m.wiltberger ncar/hao

CISM Seminar Series 2007

MHD Experiments to Isolate Different Influences on

Seasonal and Solar Cycle Variations in

MI Coupling

M.WiltbergerNCAR/HAO


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


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


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


LFM Ionospheric Simulation

• 2D Electrostatic Model– Conservation of current

P

HJ|| 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


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

• Integrating a isotropic distribution function over the region where precipitation occurs yields

1

I S

II S S

S

E E E

BE E E E

B

1/ 2

o

11 with F and

1 2 / 1

SxE E SI

o eS I Se

EB eF F N x

B x m B B

Precipitation

Reflection

E

E

/ 1I S

E

B B


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

• Integrating the third moment of the distribution function gives the energy flux of the precipitating electrons

1

2/ 1

/ /

SS

S

sS I Se

I S I So e

xEEE E x

x E

m EFE B BE J

xF B B B B N e

/

/

22

1

12

11

S

S

IxE ES

E o S S S

S SE

xE E

E EBF F E e

B E x E

F xE E E E E

xF

e


Auroral Fluxes in the LFM• Begin by computing the particle energy and number flux at the inner

boundary of the LFM simulation domain

• 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

• 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

2 1/ 2o o s oc

1/ 2S

S SRJ E

E E E E


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

• 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

• 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

78 7 0oo e

0ooe


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


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


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


Imposing the Solar Wind Driver

• 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

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


Magnetosphere Ionosphere ConfigurationEquinox

Summer

Winter

XZ

Den

Ped

Con

d


Cross Polar Cap Potential • 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

Equinox

Winter

Summer


Global Field Aligned Currents • Fedder and Lyon, 1987 showed that

the magnetosphere has current-voltage relationship that similar to a simple circuit of a generator with internal resistance driving an external resistor as proposed by Hill, 1984

• In order to explain the ordering of the currents we need to expand this model to consider hemispheres with different conductivities

PC M Ir

2NOX

EQ

RR

SUM WINEQ

SUM WIN

R RR

R R

Equinox

Winter

Summer


Global Field Aligned Currents • 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

Equinox

Winter

Summer


Substorm Behavior • 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

Equinox

Winter

Summer


Substorm Behavior • 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

Equinox

Winter

Summer


Ionospheric Structure

• 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

Equinox WinterSummer



• 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

03:00 STEquinox WinterSummer



• 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

Equinox WinterSummer05:30 ST



• 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

Equinox WinterSummer08:00 ST



• 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

Equinox WinterSummer


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


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


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


Dependence on Conductance

• Winter at solar max has similar Pedersen Conductance as Summer at solar min

• Comparing these two– Only current shows significant

difference– Onset of enhanced Joule heating

delayed• Substorm onset affected by

conductivity


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


Future Work – NW Currents

• Neutral wind driven currents are calculated from within TING

• 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

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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


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

m.wiltberger ncar/hao

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