High spatial and temporal resolution observations of an impulse-driven field line resonance in radar backscatter artificially generated with the Tromsø heater

. The CUTLASS Finland HF radar has been operated in conjunction with the EISCAT Tromsø RF ionospheric heater facility to examine a ULF wave characteristic of the development of a ﬁeld line resonance (FLR) driven by a cavity mode caused by a magnetospheric impulse. When the heater is on, stria-ting the ionosphere with ﬁeld-aligned ionospheric electron density irregularities, a large enough radar target is generated to allow post-integration over only 1 second. When combined with 15 km range gates, this gives radar measurements of a naturally occurring ULF wave at a far better temporal and spatial resolution than has been achieved previously. The time-dependent signature of the ULF wave has been examined as it evolves from a large-scale cavity resonance, through a transient where the wave period was latitude-dependent and the oscillation had the characteristics of freely ringing ﬁeld lines, and ﬁnally to a very narrow, small-scale local ﬁeld line resonance. The resonance width of the FLR is only 60 km and this is compared with previous observations and theory. The FLR wave signature is strongly attenuated in the ground magnetometer data. The characterisation of the impulse driven FLR was only achieved very crudely with the ground magnetometer data and, in fact, an accurate determination of the properties of the cavity and ﬁeld line resonant systems challenges the currently available limitations of ionospheric radar techniques. The combination of the latest ionospheric radars and facilities such as the Tromsø ionospheric heater


Introduction
The transient magnetohydrodynamic response to the impulsive excitation of the magnetospheric cavity has been the subject of a number of observational studies at high latitudes (e.g., Nopper et al., 1982;Kivelson et al., 1984;Baumjohann et al., 1984;Allan et al., 1985;Potemra et al., 1989). Impulsive excitation of the magnetosphere has also recently been the subject of a considerable number of theoretical and modelling studies, principally concerned with the coupling of the ®eld line resonance activity with the compressional mode cavity resonance activity (Allan et al., 1986a(Allan et al., , b, 1987Southwood, 1985, 1986;Inhester, 1987;Krauss-Varban and Patel, 1988;Kivelson, 1988, 1989;Lee and Lysak, 1991;Lysak and Lee, 1992;Samson et al., 1992). In discussing these models the phrase``cavity mode'' should in some cases be replaced by``wave guide mode'', as an azimuthally travelling wave is assumed .
Up to the present some of the strongest experimental evidence for the existence of magnetospheric cavity/ wave guide modes has come from the inner magnetosphere, the plasmasphere. For example, Sutclie and Yumoto (1989;, Yeoman and Orr (1989), Yumoto (1990), Yumoto et al. (1990), Lin et al. (1991), Yeoman et al. (1991) have all proposed that low-and midlatitude Pi2 pulsations are driven by compressional cavity resonances.
At high latitudes, Crowley et al. (1987) studied the damping of a ULF wave observed in ground magnetometer data and by the EISCAT radar, and concluded that energy was being fed into the ®eld line resonance by a global cavity mode. Ruohoniemi et al. (1991) and Samson et al. (1992) have demonstrated that, on occasions, nightside and early morning data from the high latitude Goose Bay HF radar, Canada, showed structured spectra with distinct spectral peaks at a discrete set of frequencies. These were interpreted as ®eld line resonances (FLRs) driven by magnetospheric cavity/wave guide modes. Similar structured spectra have recently been detected at sub-auroral latitudes by Provan and Yeoman (1996).
One highly characteristic aspect of the wave signatures predicted from a coupled cavity/wave guide ± FLR system is the initial transient wave form. This transient occurs as coupling between the magnetosonic wave mode of the resonant cavity and the AlfveÂ nic wave mode of the resonant ®eld line leads to the irreversible transfer of energy from the cavity resonance to the ®eld line resonance. McDiarmid and Allan (1990) produced a numerical simulation of the signature expected from such a coupled magnetospheric cavity/wave guide mode in auroral radar data, such as the Scandinavian Twin Auroral Radar Experiment (STARE, Greenwald et al., 1978) or the Sweden And Britain Radar-auroral Experiment (SABRE, Nielsen et al., 1983). McDiarmid and Allan (1990) noted that a latitude-dependent period occurred early in the wave packet, as the oscillation evolved from a cavity resonance, where phase is constant with latitude, to a FLR which has a characteristic phase change of 180°in latitude. McDiarmid and Allan (1990) also noted that such wave characteristics were very dicult to derive from the simulated radar data.
