Fundamental Technologies Galileo Pages

Fundamental Technologies

Galileo Spacecraft Pages

Investigation of the Magnetosphere of Ganymede with Galileo's Energetic Particle Detector
Ph.D. dissertation by Shawn M. Stone, University of Kansas, 1999.

List of Figures (Part 1, Chapters 1-5)

Figure 1 A schematic diagram of the magnetosphere of the Earth
Figure 1.2 A: Equatorial plane projection of a typical planet/satellite system; B: The resulting particle rate profile sampled by a spacecraft as it moves through the ‘hole’
Figure 1.3 Equatorial projection of the Pioneer 10 encounter trajectory at Jupiter. Three Galilean moon orbits are shown: Io (J I), Europa (J II), and Ganymede (J III)
Figure 1.4 Magnetic meridian plane projection of the trajectory of Pioneer 10 in magnetic polar coordinates for the planetary dipole model system III
Figure 1.5 Absolute omnidirectional intensities for the Jupiter Pioneer 10 encounter for the electrons
Figure 1.6 A: Satellite cross-section in the radial direction; B: The normalized rate profile for a microsignature caused by the satellite
Figure 1.7 Equatorial plane projection for the Pioneer 11 encounter at Saturn
Figure 1.8 Normalized rate profile for the microsignature of Mimas
Figure 1.9 Equatorial plane projection of the trajectory of Voyager 1 through the magnetosphere of Saturn
Figure 1.10 Normalized electron rate profile for three energy passbands of the LECP instrument at Dione for Voyager 1
Figure 1.11 Meridian plane projection of the dipole and the Z3+ current sheet magnetic field models
Figure 1.12 Encounter geometry for the G1 and G2 encounters
Figure 1.13 Magnetic field components for the G1 orbit near Ganymede 1 June 17, 1996
Figure 1.14 Components and magnitude in nT of the observed and model magnetic field for the G1 encounter
Figure 1.15 Components and magnitude in nT of the observed and model magnetic field for the G2 encounter
Figure 1.16 Components and magnitude in nT of the observed and model magnetic field for the G7 encounter
Figure 1.17 Components and magnitude in nT of the observed and model magnetic field for the G8 encounter
Figure 1.18 Frequency-time spectrogram of the plasma and radio wave observations of the G1 encounter
Figure 1.19 Frequency-time spectrogram of the plasma and radio wave observations of the G2 encounter
Figure 1.20 ZX projection of the vacuum superposition model for G2
Figure 1.21 ZY projection of the vacuum superposition of a uniform external magnetic field from a model of Jupiter's magnetic field [Khurana, 1997] and the internal magnetic field model of a dipole with 750 nT equatorial surface strength tilted 10° inward from the -z towards Jupiter [Kivelson et al., 1996]
Figure 1.22 ZX projection of the vacuum superposition model for G7 [Kivelson et al., 1996]
Figure 1.23 ZX projection of the vacuum superposition model of a uniform external magnetic field from a model of Jupiter's magnetic field [Khurana, 1997] and the internal magnetic field model of a dipole with 750 nT equatorial surface strength tilted 10° inward from the -z towards Jupiter [Kivelson et al., 1996] for G7
Figure 1.24 The electron rate profiles of three energy passbands of the EPD detector for the G2 encounter
Figure 1.25 Ion rate profiles of three energy passbands of the EPD detector for the G2 encounter
Figure 1.26 The electron rate profiles of three energy passbands of the EPD detector for the G7 encounter
Figure 1.27 The ion rate profiles of three energy passbands of the EPD detector for the G7 encounter
Figure 1.28 Normalized rate plot of feature 19:00:09 for three ion channels
Figure 1.29 Normalized rate plot of feature 19:00:09 for three electron channels
Figure 1,30 The electron lifetimes based on feature 19:00:09
Figure 1.31 Normalized ion count rates of feature 07:11:13 for the G7 encounter
Figure 1.32 Normalized electron count rates of feature 07:11:13 for the G7 encounter
Figure 1.33 Normalized rate plot of feature 07:10:14 for the G7 encounter for three ion channels
Figure 1.34 Normalized rate plot of feature 07:10:14 for the G7 encounter for three electron channels
Figure 2.1 Schematic of the solution to Equation 2.4
Figure 2.2 Schematic of a particle gyrating about a magnetic field line
Figure 2.3 A: Graphical solution to equation 2.14 in a dipole field geometry; B: resulting motion is a bounce motion between S_a and S_b which are called mirror points
Figure 2.4 A: Curvature drift: The velocity an ion would drift (V_d) whose guiding center moves along a curved field line of radius of curvature R_c. B: Gradient drift: The non-uniformity of the magnetic field allows the particle to experience regions of strong and weak field. The gyroradius of the particle is smaller in strong fields than in weaker fields.
Figure 2.5 Particles trapped in the magnetosphere of the Earth perform three basic motions: gyration about the field line, bounce between mirror points, and azimuthally drift about the planet.
Figure 2.6 A: As a particle gyrates about the magnetic field, its path encloses a surface area pr². B: From the conservation of the first adiabatic invariant it is seen that the pitch angle of the particle increases as it moves from point 1 to 2 to 3 where a=p/2.
