Transcript 1/r - GPSM

The Anisotropy of Precipitating
Auroral Electrons: A FAST Case Study
O. Marghitu (1, 2), B. Klecker (2), and J. P. McFadden (3)
(1) Institute for Space Sciences, Bucharest, Romania
(2) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany
(3) Space Sciences Lab., Univ. of California at Berkeley, USA
35th COSPAR Scientific Assembly
Paris, July 22, 2004
Background: http://climate.gi.alska.edu/Curtis/curtis
Outline
A.FAST orbit 1859: Data
B.Electron distribution: Theory
C.FAST orbit 1859: Results
D.Electron anisotropy and AAR altitude
E. Summary and Prospects
A FAST Orbit 1859: Data Overview A
FAST particle data, consistent with
repeated encounters of the AAR.
From top to bottom: Electron and
ion energy spectrograms; fieldaligned potential drop above the
satellite (green), below the satellite
(red) and total (black).
Images 4 s apart during 8:22-8:23.
FAST footprint is shown as a
square. ´11´ and ´22´ are the limits
of the first two ion beams. The arc
is stable and drifts southward with
~200m/s.
A FAST Orbit 1859: Electron Distributions A
2D
distribution
functions
in
1/cm3(km/s)3. Each plot covers 2.5s.
1D cuts in parallel (red), perp. (green),
and anti-parallel (blue) direction.
 The plateau in the parallel cuts at E < Ua points to wave-particle interactions,
stabilizing the accelerated distribution.
 At energies E > Ua the 1D cut in parallel direction shows an exponential
variation, while the iso-f contours inside the loss-cone are approx. elliptical,
supportive for a bi-maxwellian distribution.
B Electron Distribution: Theory B
Assumptions:
 A ‘source’ region exists above the AAR, where the particle distribution is bimaxwellian (reasonable, given the anisotropy introduced by the magnetic field):
fS  K
nS
AS E03|| 2S
  E
E S
exp   ||S 
  E0|| S AS E0|| S




nS
 source density
E 0|| S  source parallel temp.
AS  source anisotropy
 The non-adiabatic interactions between the source region and satellite are weak
enough, so that the ‘memory’ of the source distribution is preserved, to some
extent (reasonable, given the stable arc).
B Electron Distribution: Theory B
Consequence:
 The adiabatic motion of the source particles in the parallel electric field
superposed on the convergent magnetic field produces:
 E E
nS
E M
a
 ||M

fM  K
exp


AS E03|| 2S
AM E0|| S
  E0|| S
where:

Ea  e U ||
 AM 
1
1 AS  1
1
r AS
 r  BM BS
 measured peak energy
 measured anisotropy
 measured B Source B




C FAST Orbit 1859: Fit Procedure C
 Fit parameters:
 E 
exp  a 
 E0|| S 
nS
p1  K
AS
E 03 S2
By inverting the system one can
p2  E0|| S
find nS AS , E0|| S , and AM .
||
p3  AM E0|| S
 Fit over plasma sheet electrons inside the loss-cone:
 7 energy levels, > Ea
 10 pitch-angle channels, < 300
 In order to improve the reliability, the fit program, AURFIT, can check several
starting points in the parameter space
2
 Fit quality measured by  r
AM
TMperp
C FAST Orbit 1859: Fit Parameters C
 Parameter values consistent with recent
Polar data (Kletzing et al., 2003 =>
statistical study based on 93 orbits):
 Densities of 0.01 – 0.5 cm-3
 Temperatures of 0.1 – 4 keV
 Temperature variation correlated with
the potential drop, as noted already in DE
data (Reiff et al., 1988)
 Anisotropy variation seems to be related
to the alternation of ion beams (?): AM ≈ 1
during beams and AM < 1 between beams.
C FAST Orbit 1859: Fit Quality C
 Fit quality for 1000 starting points (10 p1 × 10 p2 × 10 p3); best fit => yellow
 Potential drop above the satellite (green), below the satellite (red), and total
(black) overplotted, in order to check the relation to the fit quality
 The fit quality tends to be better when the potential drop above the satellite is
smaller => at higher accelerating potential one expects more unstable
distributions, which deviate more from bi-maxwellian.
D Electron Anisotropy and AAR altitude: Theory D

1
AM 
(1)
1 AS  1
1
r AS
 AS ≈ 1 or r » 1 => AM ≈ 1
 AS > 1 => AM > 1
 AS < 1 => AM < 1
 If AM ≠ 1 one could derive r and, consequently, the altitude of the upper boundary
of the AAR, provided that AS is known.
 The fit produces q = nS / AS (2). Given an estimate of nS , one could find AS .
 In order to estimate nS we rely on simulation results of Ergun et al., 2000,
suggesting that the upper boundary of the AAR is located where the ionospheric
ion beam density is equal to the plasma sheet ion density => nS = 2nSIB (3).
 To find the beam density at the top of the AAR we assume stationary conditions,
with JMIB/BM = JSIB/BS (JIB = ion beam particle flux), so that:
nSIB  J SIB vSIB  J MIB r 2U T mSIB , depending on r and measurable quantities (4)
valid only inside
1
1
q fit
 1  fit 
 (1) + (2) + (3) + (4) =>
=> AAR, because of
IB
T
IB
r
AM 2 J M
2U mS
the nS estimate
D Electron Anisotropy and AAR altitude: Results D
 Ion beam 1 => pretty ‘clean’ and largest ΔU
 ‘inverted-V’ r variation
 r increases to ~4, equivalent to a AAR top
(AART) altitude of ~10000km
 Ion beams 2 & 3 => ‘noisy’ and medium ΔU
 The large (meaningless) neg. values could
be, within errors, large pos. values (1/r ≈ 0)
 The ‘inverted-V’ variation of r might be
obscured by the noise
 Ion beam 4 => ‘noisy’ and smallest ΔU
??  Unreliable, because the AAR bott. (AARB,
presumably unsteady) is probably quite close
!
?
 Ergun et al., 2000 => AARB at the alt. where
the dens. of backscatt. and sec. equals the dens. of
ionosph. ions => dep. on curr. and atm. sc. height.
 AART where nIB=nPS. When AARB goes to
lower alt., the flux tube is richer in ionospheric
ions, which dilute to PS density at higher alt.
E Summary E
 We developed a fit method which allows the diagnose of the plasma sheet
electrons above the AAR, based on measurements close to the AAR bottom.
 The method was checked with FAST data from orbit 1859; the parameter values
obtained are in good agreement with Polar and DE results.
 The fit quality,
 r2 , seems to be related to the potential drop above the satellite
and provides an indication about the importance of non-adiabatic processes.
 The electron anisotropy carries information about the altitude of the AAR top
boundary, that can be, sometimes, extracted.
 Our results suggest that when the AAR expands to lower altitudes, the
enrichment in ionospheric ions leads to expansion to higher altitudes as well.
E Prospects E
 Investigation of several orbits, under various disturbance conditions:
 Parameters
 Fit quality
 Evaluation of the error in the altitude of the AAR top boundary induced by:
 Heavy ions (He+, O+) content of the beams (influence on mIB)
 Finite EESA energy step (influence on Ea and, further, on qfit)
 Use of both the ionospheric beam ions (nIB) and plasma sheet ions (nPS, pitchangle 00 – 1500) to evaluate the density at the AAR top boundary.