Australian Cosmic Ray Modulation Research

M. L. Duldig
, PASA, 18 (1), in press.

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Ground Level Enhancements

Ground level enhancements (GLEs) are sudden increases in the cosmic ray intensity recorded by ground based detectors. GLEs are invariably associated with large solar flares but the acceleration mechanism producing particles of up to tens of GeV is not understood. To date there have been 59 GLEs recorded since reliable records began in the 1940's. The most recent event was recorded on 16 July 2000. The increases in ground based measurements ranges from only a few percent of background in polar monitors (with little or no geomagnetic cutoff) to 45 times for the 23 February 1956 event. The rate of GLEs would appear to be about one per year but there may be a slight clumping around solar maximum. For example, during 2 years centred on the last solar maximum 13 GLEs were recorded. The frequency of GLEs per annum is plotted together with the smoothed sunspot number in Figure 20.

Figure 20: Monthly smoothed sunspot numbers and annual frequency of Ground Level Enhancements (histogram) for the period 1940 - 1995. (From Cramp 2000b).
\begin{figure} \begin{center} \epsfig{file=mld-fig20.eps,height=4cm} \end{center} \end{figure}

Most solar flares associated with GLEs are located on the western sector of the Sun where the IMF is well connected to the Earth. This is shown schematically in Figure 21. To clarify this view, think of it as an equatorial slice through the neutral sheet of Figure 2 remembering that the field lines must be parallel to the sheet. The geometry of this field line is quite variable, depending on the strength of the solar wind that varies considerably, but its average structure is well represented by the figure. Because of its shape it is known as the ``garden hose'' field line.

Figure 21: Schematic representation of the ``garden hose'' field line connecting the Sun and the Earth. (From Duldig et al. 1993).
\begin{figure} \begin{center} \epsfig{file=mld-fig21.eps,height=7cm} \end{center} \end{figure}

GLEs associated with flares located near to the footpoint of the garden hose field line usually arrive promptly and have very sharp onsets. Conversely, GLEs associated with flares far from the garden hose field line are usually delayed in their arrival at Earth and have more gradual increases to maximum intensity. It is very rare to observe GLEs associated with flares to the east of the central meridian or Sun-Earth line. Although a large solar flare is invariably associated with a GLE the flare itself may not be causally related to the production of the high energy protons that produce the GLE response at Earth. Solar energetic particle events are not rare and energetic protons are produced in common with CMEs and interplanetary shocks. These protons do not have sufficient energy to produce secondary particles that reach ground level but are clearly observed by spacecraft. Such CMEs and their associated shocks are most often produced without a solar flare. It is possible that there is a continuum to the acceleration process and that flares are a by-product of the most energetic events. Alternatively, there is a possibility that the flare itself produces a seed population of higher energy protons that are further accelerated to energies sufficient to produce a GLE. For a recent short summary of GLE research see Cramp (2000a).

Modelling the Global GLE Response

The technique for modelling the GLE response by neutron monitors has been developed over many years (Shea & Smart 1982; Humble et al. 1991b) and is described in Cramp et al. (1997a). The method allows the determination of the axis of symmetry of the particle arrival, the spectrum and the anisotropy of the high energy solar protons that give rise to the increased neutron monitor response. For the technique to work effectively data are needed from neutron monitors at a range of locations around the globe. A range of latitudes of response gives spectral information due to the geomagnetic cutoff (see next section) whilst a range of latitudes and longitudes gives the necessary three dimensional coverage to map the structure of the anisotropy. During the 1990's significant improvements to the modelling have included more accurate calculations of the effect of the Earth's magnetic field on the particle arrival (Kobel 1989; Flückiger & Kobel 1990) using better and more complex representations of the field (Tsyganenko 1989) and the incorporation of least-square techniques to efficiently analyse parameter space for optimum solutions. The use of least-square techniques also made practicable fits with a larger number of variables.

