Quarter-wave modes of standing Alfvén waves detected by cross-phase analysis

We have examined the diurnal variation of the local field line eigenfrequency at L ~ 2.6 using cross-phase analysis of Sub-Auroral Magnetometer Network and Magnetometers Along the Eastern Atlantic Seaboard for Undergraduate Research and Education ground magnetometer array data. On several days the eigenfrequency was remarkably low near the dawn terminator, when one end of the field line was sunlit and the other end was in darkness. Later in the morning the eigenfrequency gradually increased to the normal daytime value. This type of diurnal eigenfrequency variation was found in both European and American meridians and in several seasons (March, June, and December). By modeling this situation we show that the extraordinarily low eigenfrequency events appeared when the ionospheric Pedersen conductance was strongly asymmetric between both ends of the field line, leading to the formation of quarter-wavelength-mode standing waves that revert to half-wavelength modes as the dawn terminator passes both conjugate points. Ground-based magnetometer measurements of local toroidal field line eigenfrequencies are often inverted to infer plasma mass density in the magnetosphere by assuming half-wavelength-mode standing field line oscillations. However, the mode structure and hence field line eigenfrequency also depend on the ionospheric conductance. In particular, we find that there is a threshold of interhemispheric conductance ratio for the quarter-wavelength mode to be established. Our results therefore show that cross-phase techniques can detect quarter-wavelength-mode waves, where the inferred mass density would be overestimated

Pc3-4 ULF waves observed by the SuperDARN TIGER radar

Despite extensive research, the mechanisms for propagation of Pc3-4 energy from the generation region at the bow shock to the high-latitude ionosphere remain unresolved. We used high temporal (6-12 s) and spatial (45 km) resolution data from the SuperDARN TIGER radar (Tasmania) to examine Pc3-4 wave signatures at the F-region heights. We focus on a case study on 28 September 2000, when large-amplitude band-limited Pc3-4 oscillations were observed across 10-20 range gates in beam #4 (which points towards the CGM pole) for about four hours preceding MLT noon. These waves were detected in sea-scatter echoes reflected from the ionospheric footprint of the plasmatrough. Nearby ground magnetometer data from Macquarie Island showed very similar variations in both the north-south and east-west components. The radar data revealed the occasional presence of quasi-FLR (field-line resonance) spatial structures with frequencies much higher than those of the local fundamental FLR modes. Detailed spectral analysis of the ionospheric and ground data shows that these structures most probably correspond to a 3rd-harmonic, poloidal-mode FLR. Such observations suggest that compressional Pc3-4 waves produced in the upstream solar wind travel earthward from the magnetopause in the magnetic equatorial plane depositing energy into the Alfvenic modes, as either forced or 3rd-harmonic FLR that reach ionospheric heights along magnetic field lines

A finite difference construction of the spheroidal wave functions

A fast and simple finite difference algorithm for computing the spheroidal wave functions is described. The resulting eigenvalues and eigenfunctions for real and complex spheroidal bandwidth parameter, c , agree with those in the literature from four to more than eleven significant figures. The validity of this algorithm in the extreme parameter regime, up to c² = 10¹⁴ , is demonstrated. Furthermore, the algorithm generates the spheroidal functions for complex order m . The coefficients of the differential equation can be simply modified so that the algorithm may solve any second order differential equation in Sturm–Liouville form. The prolate spheroidal functions and the spectral concentration problem in relation to band-limited and time-limited signals is discussed. We review the properties of these eigenfunctions in the context of Sturm–Liouville theory and the implications for a finite difference algorithm. A number of new suggestions for data fitting using prolate spheroidal wave functions with a heuristic for optimally choosing the value of c and the number of basis functions are described

Multipoint observations of Pc1-2 waves in the afternoon sector

Coordinated observations from GOES-9, DMSP F-13, and Chokurdakh (CHD) have shown concurrent Pc1-2 band wave activity in the late afternoon sector, close to 16 MLT. The left-hand polarization of the waves in space indicates that these are electromagnetic ion cyclotron (EMIC) waves. In the region of field line conjunction, DMSP also observed 6–30 keV energy ion precipitation. We have examined the propagation of the EMIC waves from the magnetosphere to the ionosphere using both time series analysis and a 2½D magnetohydrodynamic model. Our analysis suggests that the EMIC are generated by interactions with cold plasma within a drainage plume, consistent with theory, and that the waves primarily propagate earthward along geomagnetic field lines at the eastward (outer) edge of the plume