Figure 2.7 A: A planet with an atmosphere out to 100 km. A particle at the equator where B=B_o has a pitch angle a_o. B: The velocity space representation of a particle at point O.
Figure 2.8 Conservation of the third adiabatic invariant.
Figure 2.9 Loss of a trapped particle by a random walk in velocity space into the pitch angle loss cone
Figure 2.10 Numerical solution of Equation [2.36] done by Theodoridis and Paolini [1967].
Figure 2.11 A schematic diagram showing how electrons and ions respond to electric fields
Figure 2.12 Schematic diagram of the simple geometry assumed for a parallel electric field in this analysis [Stern, 1981].
Figure 2.13 A: Mirroring geometry for electrons in the presence of a parallel electric field E_||. B: Mirroring geometry for ions in the presence of a parallel electric field E_||.
Figure 3.1 A schematic representation of the Galileo spacecraft
Figure 3.2 A: The CMS detector of the EPD instrument; B: The LEMMS detector of the EPD instrument
Figure 3.3 The LEMMS and CMS detectors are mounted on a stepping platform which can be rotated into eight different positions.
Figure 3.4 Cross-section of the LEMMS detector
Figure 3.5 Diagram of a generic particle detector
Figure 3.6 A: Illustration of particle flux counted by a detector; B: Diagram of an energy dependent geometry factor in a passband of a detector
Figure 3.7 Geometric factors for the LEMMS detector as calculated by Wu and Armstrong [1988]
Figure 3.8 The inertial reference frame defined by the position of the vernal equinox g at a certain epoch (J1950 or J2000).
Figure 3.9 A: Jupiter system III(1965) coordinates; B: Jupiter Magnetic system III
Figure 3.10 A: Ganymede system I coordinates; B: Ganymede system II coordinates
Figure 3.11 A: Magnetic field coordinates; B: Spacecraft coordinates
Figure 3.12 Illustration of the angles that define the transformation from J1950 to spacecraft coordinates
Figure 3.13 Illustration of the transformation from a body-centered coordinate system to the magnetic field coordinate system. A: Rotation about the Y axis by an angle a; B: rotation about the X' axis by angle b; C: to reference the polar angle f, the radius vector to Jupiter, R'', is rotated about Z'' by an angle c; D: the completed transformation.
Figure 3.14 Illustration of the EPD look direction in SC
Figure 3.15 Trajectory of the Galileo spacecraft at the G2 encounter in GSII coordinates
Figure 4.1 Illustration of the parameters of the offset tilted dipole model in two dimensions
Figure 4.2 Schematic of the geometry required to integrate Equation [4.9]
Figure 4.3 Illustration of the coordinates and tail current system used in the calculation of the magnetic field from the Biot-Savart law [Choe and Beard, 1974]
Figure 4.4 A: Dipole of the Earth with the +x axis towards the sun; B: dipole field of the Earth with magnetopause and tail field configuration added
Figure 4.5 A: The B_x component of the magnetic field in a system where the x axis points toward the sun and the z axis is along the rotation axis of Mercury; B: B_y moment of the magnetic field of Mercury [Jackson and Beard, 1977]
Figure 4.6 A: The B_z component of the magnetic field in a system where the x axis points toward the sun and the z axis is along the rotation axis of Mercury; B: magnitude B of the magnetic field of Mercury measured along the trajectory of Mariner 10
Figure 4.7 Meridian plane projection of the magnetosphere of Mercury as a result of the re-parameterization of the Earth multipole model with the Mercury dipole model [Jackson and Beard, 1977]
Figure 4.8 The O6 model multipole field [Connerney, 1993] compared to the dipole model in JSIII(1965) coordinates
Figure 4.9 Perturbation magnetic field DB observed by Voyager 1 during passage through the Jovian magnetosphere for R<30 R_j from the GSFC O₄ model [Acuna and Ness, 1976]
Figure 4.10 Contour map showing maximum errors in the current sheet model magnetic field components for B_r and B_z for the simple analytic forms from the closed form models of the current sheet given in Equations 4.19 to 4.21 [Connerney, 1981]
Figure 4.11 Meridian plane projection of the field lines associated with the ring current as modeled in Equations 4.19 through 4.21 [Connerney, 1981]
Figure 4.12 Meridian plane projection of the Voyager outbound pass in 1979
Figure 4.13 Current sheet models [Goertz, 1976]: A: A current sheet model that is rigidly fixed to the JSMIII plane; B: the current sheet geometry of a warped ring current
Figure 4.14 Comparison of the magnetic field topology of the ring current models of Khurana [1997] and Connerney [1981]
Figure 4.15 A: Comparison of the Br components at G2 for the measured, M1, and M2; B: comparison of the B_q components at G2 for the measured, M1, and M2
Figure 4.16 A: Comparison of the B_f components at G2 for the measured, M1, and M2; B: comparison of the magnitude B at G2 for the measured, M1, and M2
Figure 4.17 A: Comparison of the B_r components at G7 for the measured, M1, and M2; B: comparison of the magnitude B_q at G7 for the measured, M1, and M2