A transient wave signature, reminiscent of the ULF waves simulated by McDiarmid and Allan (1990), was noted in the SABRE Wick radar data by McDiarmid et al. (1994). This oscillation was demonstrated to start as a compressional mode wave in spacecraft magnetometer data, and then to evolve into ®eld line resonances in both the morning and afternoon sectors, although the wave structure was quite dierent in the pre-and post-noon regions.
In the present study, a high-latitude observation of a wave signature characteristic of a coupled cavity/wave guide ± FLR is presented. This wave has been detected at very high spatial and temporal resolution by the Cooperative UK Twin Located Auroral Sounding System (CUTLASS) radar, running a SuperDARN discretionary mode experiment (Greenwald et al., 1995). The very high spatial and temporal resolution has been enabled through the generation of ®eld-aligned electron density irregularities with the European Incoherent Scatter (EISCAT) high power RF ionospheric heating facility at Tromsù, in northern Norway (see e.g. Stubbe, 1996). These irregularities then act as an arti®cially produced target for the CUTLASS coherent scatter radar system.

Instrumentation
The ionospheric convection velocities in this study are provided by the CUTLASS Finland radar. CUTLASS is a bistatic HF coherent radar, with stations in Finland and Iceland, and forms part of the international SuperDARN chain of HF radars (Greenwald et al., 1995). Each radar of the system is a frequency agile (8±20 MHz) radar, routinely measuring the line-of-sight (l-o-s) Doppler velocity and spectral width of, and the backscattered power from, ionospheric plasma irregularities. The radars each form 16 beams of azimuthal separation 3.24°. Each beam is gated into 75 range bins, each of length 45 km in standard operations, when the dwell time for each beam is 7 s, giving a full 16 beam scan, covering 52°in azimuth and over 3000 km in range (an area of over 4´10 6 km 2 ), every 2 min. Common-volume data from the two stations can be combined to provide convection velocities perpendicular to the magnetic ®eld, although no common volume backscatter was detected during the interval under study here. During this interval the Finland radar was operating a non-standard scan mode. In this mode, rather than the usual anticlockwise sweep through beams 15, 14, 13,..., 0 the Finland radar was con®ned to a single look direction, beam ®ve. This beam overlies both the EISCAT radar facility and the ionospheric heater at Tromsù. The radar operations at this time also employed a range gating of 15 km, the ®rst gate being at a range of 480 km, and an integration time of 1 s. This arrangement was designed to explore the generation of ®eld-aligned electron density irregularities at very high temporal and spatial resolution. This dataset is supplemented here by data from ground magnetometers, provided by the International Monitor for Auroral Geomagnetic Eects, IMAGE) (LuÈ hr, 1994). These instruments are¯uxgate magnetometers, with a sampling interval of 10 s for the interval under consideration here. The IMAGE stations employed in this study, and the location of the high resolution CUTLASS Finland Beam 5 are illustrated in Fig. 1.

Observations
During the interval from 18 to 26 April 1996, a series of experiments were conducted with the EISCAT Incoherent Scatter radar, the Tromsù ionospheric heating facility, the CUTLASS HF radar and a number of low power HF diagnostics. One well-known result of arti®cial modi®cation of the ionosphere with a high power RF facility such as the Tromsù heater is the generation of ®eld-aligned ionospheric electron density irregularities (see Stubbe, 1996). One of the principal scienti®c aims of this experimental campaign was the delineation of the spatial and temporal development of these irregularities with the CUTLASS coherent scatter radar, which will backscatter from irregularities of wavelength of order 10±20 m, depending on the operating frequency. The results of these experiments will be presented elsewhere (T. R. Robinson, G. E. Bond, personal communication, 1996). Coherent backscatter from these arti®cially induced targets is recorded over a region where the heater power is sucient to generate irregularities. The power backscattered is proportional to the mean square deviation of the electron density associated with the arti®cial irregularities. Backscatter signal levels obtained from arti®cial irregularities appear to be signi®cantly higher than those from natural irregularities and this allows a reduction in the integration period of the radar. Integration periods of only one second have been possible, giving observations of regions of backscatter of $150 km extent in range with signal strengths in excess of 30 dB.