Geomagnetic Effects - Asymptotic Cones of View

Cosmic ray particles approaching the Earth encounter the geomagnetic field and are deflected by it. In principle it should be possible to trace the path of such a particle until it reaches the ground as long as we have a sufficiently accurate mathematical description of the field. Such an approach would require particles from all space directions to be traced to the ground to determine the response. It is more practical to trace particles of opposite charge but the same rigidity from the detector location through the field to free space because they will follow the same path as particles arriving from the Sun. When calculated in this way it is found that for a given rigidity there may be some trajectories that remain forever within the geomagnetic field or intersect the Earth's surface. These trajectories are termed re-entrant and indicate that the site is not accessible from space for that rigidity and arrival direction at the monitor. The accessible directions are known as asymptotic directions of approach (McCracken et al. 1962, 1968) and the set of rigidity dependent accessible directions defines the monitor's asymptotic cone of view. For a given arrival direction at the monitor there is a minimum rigidity below which particles can not gain access. This is termed the geomagnetic cutoff for that direction at that location and time. Geomagnetic cutoffs quoted for a given neutron monitor usually refer to this cutoff for vertically incident particles and use an undisturbed representation of the geomagnetic field. They vary between 0 GV at the magnetic poles and $\sim $14 GV near the geomagnetic equator. Above the minimum cutoff rigidity for a given arrival direction there may be a series of accessible and inaccessible rigidity windows known as the penumbral region (Cooke et al. 1991). The penumbral region ends at the rigidity above which all particles gain access for that arrival direction. Particle trajectories that escape to free space are termed ``allowed'' and those that are re-entrant are termed ``forbidden''. Until recently most analyses considered only vertically incident directions at monitors and often that is an acceptable simplification. However, Cramp et al. (1995a) showed that this was unsatisfactory when modelling extremely anisotropic events. With the advent of increased computer power it has been possible to extend the set of arrival directions. Rao et al. (1963) showed that the response to galactic cosmic rays by a neutron monitor can be characterized by equal contributions from nine segments as shown in Figure 22.

Figure 22: The nine segments above a neutron monitor that contribute equal responses to the count rate arising from galactic cosmic rays. Circles represent zenith angles of 8o, 24o and 40o. Viewing directions are calculated at the centres of each segment as marked with a dot (zenith angles 0o, 16o and 32o for azimuths 0o, 90o, 180o and 270o). (From Cramp et al. 1997a).
\begin{figure} \begin{center} \epsfig{file=mld-fig22.eps,height=5cm} \end{center} \end{figure}

By considering these 9 arrival directions for each neutron monitor over the complete rigidity range of interest it is possible to obtain a better representation of the asymptotic cone of view. It should also be remembered that the geomagnetic cutoff of low latitude neutron monitors can show significant east-west asymmetry with the lowest cutoffs being for western directions of view. The internal geomagnetic field (ie the geomagnetic field arising from the Earth's interior, excluding the effects of solar wind pressure and induced current systems that modify the field) is modelled by a series of spherical harmonic functions. With the inclusion of secular variation terms for the harmonic coefficients this model is known as the International Geomagnetic Reference Field (IGRF). The IGRF represents the most recent parametric fit to the model and apply from a particular year until the next IGRF is released, usually every 5 years. On release of a new IGRF the previous model is modified with its secular terms adjusted to the actual changes that took place over the five year period and it becomes the Definitive Geomagnetic Reference Field (DGRF) for that 5 year interval (IAGA 1992). The Geomagnetic field is distorted by external current systems in the ionosphere resulting from interaction of the IMF with the geomagnetic field. The speed of the solar wind and the orientation of the IMF both influence these currents. The result is a compressed geomagnetic field on the sunward side and an extended tail on the anti-sunward side of the Earth. These distortions must be taken into consideration when calculating the asymptotic cones of view. Tsyganenko (1987, 1989) developed models of the external field taking into account the effects of distortion. He used the Kp geomagnetic index (Menvielle & Berthelier 1991) as a measure of the level of distortion that could be input into his model to allow a more complete description of the field. Flückiger & Kobel (1990) combined the models of Tsyganenko with the IGRF and developed software to calculate particle trajectories through the field.

Figure 23: Asymptotic viewing direction of vertically incident particles at 1805 UT on 22 October 1989. Top panel: a) assumes quiet (Kp=0) geomagnetic conditions. Bottom panel: b) includes actual disturbed (Kp=5) geomagnetic conditions at the time of the event. Sanae S and $\Box $; Mawson M; Oulu O; Terre Adelie Te; Hobart H and $\Diamond $; Inuvik I; McMurdo Mc; Thule Th; South Pole P. The viewing directions at 1, 5 and 10 GV are indicated by x , $\ast $ and + respectively. (From Duldig et al. 1993).
\begin{figure} \begin{center} \epsfig{file=mld-fig23.eps,height=12cm} \end{center} \end{figure}

