Presentación y fundamentación de la propuesta.

The Cluster mission was launched in the year 2000 to study the magnetosphere and interplanetary plasmas in three dimensions. The mission consists of four satellites flying in a tetrahedral formation. Cluster was set up in a polar orbit with apogee and perigee at 19.6RE and 4.0RE respectively. The separation of the individual Cluster

spacecraft has changed throughout the mission and was approximately _≈1000 km for the periods studied in this thesis.

Its elliptical orbit takes it through the magnetosphere and out into the fore- shock region (as discussed in 2.3.2) and eventually the solar wind, see figure 3.2. During certain intervals of time the satellite group can be used to study the solar wind and the terrestrial foreshock in situ. Cluster continuously takes measurements of electromagnetic fields, plasma velocity and charge carrier densities at a sampling frequency of_≈0.25 Hz. The FGM measurement system (see section 3.2.2) has an enhanced resolution capacity for magnetic field readings, sampling at a frequency of _≈22 Hz. It is for this reason that studies on the solar wind will be carried out predominately using magnetic field data when available.

Figure 3.1: Artist’s impression of the four satellites of Cluster in orbit, (Image from [ESA,2014b]).

distributions. Data on particle distribution functions is obtained with the Cluster Ion Spectrometer (CIS). The instrument produces spectra which are averaged over the 4-second window, as a result the resolution of plasma parameters is much lower than magnetic field. This thesis utilises data from both FGM and CIS instruments, see sections 3.2.2 and 3.2.3. To account for the difference in sampling rates the magnetic field data can be re-sampled at the lower rate of 0.25 Hz when being compared with plasma parameters. A full list of the instruments on the Cluster spacecraft is shown in table3.1.

3.2.1 Geocentric Solar Elliptical Co-ordinate System

All three dimensional Cluster data is presented in a Cartesian format with (x, y, z) components. The Cluster group uses the geocentric solar elliptical co-ordinate sys- tem (GSE). With the origin at the centre of the Earth it aligns the x-axis with the central line between the Earth and Sun centres. The z-axis is aligned with the ecliptic north pole which is defined as the normal to the plane of the Earth’s orbit. The y-axis is simply oriented such that the system forms a orthonormal axis set that points in the direction motion through the orbit, this is shown schematically in figure3.3. It is useful for magnetospheric and bow shock studies as all motion is relative to the Earth not to the Sun.

Figure 3.2: Cluster Orbit plot for the 27/01/2004, the left, displays the tetrahedral formation, the right, demonstrates Cluster’s elliptical orbit. The orbit plots also presents lines to show the average positions of the bow shock and magnetopause, from [ESA,2014a].

3.2.2 Flux Gate Magnetometer (FGM)

Each Cluster spacecraft carries an identical FGM instrument, [Balogh et al.,2001]. The instrument consists of two tri-axial fluxgate magnetic field sensors located on one of the two radial booms of the spacecraft. The primary sensor samples the magnetic field vector at 201.793 vectors s−1 however this cannot be streamed to the ground due to the small bandwidth. This rate is therefore re-sampled at a lower rate for streaming. The sample rate used in this thesis is at a rate of 22.417 vectors s−1. The magnetic field vectors are converted from Cluster’s spinning reference frame to the de-spun frame in GSE coordinates and into the scientific units nT.

3.2.3 Cluster Ion Spectrometer (CIS)

CIS is capable of measuring three dimensional ion distributions at a resolution which coincides with the spacecraft rotation time (spin resolution), [R`eme et al.,2001]. It is made up of two detectors, the Hot Ion Analyser (HIA) and the Composition and Distribution Function Analyser (CODIF). The data used in this thesis comes from HIA thus the CODIF instrument will not be discussed further.

Instrument Purpose

ASPOC Spacecraft potential control CIS Ion velocity distributions EDI Electric field drift velocity

FGM Magnetometer

PEACE Electron velocity distributions

RAPID High energy electron and ion velocity distributions

DWP Wave processor

EFW Electric field and waves

STAFF Magnetic and electric fluctuations WBD Electric field and wave forms WHISPER Electron density and waves

Table 3.1: The complete instrument list for each Cluster spacecraft, [Escoubet and Goldstein,2001]

CIS Mode Mode Name

0 SW-1 Solar Wind / SW tracking - Mode 1

1 SW-2 Solar Wind / 3D upstreaming ions - Mode 2 2 SW-3 Solar Wind / SW tracking - Mode 3

3 SW-4 Solar Wind / 3D upstreaming ions - Mode 4

4 SW-C1 Solar Wind / SW tracking - Data Compression - Mode 1 5 SW-C2 Solar Wind / 3D upstreaming ions - Data Compression-Mode 2

6 RPA RPA Mode

7 PROM PROM Operation 8 MAG-1 Magnetosphere - Mode 1 9 MAG-2 Magnetosphere - Mode 2 10 MAG-3 Magnetosphere - Mode 3

11 MAG-4 Magnetosphere / Magnetosheath - Mode 1 12 MAG-5 Magnetosheath - Mode 2

13 MAG-C1 Magnetosphere - Data Compression - Mode 1 14 MAG-C2 Magnetosheath - Data Compression - Mode 2 15 CAL Calibration / Test Mode

Figure 3.3: Schematic diagram of the geocentric solar elliptical coordinate system used by the Cluster satellite group.

The CIS instruments posses a large degree of flexibility in the selection of operational mode. CIS can maintain one of sixteen operational modes listed in table

3.2. Our data was sampled while CIS was in mode 5 exclusively to insure that the solar wind and the upstream ions were the sole contribution to the HIA moments. In this mode the solar wind beam is tracked by HIA only once every 16 spins. In the remaining 15/16 spins a broader energy sweep is used for the solar wind detection by the ‘’ section (discussed below). At the same time upstreaming ions are observed by the ‘high G’ section, which is then looking in the anti-sunward direction.

Hot Ion Analyser (HIA)

The Hot Ion Analyser (HIA) instrument combines the selection of incoming ions according to the ion energy per charge by electrostatic deflection in a symmetrical, quadrispherical analyser which has a uniform angle-energy response with a fast imaging particle detection system. HIA has two 180◦ _{sections which look in a plane}

parallel to the spin axis as shown in figure 3.6. They are known as high and low sensitivity, high G and low G, respectively. They provide different resolution in the polar angle yet have the same azimuthal resolution of 5.625◦_{. The azimuthal}

resolution arises because of the two dimensional resolution is recorded every 62.5 ms as the spacecraft spins. In this way a full three dimensional distribution can be measured every spin. The high G section’s polar range is divided into 16 equal sections, whereas the low g is divided into 8. High G is specified for hot plasmas and is dedicated to studying the magnetosphere while low g is meant for the solar wind. The plasma data from HIA presented in this work is made up solely from data taken in the low g mode.

Figure 3.4: Schematic diagram of Hot Ion Analyser (HIA) high and low sensitivity sections. (Image from [R`eme et al.,2001]).