Figure 4.18 A: Comparison of the B_f components at G7 for the measured, M1, and M2; B: Comparison of the magnitude B at G7 for the measured, M1, and M2
Figure 4.19 ZY field line tracing of the magnetic field in the region of Ganymede for the G2 encounter. The coordinates are given in the aberrated frame which is defined by a rotation about the GSII x axis by an angle of 10º, and then a rotation about the new z axis by -33º.
Figure 4.20 ZX projection field line tracing of the magnetic field in the region of Ganymede for the G2 encounter. The coordinates are given in the aberrated frame which is defined by a rotation about the GSII x axis by an angle of 10º, and then a rotation about the new z axis by -33º.
Figure 4.21 ZY field line tracing of the magnetic field in the region of Ganymede for the G2 encounter. The frame is given in GSII coordinates.
Figure 4.22 ZX field line tracing of the magnetic field in the region of Ganymede for the G2 encounter. The frame is given in GSII coordinates.
Figure 4.23 ZY projection field line tracing of the magnetic field in the region of Ganymede for the G7 encounter. The coordinates are given in the aberrated frame which is defined by a rotation about the GSII x axis by an angle of 30º, and then a rotation about the new z axis by 40º.
Figure 4.24 ZX projection field line tracing of the magnetic field in the region of Ganymede for the G7 encounter. The coordinates are given in the aberrated frame which is defined by a rotation about the GSII x axis by an angle of 30º, and then a rotation about the new z axis by 40º.
Figure 4.25 ZY field line tracing of the magnetic field in the region of Ganymede for the G7 encounter. The frame is given in GSII coordinates.
Figure 4.26 ZX field line tracing of the magnetic field in the region of Ganymede for the G7 encounter. The frame is given in GSII coordinates.
Figure 4.27 Magnetic line trace for the G2 encounter where r_o=2.0 R_g
Figure 4.28 Diagram representing the variation of the preliminary boundary by the aberration angles a and b
Figure 4.29 A: Graph of Equation [4.36] for three cases of index n; B: graph of boundary thickness vs. index n determined from field line tracing through the boundary
Figure 4.30 Magnetic field tracings at G2 for two latitudes in GSII coordinates
Figure 4.31 Results of the 45º field line trace. A: Component B_x, as a function of distance along the field line in Ganymede radii; B: component B_y, as a function of distance along the field line in Ganymede radii
Figure 4.32 Results of the 45º field line trace. A: Component B_z, as a function of distance along the field line in Ganymede radii; B: magnitude B as a function of distance along the field line in Ganymede radii
Figure 4.33 Results of the 65º field line trace. A: Component B_x, as a function of distance along the field line in Ganymede radii; B: component B_y as a function of distance along the field line in Ganymede radii
Figure 4.34 Results of the 65º field line trace. A: Component B_z, as a function of distance along the field line in Ganymede radii; B: magnitude B as a function of distance along the field line in Ganymede radii
Figure 4.35 The divergence of a magnetic field line starting from 45º latitude and 90º West longitude in a GSII coordinate system for model M1
Figure 4.36 The divergence of the magnetic field along the field line presented in figure 4.31 for model M2
Figure 5.1 A: Schematic of the optimal look direction of the EPD instrument broken into 13 sub-look directions. B: Passband of an energy channel with boundaries E_top and E_bottom broken into five sub-energies labeled as E_i.
Figure 5.2 A: Time forward trajectory of the Galileo spacecraft through the magnetosphere of Ganymede. B: The system under time reversal.
Figure 5.3 A: Diagram of an electron entering a region of uniform magnetic field. B: Diagram of the same electron under time reversal.
Figure 5.4 A: The state function f(vⁿ, xⁿ, tⁿ)=fⁿ evaluated on a time mesh at tⁿ. B: The area under the f curve (fⁿDt) is the amount of the change in velocity from tⁿ to tⁿ⁺¹.
Figure 5.5 A: The function f(u,h) is evaluated as a function of step size, where H=100s to start. B: The state of the particle is simultaneously evaluated at t+H/n, where n= 2 steps, 4 steps, and 6 steps, etc. (h=H/n)
Figure 5.6 Schematic of the spherical volume, where particles are traced by the integration of the Lorentz force equation
Figure 5.7 A: Representation of the advancement of electrons in extended bounce mode. B: Electron reintroduced into the simulation.
Figure 5.8 A: Schematic representation of the procedure of scattering. B: Example histogram constructed from the Gaussian randomization routine used in Particle_Follow for an a₀ of 45 deg. and 3000 samples.
Figure 5.9 Histogram example of a pitch angle a_o=15°. B: Histogram example of a pitch angle a_o=75°.
Figure 5.10 Flow chart of the Particle_Follow program
Figure 5.11 Rate profiles of feature G2:185651

Figures, continued

Return to dissertation table of contents page.
Return to main Galileo Table of Contents Page.
Return to Fundamental Technologies Home Page.

Updated 8/27/2007, T. Hunt-Ward
tizby@ftecs.com