Figure 23 shows the undisturbed and disturbed viewing directions for vertical incidence particles at a number of neutron monitors at 1805 UT during the GLE on 22 October 1989. The level of disturbance at that time was moderately disturbed at Kp = 5. The most obvious changes can be seen in the direction of view of the polar monitors like Thule at the top and South Pole at bottom right. It is also apparent that the equatorial viewing instruments have had their views significantly changed. Thus it is now possible to calculate the asymptotic cones of view of neutron monitors appropriate to the time of day and to the level of geomagnetic disturbance present. It should be noted that making such calculation for a dense grid of rigidities over 9 directions of arrival for each of several tens of neutron monitors is still quite an intensive computing task.

The Neutron Monitor Response

The response of a neutron monitor to particles arriving at the top of the atmosphere above a site can be described by (Cramp et al. 1997a):

\begin{displaymath} \frac{\Delta N}{N}=\frac{1}{9}\sum_{(\theta,\phi)=1}^{9} ... ...}}^{\infty}Q_{(\theta,\phi)}(P)\;J_{0}(P)\;S(P)\;\Delta P} \end{displaymath} (11)

where   $\Delta N$ absolute count rate increase due to solar protons;
N pre-event baseline count rate due to galactic cosmic rays;
P particle rigidity (GV);
Pmin lowest rigidity of particles considered in the analysis;
Pmax maximum rigidity considered;
$(\theta,\phi)$ zenith and azimuth coordinates of the incident protons at the top of the
  atmosphere above the monitor, chosen as described below;
Q 1 for accessible directions of arrival and 0 otherwise;
J differential solar proton flux;
J0 interplanetary differential nucleon flux adjusted for the level of solar cycle
S neutron monitor yield function;
G pitch angle distribution of the arriving solar protons;


latitude and longitude of the asymptotic viewing direction associated with
  $(\theta,\phi)$ and rigidity P;



axis of symmetry of the pitch angle distribution.
Pmin in the calculation is the lowest allowed rigidity as defined in the previous section except where this is less than the cutoff due to atmospheric absorption which is assumed to be 1 GV. For high altitude polar sites (South Pole and Vostok in particular) this is not accurate as lower rigidity particles do have access to the sites. Cramp (1996) has shown, however, that the resulting errors in the best fit parameters are insignificant. Pmax is taken to be 20 GV unless there is evidence from surface or underground muon telescopes of higher rigidity particles as was seen for the 29 September 1989 GLE (Swinson & Shea 1990; Humble et al. 1991b). The asymptotic cone of view calculations define Q which has a value of 0 for all ``forbidden'' directions above Pmin and 1 otherwise. Increases are modelled above the pre-event background due to galactic cosmic rays taking into account the level of solar cycle cosmic ray modulation (Badhwar and O'Neill 1994). For each monitor the background is determined by summing the the response of the solar cycle modulated cosmic ray nucleon spectrum J0 and the neutron monitor yield function S over all allowed rigidities. The neutron monitor yield function generally accepted as the best available is the unpublished one of Debrunner, Flückiger and Lockwood that was presented at the 8th European Cosmic Ray Symposium in Rome in 1982. The increases observed at each monitor are adjusted to sea level values using the two attenuation length method of McCracken (1962). This technique takes into account the different spectrum of galactic and solar cosmic rays and employs different exponential absorption lengths for the two populations to derive the sea level response. The solar particle absorption length is determined from the response of geographically nearby neutron monitors with large altitude differences. The particle pitch angle $\alpha$ is the angle between the axis of symmetry of the particle distribution and the asymptotic direction of view at rigidity P. The pitch angle distribution is a simplification of the exponential form described by Beeck & Wibberenz (1986). It has the functional form

\begin{displaymath} G(\alpha)=\exp\left[\frac{-0.5(\alpha-\sin\alpha\cos\alpha)} {A-0.5(A-B)(1-\cos\alpha)}\right] \end{displaymath} (12)

where A and B are variable parameters. It is possible to modify this function with the addition of two parameters $\Delta A$ and $\Delta B$ which may be positive or negative and represent the change in A and B with rigidity. This results in a rigidity dependent pitch angle distribution where the anisotropy can be larger or smaller with increasing rigidity (Cramp et al. 1995b). Another possible modification to the pitch angle distribution is to allow bi-directional particle flow. This is achieved by modifying the function to

