The Dynamic Spectrum of Interplanetary Scintillation: First Solar Wind Observations on LOFAR

Abstract

The LOw Frequency ARray (LOFAR) is a next-generation radio telescope which
uses thousands of stationary dipoles to observe celestial phenomena. These
dipoles are grouped in various 'stations' which are centred on the Netherlands
with additional 'stations' across Europe. The telescope is designed to operate
at frequencies from 10 to 240\,MHz with very large fractional bandwidths
(25-100%). Several 'beam-formed' observing modes are now operational and the
system is designed to output data with high time and frequency resolution,
which are highly configurable. This makes LOFAR eminently suited for dynamic
spectrum measurements with applications in solar and planetary physics. In this
paper we describe progress in developing automated data analysis routines to
compute dynamic spectra from LOFAR time-frequency data, including correction
for the antenna response across the radio frequency pass-band and mitigation of
terrestrial radio-frequency interference (RFI). We apply these data routines to
observations of interplanetary scintillation (IPS), commonly used to infer
solar wind velocity and density information, and present initial science
results.

Full text

arXiv:1206.0602v1 [astro-ph.SR] 4 Jun 2012
Solar Physics
DOI: 10.1007/•••••-•••-•••-••••-•
The Dynamic Spectrum of Interplanetary
Scintillation: First Solar Wind Observations on
LOFAR
R.A. Fallows1,2§·A. Asgekar1
·M.M. Bisi2
·
A.R. Breen2¶·S. ter-Veen3
·on behalf of
the LOFAR Collaborationk
c
Springer ••••
Abstract The LOw Frequency ARray (LOFAR) is a next-generation radio tele-
scope which uses thousands of stationary dipoles to observe celestial phenomena.
These dipoles are grouped in various ‘stations’ which are centred on the Nether-
lands with additional ‘stations’ across Europe. The telescope is designed to
operate at frequencies from 10 to 240 MHz with very large fractional bandwidths
(25-100%). Several ‘beam-formed’ observing modes are now operational and the
system is designed to output data with high time and frequency resolution,
which are highly configurable. This makes LOFAR eminently suited for dynamic
spectrum measurements with applications in solar and planetary physics. In
this paper we describe progress in developing automated data analysis rou-
tines to compute dynamic spectra from LOFAR time-frequency data, including
correction for the antenna response across the radio frequency pass-band and
mitigation of terrestrial radio-frequency interference (RFI). We apply these data
routines to observations of interplanetary scintillation (IPS), commonly used
to infer solar wind velocity and density information, and present initial science
results.
Keywords: Radio Scintillation; Solar Wind
§Moved to institute (1) from 1 February 2012
¶Deceased
kFull author list at http://www.astron.nl/authors-list-lofar-commissioning-papers
1ASTRON - the Netherlands Institute for Radio
Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands
e-mail: fallows@astron.nl
e-mail: asgekar@astron.nl
2Institute of Maths and Physics, Aberystwyth University,
Aberystwyth, SY23 3BZ, Wales
e-mail: Mario.Bisi@aber.ac.uk
3Department of Astrophysics/IMAPP, Radboud University
Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The
Netherlands
e-mail: S.TerVeen@astro.ru.nl
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1. Introduction
The observation of interplanetary scintillation (IPS) – the scintillation of com-
pact radio sources due to density variations in the solar wind (Hewish, Scott, and Wills,
1964) – is an important tool for observing the solar wind. Observations of IPS
allow the solar wind speed to be inferred over all heliographic latitudes and a wide
range of elongations from the Sun (e.g. Dennison and Hewish, 1967), giving a
global perspective to point measurements from spacecraft. The sensitivity of IPS
to small, turbulent-scale, density variations also complements the larger-scale
sensitivities of white-light observations from coronagraphs.
Advances in the study of IPS over the last decade or more allow such ob-
servations to be used to calculate three-dimensional (3D) sky maps of solar
wind electron density and speed (e.g. Asai et al., 1998; Jackson et al., 1998;
Kojima et al., 1998). These maps and other detailed analyses of observations
of IPS (e.g. Fallows, Breen, and Dorrian, 2008; Breen et al., 2008; Bisi et al.,
2007) are increasingly recognised as a valuable aid for tracking space weather
events through the inner heliosphere (e.g. Jackson et al., 2010) and to the overall
study of space weather prediction.
