Structure, Equilibrium and Pinching of Coronal Magnetic Fields
Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field
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Transcript of Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field
Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic
FieldGeorge Fisher1, Mark Cheung2, Marc DeRosa2,
Maria Kazachenko1, Brian Welsch1, Todd Hoeksema3, Xudong Sun3, and the SDO vector
magnetogram team
1Space Sciences Lab, UC Berkeley2Lockheed Martin Solar and Astrophysics
Laboratory3Stanford University
SHINE Meeting ~ 25 June 2012 ~ Maui, HI
Electric Fields at the photosphere provide
critical information for driving time-dependent
models of the solar magnetic field
We illustrate this concept by using one of the simplest possible magnetic field models
possible for the solar corona, the magneto-frictional model.
Magnetofrictional Scheme
Solve
Velocity proportional to Lorentz forceimplemented via , where is a frictional coefficient that determines relaxation timescale
Was originally implemented in a solar context by Yang, Sturrock & Antiochos (1986) and Craig & Sneyd (1986)
Magnetofrictional Scheme
Our implementation evolves vector potentialvia (guarantees and also allows relative helicity to be calculated easily)
Evolved forward in time using explicit 2nd-order derivatives, spatial discretization on a Yee (1966) grid
Follows scheme pioneered by van Ballegooijen, Priest & Mackay (2000)
Magnetofrictional Scheme
Boundary conditions specified in terms of vector potential at lower boundary; sides and top boundaries are open
We take the approach of using a temporal sequence of magnetogram data to drive the simulation
Others have also used a time-dependent Boundary Conditions with a MF scheme, e.g., Yeates, Mackay & van Ballegooijen (2008)
Data-driven Modeling of AR 11158
Evolving magneto-frictional scheme enables the construction of time-dependent models of active region coronae
Modeled fields respond to photospheric driving and energy inputs
Allows measurement of buildup of free energy and helicity in response to such driving
AR 11158 on disk from 2011 February 10 – 19 or so
Lower Boundary
Need to determine at lower boundary
Here, we use that were determined by and using methods of Fisher et al. (2012), which make use of time series of Doppler and vector field measurements from HMI. See poster by Kazachenko et al. at this meeting.
AR11158 produced an X2.2 flare on 2011-02-15 01:45
Electric Field Inversion
We decompose the partial time derivative of the magnetic vector field B into two unknown functions, the Poloidal and Toroidal potentials. This is the
origin of the name Poloidal-Toroidal Decomposition, or PTD.
Each of the three variables of the right-hand equation above obeys a 2-d Poisson equation, which depends directly on the magnetic
data:
See Fisher et al. 2010 (ApJ 715, 242)
Electric Field Inversion
From which we infer that:
The potential function(s) are very important! Without the potential functions, the PTD electric field does a poor job of reconstructing the actual field in MHD simulation test cases. Currently, we include the following terms in our
inversions: The second and third terms represent non-inductive
contributions from Doppler shifts, and pattern-motions (derived from e.g. FLCT or DAVE), respectively, from
which the inductive contributions have been
removed. The fourth term is used to enforce the condition
EB=0.
See Fisher et al. 2012, Sol. Phys. 277, p153 for details. More information about these
techniques can be found in Maria Kazachenko’s poster in the 2012 SHINE meeting.
Faraday’s law says:
Caveats and cautions
Consider these as numerical experiments
No momentum or energy equation solved (no concern for heating, radiative losses, etc.)
Cartesian domain (curvature ignored)
Initialized using potential field
AR 11158
HMI line-of-sight magnetograms, remapped onto a co-rotating Cartesian reference frame
Emissivity of fieldlines is prop. to
AR 11158 modeltop view views from sides
Emissivity of fieldlines is prop. to
AR 11158 modeltop view views from sides
Emissivity of fieldlines is prop. to
AR 11158 modeltop view views from sides
AR 11158 model
Free energy of order 15% or 20% of potential field
free energy
pot’l energy
total energy
AR 11158 model
R
X2.2 flare
Summary
Magnetofriction provides a way to perform numerical experiments of data-driven coronal magnetic field evolution
Applied scheme to AR11158, using time series of HMI Doppler and vector magnetogram data to drive the model
Can study buildup of free energy and helicity in the model and the possible ejection of flux