$G^{'}(\alpha)=G_{1}(\alpha)+C\times G_{2}(\alpha^{'})$, where G1 and G2 are of the same form as Equation 12 with independent parameters A1, B1, A2 and B2;

$\alpha^{'}=\pi-\alpha$; and C is a reverse to forward flux ratio between 0 and 1. Reverse propagating particles have opposite flow (pitch angles >90o). This could arise if particles initially travelling outward from the Sun past 1 AU encounter a magnetic shock or structure which reflects the particles back along field line toward the Sun. Alternatively, the Earth may lie on a looped field structure, possibly connected back to the Sun on both sides, and particles traveling around the loop create a bidirectional flow. The rigidity spectrum of the solar protons can be modelled as a simple power law in rigidity with a slope $\gamma$. A more useful approach has been to model the spectrum as a power law with an increasing slope. Two parameters thus define the shape of the spectrum: $\gamma$, the slope at the normalizing rigidity of 1 GV; and $\delta\gamma$, the change of $\gamma$ per GV. Such a spectrum is almost identical in shape to the theoretical shock acceleration spectrum of Ellison & Ramaty (1985). The flux of the arriving particles is determined for the steradian solid angle centred on the axis of symmetry in units of particles (cm2 s sr GV)-1. Not all the additional parameters described above are used together because there is usually insufficient observations for that number of independent variables in the fit. However the addition of least squares techniques by the Australian researchers has made it practicable to search more options in parameter space. To ensure that the minimum in parameter space has been found rather than a local minimum close to the starting parameters it is important to repeat the fit with widely varying initial estimate parameters. To date no significantly different solutions have arisen although physically unrealistic initial guesses have occasionally led to non-convergence of the fit.

29 September 1989 - The Largest GLE of the Space Era

The GLE that commenced around noon UT on 29 September 1989 was the largest recorded since the giant event of 23 February 1956 and thus the largest recorded in the space era. The maximum ground level response was observed by the Climax station with a peak 404% above the pre-event background during the 5-minute interval 1255-1300 UT. The GLE was notable for several other features. No visible flare was observed on the solar disk at the time of the enhancement, however a flare was observed from behind the western limb from $\sim $1230 UT (Swinson & Shea 1990). A looped prominence extended beyond the limb from before 1326 UT until at least 2315 UT. Intense solar radio emission of types 2, 3 and 4 was observed and soft X-rays emission commenced at 1047 UT and peaked at 1133 UT with an intensity of X9.8. The flare is believed to have been located at $\sim $25oS, 98$\pm$5oW in the NOAA active region 5698 (Solar-Geophysical Data no. 547, part 2, 1990). $\gamma$-ray line emission was reported from the solar disk (Cliver et al. 1993) indicating that there was a shock present probably driven by a CME that extended from behind the limb to the solar disk side. The time profile of the response was unusual in that some stations observed a reasonably rapid increase to maximum, others a very slow climb to maximum more than an hour after the onset and some observed two peaks - at the time of the earliest maximum and at the time of the later maximum observed by the stations with a slow rise response. Examples of these profiles are shown in Figure 24.

Figure 24: Cosmic ray increases at Mt Wellington, Goose Bay, Durham, Mawson, Alma-Ata and Rome neutron monitors and Inuvik and Deep River muon telescopes between 1100 and 1800 UT on 29 September 1989. (From Lovell et al. 1998).
\begin{figure} \begin{center} \epsfig{file=mld-fig24.eps,height=12.5cm} \end{center} \end{figure}

Another unusual feature of the event was the recording of both surface muons (Mathews et al. 1991; Smart & Shea 1991; Humble et al. 1991b) and underground muons (Swinson and Shea 1990). The underground muon increase was recorded with the Embudo telescope that had a threshold of $\sim $15 GV but was not recorded at the nearby Socorro telescope that was slightly deeper underground and had a threshold of $\sim $30 GV. Lovell et al. (1998) have published an extensive analysis of this GLE including the response of satellite instruments, neutron monitors and surface muon telescopes. In this analysis the muon telescope response was determined for 9 directions in a manner similar to the neutron monitors. Because the atmospheric absorption is different for muon telescopes the central zenith angles are 0o, 13o and 28o. The analysis also required the use of yield functions for muon telescopes. The yield functions of Fujimoto et al. (1977) that were based on earlier work, published later, of Murakami et al. (1979) adjusted for the level of cosmic ray modulation (Badhwar & O'Neill 1994) were used. There is some doubt about the accuracy of this yield function at rigidities below $\sim $10 GV, the bottom end of the muon response. It is adequate for low energy galactic cosmic rays but may not be optimal for a solar proton spectrum. The errors introduced are likely to be quite small however. The derived attenuation length for solar particles was 120 g cm-2. Lovell et al. (1998) analysed three 5-minute time intervals commencing at 1215 UT, 1325 UT and 1600 UT. These times were chosen because they were the times of the first and second peaks and late in the event during the recovery phase. The main parameters describing the spectra and axis of symmetry of the arriving particles are given in Table 2.