The LOw-Frequency ARray (LOFAR – summarised fully in Section 3) is a
major new-generation radio telescope operating in the 10–240 MHz frequency
range. It consists of arrays of dipoles grouped into stations with a central ‘core’
of stations in the Netherlands and, currently, eight international stations based
in the UK, France, Germany and Sweden. Although designed principally to be
used as a single array, it is also possible to use the stations individually making
it suitable for studies of IPS. A particular advantage offered by LOFAR is the
ability to observe with bandwidths of up to 48 MHz with a high frequency resolu-
tion. This capability is both necessary to identify and eliminate radio frequency
interference (RFI) and useful to create dynamic spectra of IPS data, a tool that
could provide new insights into solar wind microstructure and has not been
available to most prior IPS observing instruments.
This paper describes the principle science of IPS, details how LOFAR may
be used as an instrument to observe it, the principle advantages LOFAR can
offer as such an instrument and the progress made in obtaining observations of
IPS. We discuss in particular on-going efforts to develop an automated Python-
based software ‘pipeline’ to produce relevant products from raw LOFAR data.
Over time these tools will be developed to enable the study of other similar
phenomena, such as flare stars, planetary atmospheres and solar radio bursts.
The paper is laid out as follows: The study of IPS is summarised in Section 2;
Section 3 describes the LOFAR radio telescope and details how it may be used
for IPS; the current state of a dynamic spectrum data pipeline developed for
LOFAR observations is detailed in Section 4 and then some initial IPS results
are presented in Section 5.
2. Interplanetary Scintillation (IPS)
When two radio telescopes are used and their pro jected baseline on the u−
vplane is close to the radial direction centred at the Sun, a high degree of
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Figure 1. Illustration of the geometry of the lines of sight from two telescopes with respect to
the Sun and the patterns of interplanetary scintillation detected in each one. Main illustration
is from above the ecliptic plane; inset is in the uv plane (the projection of the plane on which
the antennas lie to be perpendicular to the radio source direction) as viewed from the radio
source.
correlation may be observed between the scintillation patterns recorded at the
two telescopes (e.g. Armstrong and Coles, 1972; Coles, 1996). The time lag for
maximum cross-correlation of the two simultaneously-taken radio signals can
be used to estimate the outflow speed of the density variations producing the
scintillation and, thus, a mean outflow speed for the solar wind across the line of
sight. Figure 1 illustrates the geometry and the scintillation patterns recorded
by two telescopes.
The lines of sight from the radio telescopes to the radio source may pass
through two or three solar wind streams each travelling at a different speed
and having differing densities. This may be observed directly if the baseline
between the telescopes is increased to several hundred kilometres. The cross-
correlation function may then display two or three distinct peaks, each at a
time lag corresponding to individual solar wind streams. The effect of increasing
baseline length is shown in Figure 2. Here, four cross-correlation functions cor-
responding to baseline lengths of 0 −240 km are shown, for a model observation
which assumes the presence of both fast and slow solar wind streams in the
lines of sight. The cross-correlation function at 0 km baseline is effectively an
auto-correlation function of the two input signals. As the baseline is increased,
the cross-correlation function decreases in height and becomes first skewed be-
fore separating into two distinct peaks corresponding to the two solar wind
streams. As the baseline is increased to very large distances, evolution of the
solar wind density structures will de-correlate the signals significantly. However,
cross-correlation is still e vident on bas elines of at least 2000 km (e.g. Bre en et al.,
2006).
More sophisticated analysis methods can be used to account for the line of
sight integration and provide more accurate estimates of solar wind speeds in
the line of sight. One method fits the results of a scattering model, which can
assume up to three solar wind streams in the line of sight, to the observed auto-
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Figure 2. Illustration of the effect on the cross-correlation function of increasing the baseline
from 0 km to 240 km between two radio telescopes when the lines of sight pass through both
fast and slow solar wind streams.
and cross- power spectra (Fallows, Breen, and Dorrian, 2008; Bisi et al., 2007;
Fallows et al., 2006; Coles, 1996); a second method uses a tomographic inversion
of many observations taken over the course of a whole solar rotation to provide
three-dimensional (3D) maps of solar wind speed and density via the use of a
measure of the level of scintillation; (e.g. Asai et al., 1998; Jackson et al., 1998;
Kojima et al., 1998).
