PhD thesis - Institute for Space Research - University of Calgary

22 2: Background
the top-hat are invariant under a change of scale as long as R/∆R is
fixed.
The top-hat analyzer scans particle energy by ramping the potential
across the hemispheres. The analyzed energy range typically runs from
tens of eV to several tens of keV. From Equation 2.27 it is clear that
top hats are suited to analyzing high energies per unit charge, since the
analyzer constant R/∆R > 1 translates electrode biases of hundreds
of volts to particle energies of many keV. On the other hand, sub-eV
analysis is very sensitive to errors from variations in ∆V . Nevertheless,
sub-eV ionospheric electrons have been analyzed with a top-hat by Pollock
et al. [1996]. The main drawback of the top hat is the relatively
low phase-space sampling rate due to the need to scan particle energies.
Spectrographic analyzers overcome this problem by dispersing the
particle trajectories, according to kinetic energy, onto an imaging detector.
The analyzers of Sablik et al. [1985] and Curtis and Hsieh [1988]
are early examples where a range of energies were imaged at once onto
a detector. As described in Chapter 3 of this thesis, Whalen et al.
[1994] introduced an energy-imaging variation on the top-hat whereby
particles pass through the hemispherical electrodes instead of between
them. Knudsen et al. [2003] coined the focusing system used by this
type of analyzer the “Whalen analyzer” after its inventor. The cold
plasma analyzer (CPA) was flown on the Freja satellite, although the
two-dimensional imaging capability of the analyzer was of limited scientific
value due to imperfections in the particle detection scheme [Knudsen
et al., 1998a]. In a review of space-based instruments, Young [1998]
states that the advantage of imaging analyzers over curved-plate analyzers
is the larger phase-space sampling rate, while the disadvantage is
that they are “more difficult to design and build because fringing fields
and internal scattering tend to reduce spectral resolution”.
The Suprathermal Ion Imager (SII) is a scaled-down version of the
CPA which creates an image of an ion differential directional energy
flux on a charge-coupled device (CCD). The images represent a twodimensional
slice through an ion distribution function. In principle the
ion density, bulk drift, and temperature moments can be calculated
from these images. The SII sampled a complete 2-D energy/arrivalangle
distribution at a rate of 93 images per second. This sample rate
corresponds to a spatial resolution of about 13 m perpendicular to the
geomagnetic field for the GEODESIC dataset.
2.8 Space and time ambiguities
In ascertaining the spatial scales of auroral phenomena one faces the
problem of the ambiguity inherent in single-point measurements that