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MHD Experiments to
Isolate Different Influences on Seasonal
and Solar Cycle Variations
in
MI Coupling
M.Wiltberger
NCAR/HAO
CISM Seminar Series 2007
Outline
• Overview of the LFM
– Magnetospheric Model
– Ionospheric Model
– Electron Precipitation Model
• Ways to control the magnetosphere
– Vary the Earth’s magnetic field
– Vary the solar wind electric field
– Vary the ionospheric conductivity
• Controlled Experiments with the LFM
– Changes in Season
– Changes in UV Ionization
• Conclusions
CISM Seminar Series 2007
LFM Magnetospheric Model
• Uses the ideal MHD equations to model
the interaction between the solar wind,
magnetosphere, and ionosphere
– Computational domain
• 30 RE < x < -300 RE & ±100RE for YZ
• Inner radius at 2 RE
– Calculates
• full MHD state vector everywhere within computational
domain
– Requires
• Solar wind MHD state vector along outer boundary
• Empirical model for determining energy flux of
precipitating electrons
• Cross polar cap potential pattern in high latitude region
which is used to determine boundary condition on flow
CISM Seminar Series 2007
Computational Grid of the LFM
•
Distorted spherical mesh
–
Places optimal resolution in
regions of a priori interest
–
Logically rectangular nature
allows for easy code
development
–
Uses Partial Donor Method for
advancing numerical solution
•
Yee type grid
–
Magnetic fluxes on faces
–
Electric fields on edges
–
Guarantees B = 0
CISM Seminar Series 2007
LFM Ionospheric Simulation
• 2D Electrostatic Model
– Conservation of current
•
(P+H)=J|| sin(η)
J|| determined at magnetospheric BC
–
• Conductivity Models
Solar EUV ionization
–
•
Creates day/night and winter/summer asymmetries
Auroral Precipitation
–
•
Empirical determination of energetic electron precipitation
• Electric field used for flow at magnetosphere
–
v = -B/B2
CISM Seminar Series 2007
Auroral Electron Fluxes
• Fridman and Lemaire, 1980 developed a kinetic
model for the flux downward going electrons in the
auroral acceleration region
• Starting with conservation of total energy and
adiabatic invariants you get
Reflection
E
B / BS 1
I
E E E
I
E
S
Precipitation
 BI

E  E  E  S  1  E
B

I
S
S

E
• Integrating a isotropic distribution function over
the region where precipitation occurs yields
BI
F  Fo S
B
 e xE / E
1 
1 x

S
1
2

 ES 
1
 with Fo  Ne 
 and x  I S
B / B 1

 2 me 
CISM Seminar Series 2007
Energy Fluxes
• Considering the limit where the parallel potential drop is larger than
the thermal energy in the source region we get the Knight relationship
E
S
ES
x
x
E
xE
ES
1
 B I / B S  1   2 me E s
FE S
E 


xFo B I / B S  B I / B S  
N ee


J


• Integrating the third moment of the distribution function gives the
energy flux of the precipitating electrons
BI
FE  Fo E S
B
S

E  2
E
 S
2  S  
E  1 x E


FE  S
E
 2E  E
F 



1 x

x
 1

 xE / E S
 1 e
  xE / E S 

e




  E S  E



CISM Seminar Series 2007
Auroral Fluxes in the LFM
• Begin by computing the particle energy and number flux at the inner
boundary of the LFM simulation domain
o  c
o  
2
s
1/ 2
o
• α includes effects of calculating electron temperature from the single fluid
temperature known in MHD
• β includes effects possible effects plasma anisotropy and loss cone filling
• The initial number flux is the E||=0 case of the Flux equation which allows for
the inclusion of diffuse aurora
• The total energy of the particles is
E E E E 
S
S
RJ  E

S 1/ 2

• The factor R allows for scaling the parallel potential drop based upon the sign
of the current and account for the possibility of being outside the regime of the
scaling
CISM Seminar Series 2007
Auroral Fluxes in the LFM
• The final step is to compute the flux of precipitating electrons using the
flux formula in regions of upward current or downward streaming
electrons


  o  8  7e 7o



   0


• Using BI/BS = 8 for a dipole magnetic field and 2 RE gap between the
source region and the ionosphere
• In regions of downward current we apply
  o e

