calculating magnetic energy in active regions using coronal loops for ar 11092 and ar 11112...

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Calculating Magnetic Energy in Active Regions Using for AR 11092 and AR 11112 Presentation by, Joseph B. Jensen

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Calculating Magnetic Energy in Active Regions Using Coronal Loopsfor AR 11092 and AR 11112

Presentation by,Joseph B. Jensen

Magnetic energy equation

∇ ×Β =α ( x ) Β ( x )

W =1 /8 π ∫∣Β 2∣d 3 x=1 /8 π ∫d Φ ∫ Β dl

Non-linear force-free equilibrium for coronal field

Force = J × Β + ∇ p + ρ g = 0

Magnetogram of active

region 11092 August 1, 2010

at 5:00

Active region 11092 in 171 angstrom

wavelength

The alpha and h parameter space of one coronal loop

The blue line is user input, the yellow is the computed loop

All loops identified on ar11092 at the 171 wavelength

Voronoi Tesselation

Negative footpoints Positive footpoints

Monte Carlo Method

∫ab sin ( x) ≈ (b−a )/N ∑

i=1

N

sin ( xi )

Monte Carlo Method

∫ab sin ( x) ≈ (b−a )/N ∑

i=1

N

sin ( xi )/ p (x i )

W N = 1 /N ∑i=1

N

∣Β z (x i , y i , 0 )∣C ( x i , y i )/8 π p ( x i , y i )

where

C ( x , y )=∫L ( x , y )B [ x( l )]dl

Calculating Total Magnetic Energy

Φ i =∣Β z ( x i , y i , 0)∣/ Np ( x i , y i )and

= ∑i=1

N

Φ iC ( x i , y i)/8 π

Calculating the Free Energy

W free= 1 /8π ∫d Φ ∫(Β−ΒP )dl ≈ ∑i=1

N

ΦiΔ C i /8 π

Δ C i ( x , y ) = ∫L i (Β−Β P ) •dl

where

Β total − Β free = Β potential

Ar11092 at 0500 UT

Ar11092 at 1700 UT

7.2 x 1032 ergs − 2.6 x 1032ergs=4.6 x 10 32ergs

4.5 x 1032 ergs

4.7 x 10 32ergs − 1.0 x 10 32ergs = 3.7 x 1032 ergs

3.8 x 1032ergs

ar11112

Ar11112 at 1650 UT

8.5 x 1031ergs − 1.1 x 1031ergs = 7.4 x 10 31ergs

8.7 x 1031ergs

Β total − Β free = Β potential

Lower bound on the free energy of

8.25 x 1030ergs

Conclusion

-The four different wavelengths agree well with each other.

-This method is in good agreement with some other methods of energy calculation.

References

Special Thanks to

Dr. Dana Longcope and

Lucas Tarr for programming help

Malanushenko, A., Longcope, D. W., & McKenzie, D. E. “ Reconstructing the Local Twist of Coronal Magnetic Fields and the Three-Dimensional Shape of the Field Lines from Coronal Loops in EUV and X-Ray Images” 2009, ApJ, 707, 1044

Longcope, D. W., Mulanushenko, A., “Computing Magnetic Energy from Coronal Imaging Data” 2012, journal of Still Working On It, 24, 456

Tarr, L., Longcope,D., “Calculating Energy Storage Due To Topological Changes In Emerging Active Region NOAA AR 11112” 2012, ApJ, 749:64

Monte Carlo method. (2012, August 6). In Wikipedia, The Free Encyclopedia. Retrieved 16:24, August 6, 2012, from http://en.wikipedia.org/w/index.php