3. The Low Frequency Array (LOFAR)
LOFAR is designed and constructed by ASTRON, the Netherlands Institute
for Radio Astronomy. It has facilities in several countries which are collectively
operated by the International LOFAR Telescope consortium. LOFAR operates
in the frequency range 10 −240 MHz, offering a large collecting area (∼105
m2), and is comprised of thousands of dipole antennas hierarchically arranged
in stations which come in three different configurations (Table 1). There are a
total of 33 stations in the Netherlands. These include a dense core of six stations,
called the ‘Superterp’, near Exloo, and 18 ‘core’ stations in the neighbourhood
(baselines of ∼2 km. There are currently nine ‘remote’ stations within the
Netherlands, offering baselines over ∼70 km, and eight international stations
up to ∼800 km, with the prospect of more to come. As will be discussed in
more detail later, observations of IPS can utilise all of these stations to achieve a
variety of diverse goals. Details of system architecture and signal processing can
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Table 1. (After Stappers et al. (2011)). Arrangement of elements
in the three types of LOFAR stations, along with their typical
distance from the centre of the array (baseline). In the Core and
Remote stations there are 96 LBA dipoles but only 48 can be
beam-formed at any one time. For these stations, one can select
either the inner circle or the outer ring of 48 LBA dipoles depend-
ing on the science requirements. The HBA sub-stations can be
correlated, or used in beam-forming, independently.
Station Type LBA (no.) HBA tiles (no.) Baseline (km)
Core 2×48 2×24 ≤2
Remote 2×48 48 ≥70
International 96 96 ≥300
be found in de Vos, Gunst, and Nijboer (2009) and a full description of LOFAR
is in preparation by van Haarlem et al..
LOFAR has two different types of antennas to cover the full frequency range.
The low band antennas (LBAs) cover the frequency range 10−90 MHz, although
they are optimised for frequencies above 30 MHz. There are 48/96 active LBA
dipoles in each Dutch/international station (Table 1). The high band antennas
(HBAs) cover the frequency range 110−240 MHz, and co nsist of 16 folded dipoles
grouped into tiles of 4 ×4 cross-dipoles each, which are phased together using
an analogue beam-former within the tile itself. It is possible to observe a radio
source with a maximum bandwidth of ∼48 MHz.
With large fractional (∼100%) bandwidths, sophisticated multi-beaming
capabilities (∼100 concurrent beams on the sky), and a large field of view,
LOFAR is a powerful instrument for surveys and routine monitoring of variable
sources. For more details the reader is referred to Stappers et al. (2011), where
the capabilities of LOFAR for high-time-resolution beam-formed observations
are discussed in detail.
For the study of IPS, LOFAR offers distinct advantages over other telescope
systems:
•Multiple international stations spread around the central core offer a greater
number of useful cross-correlation observing opportunities at baseline lengths
which enable the full set of determinations (speeds of multiple solar wind
streams for example) to be extracted.
•The large bandwidth and excellent frequency resolution enable dynamic
spectra to be calculated, which will undoubtedly provide a mine of addi-
tional information on solar wind micro-structure.
•With its enormous flexibility to observe many sources simultaneously, LO-
FAR offers a possibility of making detailed tomographic maps of solar wind
speed and density.
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3.1. LOFAR configuration and various beam-formed modes of operation
LOFAR offers a number of ‘beam-formed’ modes, in which one can form single
or multiple beam pointings in the direction of radio sources of interest using
one or more stations. Given the total bandwidth available for data transport,
the total amount of observing bandwidth over all the beams from the stations
is limited to 48 MHz. The various beam-formed modes probe timescales from
seconds down to microseconds. Given that most LOFAR signal processing is
carried out in software, there are many ways in which the various parts of LOFAR
(antennas, tiles, stations) can be combined to form beams. The reader is referred
to Stappers et al. (2011) for a discussion on the different options for combining
beam-formed data.
The term station beam corresponds to the beam-formed by the sum of
all of the elements of a station. For any given observation there may be more
than one station beam and they can be pointed at any location within the
wider element beam. A tied-array beam is formed by coherently combining
individual station beams (one for each station), which are looking in a particular
direction within each station beam. There may be more than one tied-array beam
for each station beam. Station beams can also be combined incoherently in order
to form incoherent array beams.
