# Using Magnetograms to Drive a Numerical Simulation

Document Sample

```					 Using Data to Drive a Numerical
Coronal Simulation
I.   The Theoretical Model:
Computational MHD
II. The Data
A. Initial condition: Force-free equilibria
B. Boundary conditions: photospheric velocity
I. The Theoretical Model
Domain for
AR Corona

EIT 195A 1998-05-01 20:15
Courtesy NASA
I. The Theoretical Model
MHD Equations:*
Fluid properties
B                                v, B, p, r
   v  B 
t

* Details: Abbett, UCB
fluid properties (v, B, p, r)
• Couples near-by grid points
Dt

0                                t
I. The Theoretical Model
Requirements:
A. Initial condition:
(v, B, p, r)
Everywhere
@ t=0

0                           t
I. The Theoretical Model
Requirements:
A. Initial condition:
(v, B, p, r)
Everywhere
@ t=0
B. Boundary conditions:
(v, B, p, r)
On Boundaries
@ all times t > 0

0                          t
II. The Data
Regnier & Canfield, MSU

AR8210

SOI/MDI, Courtesy NASA
Vector m-gram: B @ surface
IVM, Univ. Hawaii

17:00       18:00        19:00    20:00       21:00   1998-05-01
II. The Data
AR8210

5 raw m-grams                    1 avg. m-gram
sz ~ 60G, sx ~ 130G               sz ~ 25G, sx ~ 60G

17:00     18:00     19:00   20:00        21:00   1998-05-01
Data: m-gram

B @ lower boundary
15-min intervals
t=0

17:00     18:00   19:00         20:00   21:00   1998-05-01
A. Initial condition
• Assume magnetostatic equilibrium: v=0
• Assume b << 1  Force-free field
  B   (x)B(x) , B    0
• Construct solution B(x) which matches
m-gram @ t=0

t=0

19:00         20:00       21:00   1998-05-01
A. Initial condition
Force-free extrapolation Regnier, MSU
• Initial guess B(0)
• set (0) on each field line
from data (one polarity)
• calculate B(1) from current
(0) B(0)
• Repeat until converged
A. Initial condition

Force-free extrapolation of AR8210 (Regnier, MSU)
1998-05-01 19:40
Verify IC vs. coronal observations*
19:40                 19:40
14:01

17:57

Reconstructed              Vector
21:12
Active Region           Magnetogram
(emission integrated
over line of sight)       Data
Yohkoh SXT
AR 8210 1998-05-01     *Details: Lundquist, UCB
B. Boundary Conditions

• Need v @ lower boundary

B
   v  B 
t
• Must be consistent w/
observed evolution
of B(x,t)

19:00     20:00   21:00   1998-05-01
B. Boundary Conditions
1. Local Correlation Tracking   (November & Simon 1988)

Apparent motion of “features” in sequential images
B. Boundary Conditions
1. Local Correlation Tracking   (November & Simon 1988)

LCT velocity of AR8210
B. Boundary Conditions
1. Local Correlation Tracking   (Demoulin & Berger 2003)

LCT velocity = plasma velocity
v                  B
B. Boundary Conditions
1. Local Correlation Tracking   (Demoulin & Berger 2003)

LCT velocity = plasma velocity
v
B
B. Boundary Conditions
1. Local Correlation Tracking   (Demoulin & Berger 2003)

LCT velocity = plasma velocity
v
B

Apparent feature
velocity (horizontal)
u
 B 
u LCT         B v z
 v -    
 z
B. Boundary Conditions
2. Minimum Energy Fit (MEF) Longcope, MSU

• Require velocity to satisfy induction equation
Bz
 z    v  B     B  vz  v  Bz 
ˆ
t
• AND to minimize “penalty function”

W {v  , vz }   | v  |2  | vz |2  dxdy
B. Boundary Conditions
2. Minimum Energy Fit (MEF) Longcope, MSU

Test case: emerging spheromak
B. Boundary Conditions
2. Minimum Energy Fit (MEF) Longcope, MSU

Test motion           MEF results
B. Boundary Conditions
2. Minimum Energy Fit (MEF) Longcope, MSU

Application to AR8210
B. Boundary Conditions
3. Induction + LCT (I+LCT) Welsch & Fisher, UCB
                   
Bz u ILCT  vz B - Bz v      ( z)
ˆ

Bz
Induction Eqn. Constrains  :        
2

t

LCT Constrains  :      Bz u LCT   
2
B. Boundary Conditions
3. Induction + LCT (I+LCT) Welsch & Fisher, UCB
                   
Once   u I  LCT is known, v  , vz   are known:

                                 
(u   B )                     (u   B ) 
vz  - 2           Bz         v  u  - 2           B
(B  Bz )2
(B  Bz )2

Tests Against Simulations: Details from Abbett (next)
B. Boundary Conditions
3. I+LCT: Application to 8210 UCB/MSU Teams
Summary
   Prepared Data for simulating AR8210
   Critical steps to link Data & Model:
A. Initial Condition
B. Boundary Condition
   Developed methods for both steps:
A. FFF extrapolation from 1st m-gram
B. I+LCT: photospheric velocity consistent
with data & MHD equations

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 2 posted: 12/10/2011 language: pages: 26
How are you planning on using Docstoc?