During the experimental campaign, between 1600 and 1630 UT on 23 April, quite by chance, an opportunity arose to study a naturally occurring magnetospheric ULF wave within the region of arti®cially generated radar backscatter. The Tromsù heater was operating at frequencies between 3.90 and 4.01 MHz, and its interaction height in the ionosphere is estimated at $200 km. Unfortunately, the EISCAT radar had ceased operation at 1600 UT. Although modi®cation of the D and E region ionosphere at ULF frequencies can be used to arti®cially generate a magnetic response of up to 10 nT (see Stubbe, 1996 and references therein), in the current experiment of F region heating the ULF wave is clearly of natural origin. Some evidence for observations of naturally occurring travelling ionospheric disturbances with HF diagnostics scattered by the Sura ionospheric heater has been presented by Blagoveshchenskaya and Troshichev (1996). They also observed wave activity in the ULF band, but attributed these to arti®cially generated waves. Although the experimental arrangement in the present study was optimised for plasma physics studies, the data collected oer a unique opportunity to study an important naturally occurring geophysical phenomenon with a very high spatial and temporal resolution. Figure 2 presents an overview of the radar and magnetometer data during the interval. A greyscale representation of the Finland line-of-sight velocity data is given in the top panel, with¯ow toward the radar (equatorward¯ow, positive Doppler velocity) plotted in light shading and¯ow away from the radar (poleward¯ow, negative Doppler velocity) plotted in dark shading. Patches of radar backscatter are observed, covering a spatial region of $1.5°of geomagnetic latitude (throughout this study altitude adjusted corrected geomagnetic (AACGM) coordinates, based on Baker and Wing, 1989 are employed). The backscatter patches occur during periods when the Tromsù heater is operational (marked with vertical dashed lines). During this interval the heater operated the following sequence. A 2-min``tuning'' period, during which the heater power was gradually increased, was followed by a 2-min``o'' period. This was then followed by a 3-min full power heater``on'' period, and then a 3 min``o''. This sequence was repeated three times. Note that the arti®cial backscatter does not start immediately after the onset of a tuning cycle, as irregularities are only generated when the heater power has reached a threshold value. In addition, the arti®cial backscatter persists after the heater has been switched o, as the irregularities generated have a characteristic decay time. The latest results suggest that the heater-induced irregularities detected by CUTLASS decay to a level of 3 dB in $100 s (G. E. Bond, personal communication). The second panel presents a time series for a single range gate, gate 31. Sections of the ULF wave forms can be clearly distinguished in this plot, with the background ionospheric drift velocity of $150 m s A1 being modulated by the ULF wave to values between 100 m s A1 and 300 m s A1 . The ULF wave signature persists with a peak amplitude of between 100 and 200 m s A1 for the interval 1600±1624 UT. The lower four panels of Fig. 1 present the X and Y component magnetic ®eld measurements from the Tromsù (TRO) magnetometer which lies underneath beam 5, gate 31 cell of the CUTLASS Finland radar in the discretionary radar programme running at this time. AULF wave can be seen both in the ®ltered and un®ltered data from TRO at a similar frequency to that observed in the radar data. The wave signature in the magnetometer data is strongest in the interval 1603±1613 UT. Fourier analysis of the wave signature at TRO reveals a dominant wave in the X component with a period of 143 s (7 mHz).
The ULF wave in ground-based magnetic ®eld measurements is examined in more detail in Fig. 3, which displays X and Y component magnetic ®eld data from six IMAGE magnetometer stations, covering magnetic latitudes from 56.8°±71.4°geomagnetic latitude, bandpass ®ltered between 150 and 50 s (6.67± 20.0 mHz). A coherent wave packet can be seen across the magnetometer chain, with maximum amplitude of $10 nT (peak-to-peak) observed in the X component magnetic ®eld between the latitudes of TRO and SOD. Fourier power spectral analysis of the magnetometer data is presented in Fig. 4. This con®rms that the dominant frequency is generally 7±8 mHz, and that the largest power at this frequency is found in the X component at SOD and TRO. Examining the relative phase of the wave packets in Fig. 3 near the time of their maximum in amplitude, at 16:07 UT, the Y components can be seen to be approximately in phase across the stations. In contrast, a phase change in excess of 180°6 Patches of radar backscatter are observed during periods when the Tromsù ionospheric heater is operational (marked with vertical dashed lines). The second panel plots a time series for a single range gate, gate 31, which overlies the Tromsù magnetometer. Filtered (150 ± 50 s, 6.67 ± 20 mHz) and un®ltered X and Y component magnetic ®eld measurements are presented in the lower four panels. A correlated ULF wave signature can be seen in data from both instruments can be seen in the X component ®eld measurements, with the lower latitude stations leading in phase.
