Transcript Slide 1

Fall AGU 2012
SM51A-2294
Why Are Cold Electrons So Hot?
Investigating a Magnetospheric Heat Cycle
A. M.
Background.
1
Rymer ,
1Johns
J.
1
Carbary ,
B.H.
1
Mauk ,and
T.W.
3
Hill
Hopkins University, Applied Physics Laboratory, 2University of Texas at Austin, 3Rice University.
During loss-free, scatter-free radial plasma transport the first (gyration) adiabatic invariant
E sin 

B
R.
2
Livi ,
[email protected]
2
How do electrons heat in the middle magnetosphere?
(1)
(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
J  2 pLRsY ( y)
(2)
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 [1974]).
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 [1978]. 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.
Results
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.
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.
For a dipole field µ  L^3 and J  L^2.
Assuming an original phase space density, f(v), of the form
sin 
f ( v) 
En
m
(3)
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.
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
Figure 9.
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. [2007], Andripoulus et al. [2012] and Thomsen et al. [2012], 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 1. Evolution of an initially isotropic PAD under transport in a changing
magnetic field.
Figure 6. Consequence of a
noon-midnight E-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.
To investige electron PADs as a function of
local time we follow the method of Carbary
et al., [2011] and fit the data as sink,
where a positive k-value indicates a
pancake PAD and a negative value a fieldaligned PAD, as illustrated in Figure 7.
Saturn’s radial heat cycle
2.
Isothermal scattering (partially) reisotropises the electron pitch angle
populations.
1.
Inward transport
heats the electron
PADs adiabatically.
E

CII > 0
3.
Outward transport
cools the electron
PADs adiabatically.
Figure 11.
E

B
B

Figure 10.
Rc
Figure 8.

Rc
Figure 7.
4.
Isothermal scattering (partially) reisotropises the electron pitch angle
populations.
Figure 2. Saturn’s radial heat cycle and predicted PADs.
Figure 3. Cassini ELS data (corrected for positive s/c potential) in Saturn’s
equatorial plane
SUMMARY AND MUSINGS
How to build a magnetosphere:
1. Magnetosphere is empty of plasma, just neutrals and photons.
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.
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
References:
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.
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.