The modes of relevance to IPS are:
•“Fly’s Eye” (FE) mode, which allows individual station level beam-formed
data (complex voltages or coherent Stokes parameters) to be recorded
separately rather than correlated before recording;
•“Tied Array” (TA) beam mode, which forms single beams from multiple
stations (typically the Superterp).
The FE mode is necessary in order to study the cross-correlation between
individual stations as a result of IPS; it would not be possible to analyse the
IPS time series’ to obtain solar wind parameters if all stations used in a partic-
ular observation are correlated in the system as in the case for standard radio
astronomy imaging. The TA mode has been used in commissioning observations
of IPS using the Superterp. This offers an increased sensitivity and provides
beam-width comparable to that from single large radio dishes, allowing a fair
comparison with data from telescopes elsewhere.
The raw measurement for studying IPS is signal intensity sampled at a high
rate (most systems use a sampling rate of at least 50Hz); a sampling rate of
96Hz is used in the LOFAR observations presented here, chosen for system
convenience. In most traditional radio telescope systems the signal intensity is
integrated over the bandwidth before being recorded. In the case of LOFAR, the
dynamic spectrum is a necessary intermediate step as well as being of scientific
interest in itself.
The reason for recording signal intensity over a number of discrete frequency
channels, rather than integrating over the whole bandwidth before data record-
ing, is so that data contaminated by radio frequency interference (RFI) can
be identified and eliminated from any integration. Most RFI is prevalent in
particular channels which would dominate the integration were they not removed
first.
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Figure 3. RFI excision steps. The frequency range 210–240 MHz is used in this example.
The plots are of the median of the time series of each frequency channel: (a) Constructed
bias for channels; (b) We compute the running median and local standard deviation, and use
thresholding to identify bad channels; (c) The bad channels are omitted and a smooth curve
is fitted, with linear interpolation, to obtain the spectral response of the system; (d) The
spectral response can now be subtracted from the input data. The thick arrow displays the
final threshold computed for the data.
4. The Dynamic Spectrum Pipeline and Radio Frequency
Interference (RFI) Mitigation
A dynamic spectrum software pipeline is currently under construction: It needs
to process the data in a number of steps to correct the spectra for the antenna
response across the pass-band, identify channels mostly contaminated by RFI
and more random bad data points, and remove these from the resulting dynamic
spectra. These ‘corrected’ data are then integrated across the pass-band to create
the IPS time series.
We look at the LOFAR data output as a time-frequency matrix consisting
of M time steps and N channels. Such a matrix is read in blocks of a length
chosen by the user (20 s has been chosen in the results presented here, the data
arrays become unwieldy if a much higher length is chosen). The first block is
then processed to calculate the spectral reponse across the pass-band (illustrated
in Figure 3) and remove interference using the steps as follows:
1. We compute median spectrum from the time-frequency matrix.
2. For each channel we compute a ‘bias’ using the kurtosis of the time samples
in that channel, the standard deviation and the difference of the median
from medians of nearby channels. We apply a moderate clipping on this bias
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to provide us with the first guess of channels heavily contaminated by RFI
(Figure 3a).
3. A 1-d array of the medians of the time series’ for each channel is computed
and further RFI-dominated channels identified using a 1-d walk through this
array. Typically a small 32-channel window is used for this step to identify
interfering sources which affect only a couple of neighbouring channels at
most. Any channel with an anomalously large deviation from the median of
the window is flagged.
4. The previous step is repeated with a large frequency window (∼256 channels),
to identify wide-band interfering sources. At this point most, if not all, of the
remaining RFI-affected channels are identified (Figure 3b).
5. The RFI-laden channels are then omitted from processing. The remaining
channels are fitted with a smooth function in the frequency dimension after
simple linear interpolation, which can then be used to remove the spectral
response from the input time-frequency array (Figure 3c).
6. A simple threshold of significance (usually 5σ) above the (local or global)
median value of the flattened time-frequency array is then applied to identify
remaining RFI (Figure 3d).
7. The time series for IPS is calculated from the time-frequency matrix after
zeroing the identified RFI-contaminated channels and other RFI points.
In subsequent blocks the data are flattened using the same spectral response
curve calculated for the first block and then processed according to the final two
steps given above.
