Construction of 3D Active Region Fields and Plasma Properties using Measurements (Magnetic Fields &...
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Construction of 3D Active Region Fields and Plasma Properties using Measurements (Magnetic Fields & Others) S. T. Wu, A. H. Wang & Yang Liu 1 Center for Space Plasma & Aeronomic Research and 2 Department of Mechanical and Aerospace Engineering The University of Alabama in Huntsville, Huntsville, Alabama 35899 USA 3 W.W. Hansen Experimental Physics Laboratory Stanford University, Stanford, CA 94305 USA Presentation at SDO Science Team Meeting, March 25-28, 2008, Napa, CA
Construction of 3D Active Region Fields and Plasma Properties using Measurements (Magnetic Fields & Others) S. T. Wu, A. H. Wang & Yang Liu 1 Center for
Construction of 3D Active Region Fields and Plasma Properties
using Measurements (Magnetic Fields & Others) S. T. Wu, A. H.
Wang & Yang Liu 1 Center for Space Plasma & Aeronomic
Research and 2 Department of Mechanical and Aerospace Engineering
The University of Alabama in Huntsville, Huntsville, Alabama 35899
USA 3 W.W. Hansen Experimental Physics Laboratory Stanford
University, Stanford, CA 94305 USA Presentation at SDO Science Team
Meeting, March 25-28, 2008, Napa, CA
Slide 2
Table of Contents I.Description of the MHD Model A.Governing
Equations, Boundary Conditions and Code B.Model Inputs C.Model
Outputs D.Examples AR8100 and AR8210 II.Model Tests A.Initial
Potential Fields (PF) B.Initially Observed Non-Linear Force-Free
Fields (NLFFF) C.Initial Analytical NLFFF (B. C. Lows Solution)
III.Open for Suggestions
Slide 3
I. Description of the MHD Model A.Governing Equations, Boundary
Conditions and Code Governing Equations A set of standard
compressible, resistive MHD equations with higher order transport.
Boundary Conditions Top and side boundary condition are
non-reflective (i.e. linear extrapolation). Bottom boundary
conditions are evolutionary boundary conditions obtained from the
method of characteristics shown on the next slide.
Slide 4
Expressions derived from the method of characteristics for the
physical parameters of pressure, density, the components of
velocity, and magnetic field vary with time on the lower boundary
are:
Slide 5
where the coefficients A_, B_, and C_ are given below.
Slide 6
Slide 7
Slide 8
Alfvn speed Fast MHD wave speed Slow MHD wave speed with Sound
speed
Slide 9
Computational Flow Chart for the 3D MHD code where F and T
represent the false and true, respectively. Note, the upper box
represents the code to compute the equilibrium solution and the
lower box is for computing the evolutionary solution. Numerical
Code Flow Chart Trial Values Iteration F T Error Check Initial
State Bottom Bdy Conditions Predict Step Top & Side Bdy
Conditions Bottom Bdy Conditions Correction Step Top & Side Bdy
Conditions Artificial Dissipation Time =T SAVE FT Save Data Time T
STOP Terminating Code MHD Equilibrium Solution Evolution Solution
Drivers: Magnetic field measurements Differential rotation 0
Meridinal flow
Slide 10
B.Model Inputs For our examples, the model inputs are observed
vector magnetograms. In principle, the model inputs could be all
available observed physical quantities such as magnetic field,
density, temperature and velocity.
The simulated initial state of AR8100 at 14:27 UT 1997, Oct,
31; (a) the transverse magnetic field vector (5 G |B t | 6 G) and
contours of the line- of-sight magnetic field (B z ) with the solid
lines and broken lines representing the positive and negative
polarity, respectively. The color bar on the upper right side
indicates the strength of the line-of- sight magnetic field (-10 G
B z 10 G) contours, (b) the transverse velocity (maximum is 1.9 km
s -1 ) and B z contours, (c) the density contours at surface with
transverse magnetic field, and (d) the plasma beta [ = (16 nkT)/B 2
] distribution on the surface. The color bar at the lower right
side is for both density and contours. Active Region 8100
Slide 14
The simulated evolution of magnetic field at 14:27 UT, 16:03
UT, 17:39 UT and 19:12 UT Oct 31, 1997. The representation is
similar to Figure 1. The color bar on the right-hand side indicates
the strength of LOS magnetic field. The white arrows represent the
non-potential transverse magnetic field, and black arrows represent
the potential transverse magnetic field. Active Region 8100
Slide 15
The evolution of the vertical velocity (km s -1 ) (color coded
on the right-hand side) of AR 8100. The color bar on the right-hand
side represents the magnitude of the vertical velocity, where the
positive- polarity region (solid lines) give the upward velocity,
and the negative region (dotted lines) gives downward velocity.
Active Region 8100
Slide 16
The simulated evolution of surface transverse velocity vector
(V t ), and the contours of the line-of- sight magnetic field for
AR 8100 on Oct 31, 1997; (a) at 14:27 UT with 0.0002 kms -1 V t 1.9
km s -1 (b) at 16:03 UT with 0.0018 kms -1 V t 3.7 kms -1, (c) at
17:39 UT with 0.0088 kms-1 V t 5.0 kms -1 and (d) at 19:12 UT with
0.0164 kms -1 V t 7.1 kms -1. Active Region 8100
Slide 17
The magnetic energy (10 22 erg/km -2 ) across the low boundary
to the AR8100. Active Region 8100
Slide 18
Simulated energy flux through the photosphere for the Active
Region AR8100. Active Region 8100
Slide 19
Active Region 8210
Slide 20
Nonpotential magnetic parameters
Slide 21
HINODE Event December 12,13, 2006 AR 10930 Line-of-sight
current helicity (G 2 /m) pre-flare Line-of-sight current helicity
(G 2 /m) post-flare
Slide 22
HINODE Event December 12,13, 2006 AR 10930
Slide 23
II. Model Tests A.Initial Potential Field (PF) B.Initially
Non-Linear Force-Free Field (NLFFF) C.Initial Analytical NLFFF
(B.C. Lows Solution)
Slide 24
MHD Magnetic Field Configuration for AR8210 PF NLFF
Slide 25
Active Region 8210 Initial NLFFF Initial PF
Slide 26
Initial NLFFF
Slide 27
Magnetic Energy Analysis Table Magnetic Energy Ratio AR 8210
(3D) Analytic Solution (B. C. Low) Force- Free/Potential 0.954.21
MHD/Potential 1.211.14 MHD/Force-free 1.151.13 CPU Computer 1: a
Compaq/HP DS20 Alphaserver with dual 667 MHz Alpha processors, 1 GB
of RAM, and 200 GB of disk storage. 2 VA : For dimension 121 x 121
x 21 ~ 7 CPU For dimension 121 x 121 x 121 ~ 45 CPU Computer 2: a
12-node PSSC P4 PowerWulf Beowulf cluster, based on P4 2.8 GHz
processors with 40 GB storage per node and 240 GB head node
storage. 2 VA : For dimension 121 x 121 x 21 ~ 4 CPU For dimension
121 x 121 x 121 ~ 25 CPU For dimension 320 x 320 x 64 ~ 56 CPU