Why Are Cold Electrons So Hot? Investigating a Magnetospheric Heat Cycle A. M. Rymer 1 , R. Livi 2 , J. Carbary 1 , B.H. Mauk 1 , and T.W. Hill 3 1 Johns Hopkins University, Applied Physics Laboratory, 2 University of Texas at Austin, 3 Rice University. Fall AGU 2012 SM51A-2294.
Investigating a Magnetospheric Heat Cycle
A. M. Rymer1, R. Livi2, J. Carbary1, B.H. Mauk1,and T.W. Hill3
1Johns Hopkins University, Applied Physics Laboratory, 2University of Texas at Austin, 3Rice University.
Fall AGU 2012
Saturn’s radial heat cycle
2. Isothermal scattering (partially) re-isotropises the electron pitch angle populations.
1. Inward transport heats the electron PADs adiabatically.
3. Outward transport cools the electron PADs adiabatically.
CII > 0
4. Isothermal scattering (partially) re-isotropises the electron pitch angle populations.
Outward transport of an isotropic distribution produces “field aligned” PADs.
Inward transport of an isotropic distribution produces a “pancake” PAD.
Outward transport of a pancake distribution can produce “butterfly” PADs, (depends on distance travelled and steepness of original distribution).
Initially isotropic distribution
Inspired by the results of Thomsen et al. 2012 we have used electron temperatures derived by Livi et al. [AGU poster SM51A-2281] to explore the electron temperature variation as a function of local time and radial distance. We find that the cold electron component heats and transitions from fairly field-aligned to isotropic temperature with increasing distance from Saturn. The hot electron component has the opposite temperature profile and more complicated PAD evolution, Figure 9. There is no obvious dawn/dusk asymmetry, Figure 10. The cold component is hotter at midnight than noon, as found by Thomsen et al., 2012. The gradient is somewhat different, Figure 11.
During loss-free, scatter-free radial plasma transport the first (gyration) adiabatic invariant
(non-relativistic form) is expected to be conserved, where E is energy, B is magnetic field magnitude and is pitch angle. For a dipole field µ L^3.
Likewise in the absence of bounce-resonant field variations, the second (bounce) adiabatic invariant is expected to be conserved. In a dipole field this is
where p is the particle’s total momentum (conserved during the bounce motion), L is equatorial crossing distance in units of Rs and Y(y) is given in equation 1.29b of Schulz and Lanzerotti ).
For a dipole field µ L^3 and J L^2.
Assuming an original phase space density, f(v), of the form
the index m can be varied to describe more or less isotropic PADs and n to describe more or less steep energy spectra. We then assign the f(v) from the source population to the evaluated pitch angle at our chosen destination in accordance with Liouville’s theorem to explore the predicted PAD evolution under transport.
Figure 1. Evolution of an initially isotropic PAD under transport in a changing magnetic field.
Resultant PADs are summarized in Figure 1. Dotted curve f(v) E-2 inward (weak B to strong B) from L=10 to L=6. Dashed curve for an isotropic distribution transported outward from L=6 to L=10 and the solid curve for transport of an initially ‘pancake’ electron pitch angle distribution with f(v) sin0.5/E2 outward over the same distance.
How do electrons heat in the middle magnetosphere?
The same question at Jupiter has remained unanswered since the Voyager era [e.g., Hill et al., 1983]. To address this mystery we investigate an azimuthal heating cycle that might operate in the middle, non-dipolar magnetospheric region. This idea was first proposed by Goertz . In this cycle “magnetic pumping” energises plasma by azimuthal transport in magnetic field configurations which are compressed at some longitudes (e.g. the dayside magnetosphere) and stretched at others (e.g. the tail-like nightside magnetosphere). This results in pitch angle dependent heating exactly analogously to the radial heat cycle. That combined with isothermal scatter can result in net azimuthal heating, as illustrating in Figure 5.
Figure 8 shows our results for a few ELS energy levels, there are no obvious local time asymmetries evident, maybe a slight tendency for the colder electrons to be more field aligned at midnight than noon. A larger dataset will be illuminating, but at present we conclude that there is no clear evidence for the PAD evolution predicted by the azimuthal pumping scenario.