An option to calculate a ‘clean’ 2D data matrix without ‘zeros’ is also pro-
vided. To achieve this every ‘bad pixel’ in the matrix is replaced by a random
‘good’ pixel from the surrounding (8×32) pixel region. Whilst the good pixels are
not modified by this method, it undoubtedly introduces more noise to the array
and would not be safe to use when calculating the IPS time series. However,
it does provide a useful way by which general trends across the array can be
observed in a more convenient fashion. It will also allow 2D analysis of the
complete observed time-frequency data without any obvious artefacts produced
by the zero-mask. Since LOFAR offers a large fractional bandwidth, the 2D
dynamic spectra contain more information than mere time series. The random
substitution mode therefore may be relevant for the analysis of 2D spectra.
Figure 4 displays the output data processing for an observation of 3C48 taken
in April 2011. The pixels wihin the RFI-affected regions are either blanked out
or substituted with a random good neighbouring pixel.
5. Results
Whilst the dynamic spectrum pipeline is still under development, initial analyses
of LOFAR commissioning observations of IPS are encouraging. Two examples
of 30 seconds worth of data are given in Figure 5.
Clear differences can be seen in the dynamic spectra from these two ob-
servations: In the observation of 3C48, clear bands of maxima and minima
corresponding to the IPS signal are seen right across the pass-band, though
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Figure 4. The dynamic spectrum of the first 30s of data from an observation of 3C48 taken
on 9th April 2011. Left: The identified RFI points are left blank. Right: The RFI pixels are
replaced by random substitution from the neighbourhood.
Figure 5. Left: The dynamic spectrum of the first 30 s of data from an observation of 3C48
taken on 9th April 2011. Right: The same for an observation of 3C84 taken on 7th May 2011.
Identified RFI is blanked out.
it can also be noticed that the levels of the maxima appear to diminish at higher
frequencies. The IPS signal is not so readily apparent in the dynamic spectrum
of the 3C84 observation; the scintillation only becomes apparent in the 1D time
series and further observations since suggest that this is more the norm.
In both example observations, power spectra from the resulting time series
have been produced and are shown in Figure 6. A simultaneous observation of
3C84 was also taken using the EISCAT (European Incoherent SCATter)Svalbard
Radar (ESR) in the high Arctic at a higher observing frequency o f 500 MHz
and this is also shown for comparison; in this case two LOFAR spectra are
shown, each corresponding to 5.4 MHz of bandwidth from the upper and lower
frequencies of the observation to match the bandwidth of the ESR observation.
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Figure 6. Left: The power spectrum of the time series integrated over the band-pass for the
LOFAR observation of 3C48 taken on 9 April 2011. Right: The power spectra of time series’
calculated for the highest and lowest 5 MHz of the total LOFAR frequency band for the LOFAR
observation of 3C84 taken on 7 May 2011, alongside the power spectrum for a simultaneous
observation taken on the ESR. The low-frequency parts of these spectra (usually ignored in
analysis) have been removed for ease of viewing.
It is expected (P.K. Manoharan, private communication, 2011) that the Fres-
nel knee for a lower-frequency observation will be at a slightly lower spectral
frequency, but the power laws of each spectrum are expected to be similar.
Neither of these expectations appears to be met for the 3C84 observations (Fig-
ure 6), although the power laws are arguably similar for the higher-frequency
LOFAR and ESR power spectra. The unexpected excess of power at higher
frequencies apparent in the 3C48 observation is only apparent in the higher-
frequency LOFAR power spectrum of 3C84. Unfortunately, further comparisons
on different observations have not proved possible to date.
Figure 7 shows the dynamic spectrum for three LOFAR stations of the first
20 seconds of data of an observation of 3C279 taken on 1st October 2011. This
observation was taken using the lower end of the HBA frequency range, centred
on 15 0 MHz at a time when 3C279 was only 8◦away from the Sun. This is
well into the ‘strong’-scattering regime (a regime where it can no longer be
assumed that the scattered radio waves do not interfere amongst themselves)
for IPS at this observing frequency and the dynamic spectrum certainly appears
to show structure which are consistent with that. The larger structures at lower
observing frequencies may be indicative of refractive (as opposed to diffractive)
scintillation from large-scale density variations in the solar wind. However, the
dynamic spectra from the three stations all show exactly the same structures at
exactly the same times.
Further observations taken that day and in July also showed a high degree of
correlation with zero time delay in the data between different LOFAR stations.