o
  0
• With the additional correction that the factor R is taken to be 5 time
smaller in these regions
• We also utilize the linearization the energy flux is simply the product of
the average energy and the number flux
CISM Seminar Series 2007
Using LFM to Study
Seasonal/Cycle Effects
• Ways to control the magnetosphere
– Vary the Earth’s magnetic field
• Earth’s dipole field flips polarity
– Vary the solar wind electric field
• CMEs, High Speed Streams, Orbital Effects
– Vary the ionospheric conductivity
• UV ionization
• Auroral Precipitation
• Controlled Experiments with the LFM
– Constant solar wind electric field with active ionosphere
– Changes in UV Ionization by altering F10.7 Flux
CISM Seminar Series 2007
Vary the electric field
• Russell & Mcpherron [1973] noted that the solar wind Parker spiral is
ordered in the GSEQ coordinate system which results in a seasonal
variation in the average rectified GSM Bz magnetic field
– A statistical correlation exists between this variation and geomagnetic
activity
• “Spring towards, fall away”
– Idealizing the magnetosphere as a circuit in this case means that you want
to vary the driving voltage and keep the resistance constant
CISM Seminar Series 2007
Vary the conductivity
• Variation of the dipole tilt angle with season controls the amount of
EUV radiation reaching the ionosphere and thus changing the amount
and distribution of conductivity
– They argue that auroral and geomagnetic activity depends on EUV and
solar wind input
• Peak in activity at equinox because aurora is in darkness for both hemispheres
– Idealizing the magnetosphere as a circuit in this case means that you want
to vary the resistance and keep the driving voltage constant
CISM Seminar Series 2007
Imposing the Solar Wind Driver
VX
VY
VZ
BX
BY
BZ
EX
EY
EZ
-3.41º Tilt - Mar 20
-399
0
24
1.82
-2.00
-3.11
47.4
-1200
-798
34.4º Tilt - Jun 20
-330
0
-226
3.34
-2.00
-1.35
-452
-1200
660
-34.4º Tilt - Dec 21
-330
0
226
-0.0447
-2.00
-3.61
452
-1200
660
GSM Values
-400
0
0
2.00
-2.00
-3.00
0
-1200
800
• We start the simulation in a SM coordinate system
and then rotate it into a GSM coordinate system
– We start with values for V and B which result in the same
GSM values at the times of maximum dipole tilt during
equinox, winter, and summer
– EY has the same value for all rotation angles and all
coordinate systems
CISM Seminar Series 2007
Ped Cond
XZ Den
Magnetosphere Ionosphere
Configuration
Equinox
Winter
Summer
CISM Seminar Series 2007
Cross Polar Cap Potential
Summer
Equinox
Winter
• Prior to the arrival of southward
IMF Summer has a larger
potential then either Winter or
Equinox
– This is likely due to a dipole tilt
effect
• After southward IMF arrival
Equinox rises to the highest
values and shows more
variability
• Seasonal variations in potential
maximum have been reported by
Weimer [1995]
– Most pronounced durting cases
with small BY
– Positive IMF BY has slightly less
potential in Summer hemisphere
• This is opposite to what we see
here
CISM Seminar Series 2007
Global Field Aligned Currents
•
Summer
Equinox
Winter
Fedder and Lyon, 1987 showed that
the magnetosphere has currentvoltage relationship that similar to a
simple circuit of a generator with
internal resistance driving an
external resistor as proposed by Hill,
1984
 PC   M  Ir
•
In order to explain the ordering of
the currents we need to expand this
model to consider hemispheres with
different conductivities
REQ 
REQ 
CISM Seminar Series 2007
RNOX
2
RSUM RWIN
RSUM  RWIN
Global Field Aligned Currents
•
Summer
Equinox
Winter
Adding the currents flowing through
each hemisphere yields some
interesting results
– Effectiveness of driver for northward
IMF is dependent on dipole tilt
– Immediately after arrival of
southward IMF total currents are the
same
– At 5:21 the equinox case shows a
clear spike in currents and difference
between the systems for solstice and
equinox
• Simple circuit analogy implies same
potential drop across each
hemisphere and that is not the case
in these results
• Simple circuit analogy does not
consider any inputs from the
magnetotail
CISM Seminar Series 2007
Substorm Behavior
•
Summer
Equinox
Winter
Calculation of a AL proxy was
conducted by applying Ampere’s
Law to location directly beneath the
maximum of horizontal current in the
simulated ionosphere
– The Equinox case shows a clear
onset signature at 5:21ST with on a
small perturbation present in the
Solstice intervals
– The Summer case shows a smaller
feature at 05:30 ST with a smaller
perturbation present in the Winter
case which is not well correlated
with other global diagnostics
– The is also some additional activity
in the solstice cases after 06:30 ST
although none of it rises to the level
of the equinox interval
CISM Seminar Series 2007
Substorm Behavior
•
Summer
Equinox
Winter
The total energy flux is computed by
integrating the energy precipitating
electrons over the entire hemisphere
– Equinox case shows a clear increase
in flux after the substorm onset time
seen in the FAC and the simulated
AL
– No clear indication of abrupt
increase flux present in either Winter
or Summer cases
– More flux is clearly flowing into
Equinox
– Interestingly Summer case has
slightly more flux then Winter case
CISM Seminar Series 2007
Ionospheric Structure
Equinox
Summer
Winter
• Animation of ionospheric evolution during entire interval
made with the CISM-DX package
– Potential contours are plotted at 10 kV intervals
– Hall Conductance is background color with a range of 2 (blue) to