Figure 25: Rigidity spectra derived for 1215 UT (solid line), 1325 UT (dashed line) and 1600 UT (dotted line) on 29 September 1989 GLE. (From Lovell et al. 1998).
\begin{figure} \begin{center} \epsfig{file=mld-fig25.eps,height=8cm} \end{center} \end{figure}

As can be seen from Figure 25 and Table 2 the spectrum was extremely hard early in the event and even during the recovery phase at 1600 UT was still harder than many GLEs. The steepening of the spectra is similar to the Ellison & Ramaty (1985) form and is consistent with shock acceleration rather than an impulsive injection of particles. Lovell et al. (1998) extended the spectral analysis by including low energy hourly average measurements from the IMP 8, GOES 6 and GOES 7 spacecraft. They fitted an Ellison & Ramaty (1985) shock acceleration spectrum to the increased energy range (now 4 orders of magnitude). The results of this fit are reproduced in Figure 26. Note that the neutron monitor derived spectrum is now in terms of energy rather than rigidity. In making the fit the shock compression ratio and e-folding energy are variable parameters. The shock compression ratio is defined as

$\sigma=3r/(r-1)$ where r is the ratio of upstream to downstream plasma velocities and was found to be 2.3$\pm$0.2. The e-folding energy was 770$\pm$90 MeV. It appears that shock acceleration is likely to be the mechanism responsible for the solar energetic particle production during this GLE.

Figure 26: Hourly proton and alpha particle data from IMP 8, GOES 6 and GOES 7 spacecraft and neutron monitors (shaded region) during 29 September 1989 GLE. The fitted curves are Ellison & Ramaty (1985) shock acceleration spectral forms for protons and alpha particles. (From Lovell et al. 1998).
\begin{figure} \begin{center} \epsfig{file=mld-fig26.eps,height=8cm} \end{center} \end{figure}

Table 2: 29 September 1989 GLE - Spectrum and Arrival Direction. From Lovell et al. (1998).
         Geographic GSE  
 Time $\gamma$ $\delta\gamma$ Flux Latitude Longitude Latitude Longitude $\Psi$
 UT     (cm2 s sr GV)-1 deg deg deg deg deg
 1215-1220 -2.2 0.3 8.8 37 254 14 258 100
 1325-1330 -4.7 0.4a 139.2 22 258 0 282 78
 1600-1605 -5.8 0.1 220.2 -42 246 -56 306 53
 a >6 GV only                

In Table 2, $\Psi$ represents the angle between the axis of symmetry of the arriving particles and the Sun-Earth line. Nominally this would be expected to be 45o but it does depend strongly on interplanetary conditions. The Geocentric Solar Ecliptic (GSE) coordinate system shown in Table 2 has its X-axis pointing from the Earth to the Sun, its Y-axis in the ecliptic plane pointing toward dusk and its Z axis pointing toward the ecliptic pole. It is commonly used in geophysical research for IMF related work because it is aligned to the Sun-Earth line. For a full description of the coordinate system and transformations between it and other common systems see Russell (1971). This paper is also available on the world wide web at No in-situ IMF observations were available from 0300 UT on 26 September 1989 until 2200 UT on 1 October 1989. As is indicated in Table 2 the results show a transition from mid-northern to mid-southern latitudes for the axis of symmetry of the arriving particles. Similar latitudinal changes in IMF direction were observed between 1700 UT and 2100 UT on 25 September 1989 when direct measurements were available. It thus seems reasonable to accept that the latitudes of the axis of symmetry described by Lovell et al. (1998) as realistic. The solar wind speed measured on 25 and 26 September 1989 was very low (down to $\sim $280 km s-1) and may have remained low during the GLE. Such low wind speeds will result in angles between the IMF and the Sun-Earth line of somewhat greater values than the typical 45o. Furthermore, the footpoint of the IMF line connecting to the Earth will be closer to the western limb of the Sun than the average value of 60o. This would place the footpoint closer to the flare site as might be expected for such a large GLE. The axis of symmetry direction moves toward more typical geometries throughout the event.

