. The core helium burning stars with masses 8M _⊙ ≤ M ≤ 20M _⊙ and effective temperatures T _eff < 4000 K are shown to be unstable against radial pulsations in the fundamental mode. The oscillation periods range between 45 and 1180 days. The pulsational instability is due to the κ-mechanism in the hydrogen and heliumionization zones. Radial pulsations of stars with mass M < 15M _⊙ are strictly periodic with the light amplitude ΔM _bol ≤ 0?5. The pulsation amplitude increases with increasing stellar mass and for M > 15M _⊙ the maximum expansion velocity of outer layers is as high as one third of the escape velocity. The mean radii of outer Lagrangean mass zones increase due to nonlinear oscillations by ≤30% in comparison with the initial equilibrium. The approximate method (with uncertainty of a factor of 1.5) to evaluate the mass of the pulsating red supergiant with the known period of radial oscillations is proposed. The approximation of the pulsation constant Q as a function of the mass-to-radius ratio is given. Masses of seven galactic red supergiants are evaluated using the period-mean density relation.     

Simple Pi burst micropulsation events and associated aurora at two sites in Alaska

Type Pi magnetic-field pulsation bursts were selected for which the associated aurorae were relatively simple and stable and occurred in the ionosphere between College and Fort Yukon in alaska. Power spectral-density traces for College and Fort Yukon HandD were computed and were studied relative to the aurora and to more complex events presented in earlier studies. The power spectral-density traces associated to simpler aurora were found to be consistent with the assumption of simpler 3-dimensional current systems as generators of the Pi waves. The spectra of associated precipitation pulsations had a peak near 10mHz in common with the magnetic field spectra in all events, and also near 3 mHz in one event. The precipitation pulsations at 3 and 10mHz may have enhanced the magnetic field spectra at those frequencies through modulation of the ionospheric resistance to the current.