The latitude variation of the line-of-sight CUTLASS data is displayed in Fig. 5. Stacked time series of Finland line-of-sight velocity data for nine 15 km range gates (gates 28±36, ranges 900±1035 km) are included. Although the analysis of the ULF wave, which has a period of $2 min, is limited by the heater cycle, which restricts the available data to 2-and 3-min sections, the very high temporal and spatial resolution of the data enable a detailed picture of the wave parameters to be obtained for a number of intervals during the wave packet. The ULF wave signature is well de®ned over the 135 km of latitude illuminated by the Tromsù heater. The wave is of a fairly constant amplitude over the nine range gates early in the wave packet, but has a peak amplitude in the equatormost range gates by 1620 UT. The early wave cycles are also in phase over the nine range gates, whereas by the later parts of the wave packet a phase change of $180°can be seen over the 135 km separation, with the lower latitude range gates leading in phase. The characteristics of these wave packets in the radar data are presented in detail in Fig. 7.
The spatial and temporal variation of the wave parameters in the ground magnetometer and ionospheric drift velocity measurements will now be examined in more detail. In Fig. 6 wave parameters derived from the magnetometer data presented in Fig. 3 are examined. Panels a and b present the amplitude and phase of the dominant Fourier component of the X and Y component magnetometer data. The magnetic ®eld data for the entire ground-observed wave packet, between 1557 and 1618 UT, bandpass ®ltered between 150 and 100 s (6.67±10.0 mHz) has been included in the Fourier analysis, and the average frequency of peak spectral power over the array is 7.9 mHz. The spectral amplitude and phase at this frequency are presented. Analysis of this spectral component reveals a pattern typical of a classical FLR signature. There is a clear peak in spectral power in latitude, in this case at SOD, with the X component the dominant component in the ground magnetic ®eld. The spectral phase is fairly constant in latitude for the Y component magnetic ®eld, but has a the X component measured here is, however, almost 360°, rather than the 180°predicted by ®eld line resonance theory (Southwood, 1974;Chen and Hasegawa, 1974). The horizontal shaded bar shows the latitudinal extent of the radar data presented in Figs. 5 and 7. Figure 7 presents wave parameters derived from the CUTLASS radar line-of-sight velocity data. Following McDiarmid and Allan (1990), wave parameters are calculated directly in the time domain from the velocity measurements, with the time shifts between the wave peaks and troughs being used to derive wave period and phase. This technique was found to be the most useful by McDiarmid and Allan (1990) and, in addition, allows the eect of the heater cycle to be deconvolved from the wave parameter analysis. In each panel, wave parameters have been derived for ®ve short sections of the CUTLASS velocity timeseries during heater``on'' intervals at 1601±1603, 1606±1608, 1611±1613, 1616±1618, and 1621±1622 UT. Figure 7a presents the calculated wave periods. There is, in general, no clear variation of wave period with latitude, but the pro®le measured at 1611±1613 UT shows the strongest latitude variation. The wave phase, relative to the lowest latitude range gate available for each time interval is shown in Fig. 7b. This analysis clearly shows the evolution of the wave packet from a latitudinal sequence of in-phase time series from 1601±1613 UT to a sequence displaying the characteristic latitudinal phase variation of a FLR (Southwood,Fig. 4. Fourier power spectral analysis (linear arbitrary units) for the magnetometer data presented in Fig. 3, in this case detrended with a 300 s (3.3 mHz) high pass ®lter 1974; Chen and Hasegawa, 1974). Figure 7c displays the peak-to-peak wave amplitude. Again a clear evolution can be seen during the wave packet, from a latitude-independent pro®le early in the oscillation to a sharply peaked resonant structure at 66.25°geomagnetic latitude. This transition appears to be surprisingly sharp, occurring between 16:13 and 16:16 UT, although this may, in part, be an artefact of the observational constraints imposed by the heater cycle.
Wave period estimates have also been derived from the ground magnetometer data using the technique employed for Fig. 7. Figure 6c presents the dominant wave period in the horizontal ground magnetic ®eld data for two intervals during the wave event, one early in the wave packet (1605±1608 UT) and one late in the ground-observed wave packet (1608±1612 UT). The wave period can be seen to have a distinct latitudinal variation, with the ®eld oscillating at a longer period at higher latitudes in the early part of the ground magnetometer recordings. However, this trend becomes less apparent as the wave packet develops.