Figure5. Cartoon illustrating PADs associated with azimuthal magnetic pumping.
An interesting twist has recently been introduced to this picture as a consequence of work by Roussos et al. , Andripoulus et al.  and Thomsen et al. , who identify evidence for a noon midnight field in the inner magnetosphere. If this persists in the non-dipolar middle magnetosphere the result is a slight dawnward flow that will act to cancel out the effect of magnetic pumping.
Figure 6. Consequence of a noon-midnight E-field
To investige electron PADs as a function of local time we follow the method of Carbary et al.,  and fit the data as sink, where a positive k-value indicates a pancake PAD and a negative value a field-aligned PAD, as illustrated in Figure 7.
SUMMARY AND MUSINGS
How to build a magnetosphere:
1. Magnetosphere is empty of plasma, just neutrals and photons.
2. Photolysis of the neutrals creates an extended plasma cloud that slowly expands due to centrifugal forces.
3. The plasma reaches the non-dipolar region of the magnetosphere and azimuthal Carnot cycle heats the plasma. EVIDENCE NOT FOUND
4. Hot plasma injects planetward heating via radial Carnot cycle. (injection in small channels, driven by some instability) SUPPORTED
5. Injected plasma drifts and provides additional hot electron component and therefore enhanced ionisation of the neutral cloud via electron impact. SUPPORTED
Figure 3. Cassini ELS data (corrected for positive s/c potential) in Saturn’s equatorial plane
Carbary, J. F., et al., (2011), Pitch angle distributions of energetic electrons at Saturn, JGR, 116, A01216, doi:10.1029/2010JA015987.
Goertz, C. K. (1978) Energization of charged particles in Jupiter\'s outer magnetosphere, JGR, 83, 3145.
Hill, T. W., A. J. Dessler, and C. K. Goertz (1983), Magnetospheric Models, in Physics of the Jovian Magnetosphere, Chap. 10, A. J. Dessler, ed., Cambridge Univ. Press.
Rymer, A. M., et al. (2007), Electron sources in Saturn’s magnetosphere, JGR, 112, A02201, doi:10.1029/2006JA012017.
Rymer, A. M., et al., (2008), Electron circulation in Saturn’s magnetosphere, JGR, 113, A01201, doi:10.1029/2007JA012589.
Rymer, A.M., Electron-Ion Thermal Equilibration at Saturn: Electron Signatures Of Ion Pick-Up? 9th Annual International Astrophysics Conference, doi:10.1063/1.3529979, 2010.
Roussos et al., (2007), Electron microdiffusion in the Saturnian radiation belts: Cassini MIMI/LEMMS observations of energetic electron absorption by the icy moons, JGR, 112, A06214, doi: 10.1029/2006JA012027.
Andriopoulou et al., (2012), A noon-to-midnight electric field and nightside dynamics in Saturn’s inner magnetosphere, using microsignature displacements, Icarus, 220, 503.
Thomsen et al., (2012), Saturn’s inner magnetospheric convection pattern: Further evidence, JGR, 117, A09208, doi:10.1029/2011JA017482.
Figure 2. Saturn’s radial heat cycle and predicted PADs.
Newly produced charged particles are ‘picked up’ by the planetary magnetic field, the energy gained is proportional to particle mass. Electrons heat slowly to the proton corotation energy (see Rymer et al. 2007 and Rymer 2010 for more info), at L=7 that is location A on Figure 3. Electrons created at A move slowly outwards and cool to location B. They heat (see next section) forming population C/D, this is the seed population for inward injection events that move along lines of adiabatic invariant to location E. Pitch angles predicted from this model are observed – as shown in Figure 4 (from Rymer et al., 2008).
Figure 4 (on right). Cassini ELS data showing an inward injection event and associated PADs.
Acknowledgements. This work was supported in part by the Cassini Data Analysis Program under grant NNX11AK65G to Johns Hopkins University, NASA-JPL contract NAS5-97271 between the NASA Goddard Space Flight Center and Johns Hopkins University for the MIMI investigation, by NASA-JPL contract 1243218 for the CAPS investigation at the Southwest Research Institute.