The cause of this is still being investigated.
Observations taken with multiple stations on 14 and 17 November 2011 show
cross-correlation functions with time delays corresponding to those expected for
a slow solar wind stream. Two correlation functions are shown in Figure 8, from
observations of 3C298 on 14th November and of 3C279 on 17th November 2011.
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Figure 7. Dynamic spectra of the first 20 s of data taken on three LOFAR stations as part
of an observation of 3C279 on 1 October 2011.
Figure 8. Left: Auto- and cross-correlation functions for an observation of 3C298 taken on
14 November 2011. Right: Same for an observation of 3C279 taken on 17 November 2011.
The observation on 14 November indicates a slow solar wind stream travelling
at approximately 300 km s−1; the negative lobe near zero time lag in the cross-
correlation function of the 17th November observation may indicate the presence
of a Coronal Mass Ejection (CME) in the lines of sight.
6. Conclusions
The dynamic spectrum results obtained so far hint at a wealth of new information
on solar wind micro-structure and turbulence. Previous studies are few, but
Cole and Slee (1980) did observe a dynamic spectrum over the frequency range
280–520 MHz of IPS seen in an observation of 3C273. This study showed a curve
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in the scintillation maxima over the frequency band, later attributed to refraction
due to large-scale components of a Kolmogorov turbulence regime in the solar
wind (Coles and Filice, 1984). Such a curve is not seen in LOFAR observations
of IPS taken so far, most likely because the 40–48 MHz bandwidth used is not
large enough for it to be seen clearly.
The level of scintillation is known to vary with both distance from the Sun
and observing frequency (e.g. Coles, 1978); within the ‘weak’ scattering regime,
lower observing frequencies will exhibit stronger scintillation at the same solar
elongation. The observation of 3C48 shown in Figure 5 illustrates this nicely,
with the scintillation being stronger at the lower frequencies.
The power spectra shown in Figure 6 are consistent with typical IPS spectra,
but also show some inconsistencies. The excess power evident at higher spectral
frequencies in the observation of 3C48 and the inconsistency in the observation
of 3C84 when compared to a simultaneous observation from a known antenna
are particular points of concern. It is possible that at least some of these incon-
sistencies are due to the high LOFAR observing frequencies used: It is known
that a grating lobe of the main station beam (an artifact of the use of an array
of dipoles) can be present above the horizon for frequencies in the high-band
of LOFAR (Ger de Bruyn, private communication, 2011), potentially causing
issues with excess noise. This is not well-characterised yet making predictions
of whether it will or will not be above the horizon for a particular observation
difficult. It is clear from all the observations of IPS taken so far that the excess
power noted in the observation of 3C48 in Figure 6 is apparent in many observa-
tions using the HBA, but not in all. Restricting the sub-bands used in creating
the time series to those at the lower or higher ends of the observing band may
occasionally make a difference but, again, not in every case.
The correlation functions shown in Figure 8 indicate the presence of slow solar
wind streams in the lines of sight. This is consistent with the low heliographic
latitudes of both these observations. The cross-correlation function of the 3C279
observation shows a ‘negative lobe’ at zero time-lag. This is often associated
with the presence of a Coronal Mass Ejection in the line of sight. A slow CME
was observed to launch from the Sun late on 14 November 2011 and was pre-
dicted to pass close to the Earth on 18-19 November 2011. An initial check of
coronagraph data indicate that this CME was launched in a direction that could
cross the line of sight of the IPS observation and the observation timing makes
it a promising candidate. However a full geometrical analysis will be required to
confirm whether or not this CME is seen in these IPS data.
In conclusion, these observations show a high degree of promise, but also
reveal that some issues remain. This is to be expected from an instrument which
is still undergoing commissioning.
Acknowledgements LOFAR, the Low Frequency Array designed and constructed by AS-
TRON, has facilities in several countries, that are owned by various parties (each with their
own funding sources), and that are collectively operated by the International LOFAR Telescope
(ILT) foundation under a joint scientific policy. The authors thank the director and staff of
EISCAT for the ESR data used in this study. EISCAT is funded by the research councils of
Norway, Sweden, Finland, Japan, China, the United Kingdom and Germany. Two of us (RAF
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and MMB) were funded by the UK Science and Technology Facilities Council during the course
of this work.
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