Discussion
The combination of the Tromsù heater and the CUT-LASS Finland HF coherent scatter radar has enabled a high temporal and spatial resolution study of a highlatitude ULF wave. The high resolution study possible with the radar data has been compared with an analysis of the lower resolution, but more spatially extensive, magnetometer data. The wave has the characteristics of the transient signature of a coupled cavity/waveguide ± FLR driven by an impulse on the magnetopause. The period of the observed wave suggests that it is a harmonic of the local ®eld line eigenperiod (Poulter et al., 1984). A similar wave observed by McDiarmid et al. (1994) was demonstrated to be most probably a second harmonic. The observed wave signatures can  c Shows the dominant wave period for two intervals during the wave event (see text for details). The horizontal shaded bar shows the latitudinal extent of the radar data presented in Fig. 5 and 7 most readily be compared with the simulation of an impulse driven ®eld line resonance in VHF coherent radar data presented by McDiarmid and Allan (1990). They used the output of the time-dependent numerical model of Allan et al. (1986b) to model the development of a FLR driven by a cavity mode caused by a magnetospheric impulse. The most characteristic signature of these simulations was the evolution of the response from the constant period-constant phase characteristic of a cavity resonance, through a transient, latitude-dependent frequency region, where each ®eld line oscillated at its natural frequency, to a resonant signature with an amplitude peak accompanied by a 180°phase change in latitude, as the energy of the cavity/waveguide mode was channelled into a FLR. The simulation showed that the latitude-dependent pulsation period was observed most strongly in the early wave cycles of the oscillation, and had almost entirely disappeared by the latter half of the modelled wave. Another important result of this modelling was the prediction that even with the good spatial (20 km) and temporal (20 s) resolution of the STARE/SABRE type radars, the transient features of these resonances would be dicult to observe. The diculty in making accurate observational studies of such wave phenomena is clearly illustrated in the contrast between Fig. 6 and 7. The magnetometer data suggest a latitudinally broad, resonant structure. However, this is a consequence of the temporal evolution of the signal during the wave packet and the spatial integration of the ground magnetometers (see Sect. 4.3). The radar data reveals that the resonance is actually con®ned to a very narrow region (Fig. 7; the latitude region of this ®gure is indicated in Fig. 6 by the horizontal shaded bar). The oscillation will be discussed in detail in three sections: (a) the initial cavity oscillation, (b) the coupled transient and (c) the driven ®eld line resonance.

The cavity resonance
The initial wave cycles of the transient pulsation observed here are most characteristic of the impulsedriven cavity/wave guide resonance. The amplitude and phase are relatively constant with latitude, as expected for a large-scale cavity resonance. This section of the wave packet appears strongly in the ground magnetometer data. The early wave packet does not have a simple damped envelope, however, as might be expected for an impulse-driven resonance. Rather it grows between 1601 and 1608 UT in both the ground magnetometer data and the ionospheric velocity data, before damping and coupling to a FLR reduce the amplitude.

The coupled transient
The transition between a cavity resonance-like and a FLR-like signature is characterised by a latitude-dependent period. Latitude-dependent periods, due to magnetospheric ®eld lines freely ringing at their natural frequencies have been observed at high latitude by Poulter and Nielsen (1982) and Allan et al. (1985). In the present study this transition region can be seen in the early part of the ground-observed oscillation from 1605± 1608 (Fig. 6c), where the wave period varies from 110± 130 s. The later parts of the wave form give unclear results. The results from the analysis of the ionospheric velocity time series do not show a clear dependence of period with latitude, although a latitude variation of 130±150 s is observed from 1611±1613 UT.

The ®eld line resonance
The resonant ®eld line section of the oscillation modelled by McDiarmid and Allan (1990) has a Fig. 7 a±c. Wave parameters derived from the CUTLASS radar lineof-sight velocity data presented in Fig. 5. a Wave periods, b wave phase relative to the lowest latitude range gate and c peak-to-peak wave amplitude. Each panel presents parameters derived from ®ve sub-intervals of the wave packet at 1601±1603, 1606±1608, 1611±1613, 1616±1618, and 1621±1623 UT (see text for details) resonance width of $0.6°latitude (67 km) and a phase slope of 160±195°/°latitude. In the simulated radar data most appropriate for HF radars, with no velocity threshold eects, this appeared as a phase slope of 110°/°lat., with a 0.8°latitude (90 km) width. Probably the best observational candidates for such a wave previously reported were the oscillations studied by McDiarmid and Nielsen (1987) and McDiarmid et al. (1994). In the present study, using a radar experiment of spatial resolution 15 km, slightly superior but comparable to the VHF radars, but with much improved temporal resolution (1s rather than 20s), a peak phase slope of 270°/°Lat. is observed and the full width at half maximum (FWHM) of the resonance can be estimated at 0.54°Latitude or 60 km. Previous observations of the widths of ®eld line resonances using the STARE radar (20 km, 20 s resolution, Walker et al., 1979) and the Goose Bay HF radar (45 km, 96 s resolution, Walker et al., 1992) gave results of FWHM $100 km. McDiarmid et al. (1994) inferred a resonance width of 2°l atitude (220 km) for their observation of an impulsedriven FLR.