14 (red) mhos
CISM Seminar Series 2007
Ionospheric Structure
Equinox
•
Summer
03:00 ST
Winter
At the beginning of the simulation interval the strong seasonal difference in
the conductance is clearly present
– All convection patterns clearly show the effect of IMF BY
– Equinox case shows weak diffuse auroral activity
– Summer case has almost diffuse auroral activity and clearly dominat dawn cell in
convection pattern
– Winter case scattered weak diffuse auroral activity
CISM Seminar Series 2007
Ionospheric Structure
Equinox
•
Summer
05:30 ST
Winter
This frame is from shortly after the substorm onset seen in the equinox interval
– Strong enhancement of conductance seen in the Equinox case that bridges midnight
and is not clearly seen Summer and only weakly present in Winter interavals
• Activity occurring in region not illuminated by Sun in Equinox case
– Examination the FAC structure for the Equinox case clearly indicates that the
enhancement is due to an energy increase in precipitation caused by a parallel
potential drop
CISM Seminar Series 2007
Ionospheric Structure
Equinox
•
Summer
08:00 ST
Winter
At the end of simulation interval significant enhancements are seen in call
cases
– Equinox case shows the strongest auroral zone enhancements with expansion in the
predawn sector as expected
– Strongest conductance are seen in Summer interval
• Dusk side region 1 and dawn side region 2 current systems
– Winter shows region 1 enhancement and diffuse auroral in predawn sector
CISM Seminar Series 2007
Ionospheric Structure
Equinox
Summer
Winter
• Activity diminishes as IMF remains northward
• After the arrival of southward IMF two cell convection pattern grows
with IMF BY effects most clear in Winter interval with displacement
in cell peak locations and strengths
• As IMF remains southward auroral oval expands across nights and to
lower latitiudes
CISM Seminar Series 2007
Effects of UV Ionization Level
• Prolonged period of
southward IMF with
northward turning at
the end
• Seasonal Variation
through date changes
– Equinox 3/21
– Summer Solstice
6/28
• Cycle Variation
through Year and
F10.7 changes
– Min 1996 – 70
– Max 2001 – 190
CISM Seminar Series 2007
LFM Seasonal Variation
• At Solar Min
– Winter potential is
higher and summer
– Stronger currents
flowing into summer
hemisphere
– More Joule Heating in
Summer Hemisphere
– Little difference in
prcecip eng.
• At Solar Max
– Differences between
seasons are more
pronounced
• Especially strong in
FAC
• Still little diff in
precp eng
CISM Seminar Series 2007
LFM Seasonal Variation
• At Solar Min
– Winter potential is
higher and summer
– Stronger currents
flowing into summer
hemisphere
– More Joule Heating in
Summer Hemisphere
– Little difference in
prcecip eng.
• At Solar Max
– Differences between
seasons are more
pronounced
• Especially strong in
FAC
• Still little diff in
precp eng
CISM Seminar Series 2007
LFM Solar Cycle Variation
• Summer
Hemisphere
– Magnitude of
variation by cycle
similar to seasonal
• Winter
Hemisphere
– All parameters
show virtually no
difference
• Delayed onset of
peak under solar
min conditions
CISM Seminar Series 2007
LFM Solar Cycle Variation
• Summer
Hemisphere
– Magnitude of
variation by cycle
similar to seasonal
• Winter
Hemisphere
– All parameters
show virtually no
difference
• Delayed onset of
peak under solar
min conditions
CISM Seminar Series 2007
Dependence on Conductance
• Comparing these two
– Only current shows significant
difference
– Onset of enhanced Joule
heating delayed
• Substorm onset affected by
conductivity
• Winter at solar max has
similar Pedersen
Conductance as Summer
at solar min
CISM Seminar Series 2007
Future Work - Conductance
• This research indicates several interesting
directions for further study
– Dipole tilt effects
• Northward IMF case showed that while keeping solar wind
electric field constant not all dipole tilt effects are removed
• Planning to modify code to include zenith angle effects without
tilting dipole
– Active Ionospheric Feedback
• Developing a version of the code which only includes the EUV
ionization to study evolution of system without auroral
conductance enhancements
CISM Seminar Series 2007
Future Work – NW Currents
• Neutral wind driven
currents are calculated
from within TING
S1


J n     P E    H B  E  ds
S0
E  u  B
• After strong driving we
see clear development of
system with expected
dusk/dawn asymmetry
• Need to study how these
parameters are affected
by both season and solar
cycle
CISM Seminar Series 2007
Conclusions – Part I
• Clear indication of the influence of EUV
ionospheric conductance on the response of the
coupled magnetosphere-ionosphere system
– In Equinox case a clear substorm is seen in a variety of
global parameters
– In Solstice case a smaller perturbation is seen only
simulated AL
• Removal of RM Effect from solar wind driver and
stronger activity in Equinox case supports a role
for ionospheric conductance controlling
geomagnetic activity
CISM Seminar Series 2007
Conclusions – Part II
• Seasonal Effects
– During Southward IMF Cross polar cap potential
highest in winter Hemisphere
– Upward FAC strongest in summer hemisphere
– Joule heating largest in summer hemisphere
– Energy Precip shows little difference between
winter and summer
• Cycle Effects
– Upward FAC increases with increasing EUV
output
– Stronger variation seen in summer hemisphere
implies dependence on conductivity nonlinear
CISM Seminar Series 2007
CISM Seminar Series 2007