Figure 27: Rigidity dependent pitch angle distribution derived for 1215 UT on 29 September 1989 (top). Rigidity independent pitch angle distributions for 1215 UT (solid line), 1325 UT (dashed line) and 1600 UT (dotted line) for the same GLE (bottom). (From Cramp 1996, 2000a; Lovell et al. 1998).
\begin{figure} \begin{center} \epsfig{file=mld-fig27a.eps,height=3.7cm} \end{center} \end{figure}

\begin{figure} \begin{center} \epsfig{file=mld-fig27b.eps,height=3.7cm} \end{center} \end{figure}

The pitch angle distributions derived for this GLE are shown in Figure 27. At the first peak time a rigidity dependent pitch angle distribution has been determined. At the lowest rigidities the particle arrival is strongly anisotropic the flux reduced to half at pitch angles of 40o. At the highest rigidities present it is closer to 80o. At the time of the second peak, 1325 UT, there is marginally significant evidence for reverse particle propagation. This was expected as the monitors seeing only the second peak had asymptotic cones of view that looked anti-sunward along the field. Monitors seeing only the first peak were viewing roughly along the IMF field in the sunward direction and those observing both peaks were viewing between these two extremes. Also at the time of the second peak the level of isotropic flux is high at about 0.5 times the flux along the axis of symmetry. This means that there was significant scatter of particles in all directions. Late in the event there is no evidence of reverse propagation but otherwise there is little change from the second peak distribution.

22 October 1989 - An Unusual GLE

The GLE on 22 October 1989 was the second of three events occurring within a period of 6 days and all arising from the same active region on the Sun. The enhancement was characterized by an extremely anisotropic onset spike observed at only six neutron monitors of the world-wide network. Following the spike, a more typical GLE profile was observed worldwide. In many respects this GLE was reminiscent of the 15 November 1960 event (Shea et al. 1995) although the spike during the earlier event was not as well separated from the global GLE. The peak intensity of the spike observed at McMurdo was almost five times larger than the peak of the global GLE. The global response peaked at different times for different monitors. Cramp et al. (1997a) reported on an extensive analysis of this GLE. In Figure 28 observation of the anisotropic spike are shown. In the lower two traces the spike is not readily apparent due to the scaling necessary to show the complete spike however it was statistically significant. In this figure the error on the increases is of the order of a few percent.

Figure 28: Neutron monitor observations between 1600 and 2300 UT on 22 October 1989 of the extremely anisotropic onset spike and main increase of the GLE. (From Cramp 2000a).
\begin{figure} \begin{center} \epsfig{file=mld-fig28.eps,height=9cm} \end{center} \end{figure}

The global response to the GLE following the spike was more typical although there were clear indications of additional anisotropy with small irregularities in the recovery profiles seen by some monitors including McMurdo, Thule, Kerguelen and Goose Bay. Figure 29 shows the count rate profiles for several monitors. Data from 25 monitors in the world-wide network were used for the analysis of this event.

Figure 29: Neutron monitor observations between 1600 and 2300 UT on 22 October 1989 of the global increase of the GLE. (From Cramp 2000a).
\begin{figure} \begin{center} \epsfig{file=mld-fig29.eps,height=9.5cm} \end{center} \end{figure}

Modelling of the event was undertaken in the same manner as described above. A flare attenuation length of 100 gm cm-2 was employed to correct the responses to sea-level. The spectrum deduced during all phases of this GLE was unremarkable with only very slight steepening beyond a pure power law. The spectral results have been reported in Cramp et al. (1997a) and are not reproduced here.