The theoretical minimum FLR width in the magnetospheric equatorial plane was evaluated as 0.005 LR E by Newton et al. (1978), corresponding to $6 km in the ionosphere at the latitude of Tromsù, where a separation of 100 km in the ionosphere will map to 0.59 R E in the magnetospheric equatorial plane. This calculation assumed a light damping due to ionospheric Joule dissipation only, with the height integrated Pedersen conductivity, 10 S. Any additional damping effects will act to widen the resonance.
In the present study, although the EISCAT radar ceased to operate before the occurrence of the ULF wave, at 16:00 UT, data from 15:00±16:00 UT show that the height-integrated Hall and Pedersen conductivites, r and , both had a steady value of 3 S. It thus seems reasonable to take this value as appropriate for the wave from 16:00±16:30 UT. These values have been calculated from the EISCAT alternating code electron density pro®les in the ®eld-aligned pointing position, along with the IGRF magnetic ®eld model and the MSIS86 model of the neutral atmosphere. The conductivities have been height-integrated between 90 and 200 km. A value of 3 S implies a resonance width in the ionosphere of 30 km and 9 km respectively for a fundamental and second harmonic toroidal mode (based on the curves of Newton et al., 1978). These narrow theoretical resonance widths suggest that damping mechanisms other than ionospheric Joule dissipation are important in the wave event under study. A similar conclusion was reached for an impulse-driven wave by McDiarmid et al. (1994). Recently, Mann et al. (1995) have suggested that the asymptotic width of a ®eld line resonance coupled to a magnetospheric cavity mode is in fact determined by the damping of the cavity mode rather than the resonant ®eld line, and predicted a resonance width of 0.4 R E in the magnetospheric equatorial plane at v 7 (corresponding to 68 km in the ionosphere above Tromsù). This value very closely matches the observations presented here.
It is dicult to con®rm these calculations with a direct estimate of the wave damping from the observed time series. For a coupled cavity mode a damping rate of lower than that due to ionospheric Joule dissipation will be inferred, if the cavity mode is still driving the ®eld line resonance. In addition the diculty in estimating damping rates of transient pulsations from ground magnetic ®eld data has been demonstrated in the modelling of Poulter and Allan (1985). In the example studied here, clearly the ground magnetometer data would give a very deceptive estimate of damping rate. Unfortunately in this case, the driven ®eld line resonance is not detected for long enough for the ionospheric radar data to provide a good estimate of the damping either.
The ®eld line resonance part of the oscillation, although clearly delineated in the radar data, is not apparent in the ground magnetometer data. For such a narrow resonance this is perhaps not surprising. Ground magnetometer signals are attenuated at small-scale lengths, due to the spatial integration of the E region current systems responsible for the magnetic signature over an area of the ionosphere of radius of the same order of the E region height. Hughes and Southwood (1976) demonstrated that a signal attenuation of $1 order of magnitude occurred if the azimuthal scale length of the ULF wave was 50 km. Attenuation increases of a factor of 5 were observed by Yeoman et al. (1992) in a comparison of pulsations in ionospheric radar and ground magnetometer data as the azimuthal wave number, m, increased from 3 to 18.

Summary
AULF wave characteristic of the development of a FLR driven by a cavity mode caused by a magnetospheric impulse has been investigated by means of a novel experimental technique. The time-dependent signature of the waveform has been examined as it evolves from a large-scale cavity resonance, through a transient where the wave period was latitude-dependent and the oscillation had the characteristics of freely ringing ®eld lines, and ®nally to a very narrow, small-scale local ®eld line resonance. The FLR was only 60 km in width and was highly attenuated in the ground magnetometer data.
The characterisation of impulse driven FLRs can only be achieved very crudely by ground magnetometer arrays and, in fact, an accurate determination of the properties of the cavity and ®eld line resonant systems challenges the currently available limitations of ionospheric radar techniques.
The results reported here demonstrate that the combination of the latest ionospheric radars and an ionospheric heater, such as that at Tromsù, provide a powerful new tool for active geophysical research.