Figure 30: Neutron monitor observations between 1600 and 2300 UT on 22 October 1989 of the global increase of the GLE. (From Cramp 2000a).
\begin{figure} \begin{center} \epsfig{file=mld-fig30.eps,height=10cm} \end{center} \end{figure}

By contrast the pitch angle distributions are extremely unusual and change significantly throughout the event. In Figure 30 we can see the extreme anisotropy of the initial spike with the half forward flux level confined to within $\sim $20o of the axis of symmetry. The global GLE increase was observable $\sim $15 minutes after the spike and the derived pitch angle distribution at 1820 UT shows a much smaller flux but still with a highly anisotropic arrival. There is some evidence for general scattering with particles arriving at all pitch angles. By 1830 UT the flux had increased and there was clear evidence of reverse propagation of particles arriving from the anti-sunward direction. This reverse propagation was well above the general local scattering which is represented by the minimum in the pitch angle distribution curves. The level of anisotropy in the reverse propagating particle distribution is also quite pronounced but is broader than the forward propagating distribution. The reverse propagating distribution is also about twice as broad as the inital spike. By 1900 UT the reverse propagation has almost disappeared and the level of local scattering has increased substantially. Unusually for a GLE there is still a fairly strong forward anisotropy suggesting that the source of particles is still active even after an hour or more. The extreme anisotropy of the initial spike implies very little scattering between the source of the particle acceleration and the Earth. Using the method of Bieber et al. (1986) it was possible to calculate the mean free path associated with the various phases of the GLE. This method assumes that steady state conditions and that the spiral angle of the field at Earth is known. It is reasonable to assume that the axis of symmetry gives an estimate of the IMF direction. Cramp et al. (1997a) conducted such an analysis assuming a nominal IMF direction as well as using the arrival direction as an indication of the IMF orientation. They found very large mean free paths early in the event when the steady state assumption is clearly invalid. The value during the spike was 7.9 AU decreasing to 4.0 AU early in the global increase and quickly reducing further to a relatively steady value of around 2 AU (1 AU using the arrival direction) for the rest of the analysed period. It was not clear whether the large values early in the event were real or an artifact of the dynamic rather than steady state conditions. A perturbed plasma region of high field strength was observed by IMP-8 and Galileo spacecraft to have passed the Earth between 1000 UT on 20 October and 1300 UT on 21 October (Cramp et al. 1997a). This plasma would have moved to a region 1.8-3.0 AU from the Sun at the time of the GLE. If we consider the reverse propagating particles to have arisen as a result of the spike particles being scattered back along the field beyond the Earth then the timing between the spike and the first sign of reverse propagating particles would put such a region 1.7 to 2.0 AU from the Sun. This is consistent with the expected position of the plasma region. The broader pitch angle distribution of the returning particles is also consistent with scattering at such a distance. The spectrum is consistent with Ellison & Ramaty (1985) shock acceleration but the time profile suggests an impulsive acceleration for the initial spike. Thus it would appear that this GLE was characterised by an impulsive injection of particles followed by continuous shock acceleration over an extended period of time. This is also the conclusion of several other authors (Reames et al. 1990; Van Hollebeke et al. 1990; Torsti et al. 1995).

7-8 December 1982 - Effect of a Distorted IMF

Onset of a GLE was observed at approximately 2350 UT on 7 December 1982 with peak responses at neutron monitors around the globe varying between 0000 UT and 0030 UT on 8 December. Figure 31 shows the response profiles from a number of monitors. Some recorded a rapid increase to maximum followed by a quite rapid decline. Other stations recorded long declines after a sharp rise and others still recorded slow rises and long decays.

Figure 31: Neutron monitor observations between 2300 UT, 7 December and 0300 UT, 8 December 1982. (From Cramp et al. 1997b).
\begin{figure} \begin{center} \epsfig{file=mld-fig31.eps,height=7cm} \end{center} \end{figure}

Figure 32: IMF magnitude (top panel), latitude (second panel), longitude (third panel) in GSE coordinates and plasma density (bottom panel)for 7 and 8 December from IMP-8. (From Cramp et al. 1997b).
\begin{figure} \begin{center} \epsfig{file=mld-fig32.eps,height=10.5cm} \end{center} \end{figure}

During 7 December a moderate geomagnetic storm of Kp=6+ occurred but the disturbance level had reduced to Kp=4 at the time of the GLE. IMF data measured by IMP-8 were available for this event. The IMF direction was measured at 110o west of the Sun-Earth line. This requires the field to be strongly looped back toward the Sun ($\sim65^{o}$ from the nominal field orientation) or that the field was grossly distorted, locally approaching the Earth from $\sim70^{o}$ east of the Sun-Earth line. Field and plasma data for the two days of interest are reproduced in Figure 32. The figure shows the hourly average field magnitude, latitude and longitude (in GSE coordinates) and the 5-minute average plasma density. No plasma temperature data were available. Examination of the IMF direction shows that there was a smooth rotation of the field between $\sim $0500 UT and 2300 UT on 7 December. At the same time the field magnitude was high at $\sim $20 nT and the plasma density was low. Burlaga (1991) has stated that high field strength accompanied by a rotation in the field direction and low plasma temperatures indicates the presence of a magnetic cloud. Although we do not have plasma temperature data the low density present during this interval and the higher densities before and after would strongly suggest a discontinuous plasma regime. It is highly likely that this structure represents a magnetic cloud passing the Earth. This interpretation is also consistent with the geomagnetic disturbance and with evidence of bidirectional flows in satellite measurements. The passage of the cloud would have influenced the IMF structure at Earth for some time after its passage and thus would also affect GLE particle propagation to the Earth.

Figure 33: Viewing directions for Apatity (A), Deep River (DR), Durham (D), Kerguelen Island (K), Leeds (L), Moscow (M), Oulu (O) and South Pole (S) for 0000 UT on 8 December 1982, rigidities from 20 GV to the station cutoff. Viewing directions at 20, 10 and 5 GV are indicated. Stations whose response was over-estimated by the standard model are shown with solid lines, those which were under-estimated are shown with dotted lines and the normalisation station is shown with a dashed line. The measured IMF direction is marked with a solid circle and the fitted particle arrival direction with a diamond. The best fit deficit ellipse in the modified model is shown along with the apparent particle arrival direction derived from this model (square). (From Cramp et al. 1997b).
\begin{figure} \begin{center} \epsfig{file=mld-fig33.eps,height=5.5cm} \end{center} \end{figure}

Attempts by Cramp et al. (1997b) to fit the neutron monitor responses worldwide using the standard modelling technique proved difficult with no satisfactory fits obtained. The fit always produced too great a response in monitors viewing along the derived particle arrival direction and too small a response for monitors viewing a short distance from that direction. It was apparent that there was some form of suppression of the response and that this was most likely related to the magnetic cloud. The standard modelling technique was modified to include an elliptical region of suppressed response. The centre, eccentricity, orientation and length of the semi-major axis were all variables in the modified model. Excellent fits were achieved using the modified model and the arrival axis of symmetry, deficit ellipse, IMF direction and viewing directions of some monitors is summarised in Figure 33. The best fit suppression inside the ellipse was a multiplicative factor of 3.0 x 10-2. A deficit cone has been invoked by Nagashima et al. (1992) to explain time dependent decreases preceding Forbush decreases. The deficit ellipse is clearly a simplification from physical reality. More complex models would require a greater number of parameters which would be unjustifiable with the amount of data available. A sharp decrease in the response at the ellipse edge is unlikely but the model does assist in picturing possible IMF structures that may be responsible for the unusual global response observed. Figure 34 shows one such representation with the magnetic cloud having passed the Earth and the field distorted behind it in a way that is compatible with both the particle arrival (including the deficit region) and with the measured IMF direction.

Figure 34: Possible IMF configuration at the time of the 7-8 December 1982 GLE. The shaded region is the magnetic cloud and the hatched region represents the turbulent magnetic field region in the wake of the outward moving cloud. Possible IMF lines (dashed) that would produce the observed direction of $\sim $110o) west of the Sun-Earth line are shown. (From Cramp et al. 1997b).
\begin{figure} \begin{center} \epsfig{file=mld-fig34.eps,height=6.5cm} \end{center} \end{figure}

In the modelling, the deficit region was not required at 0015 UT and later times. The cloud would have moved only a further 0.002 AU away from the Earth in that time which is comparable to the gyroradii of 1-3 GV particles in field strengths of $\sim $7-8 nT that were present. Higher rigidity particles should still have been affected though to a lesser extent. The derived spectrum did steepen at 0015 UT which may have been a compensation by the least square process for a deficit region affecting only higher rigidities. Furthermore, significant scattering in the turbulent field near Earth is likely and thus the deficit region would rapidly fill with solar particles. The pitch angle distributions derived by Cramp et al. (1997b) showed very little isotropic flux at 0000 UT but an isotropic response of more than 30% of the anisotropic component by 0015 UT rising to nearly 80% by 0050 UT. This supports the argument for increased scattering behind the cloud. The fact that there is still evidence of an anisotropic component an hour after the onset would also imply continuous shock acceleration.
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