Solar Applications of the Space Weather

Modeling Framework

R. M. Evans1,2, J. A. Klimchuk1

1NASA GSFC, 2GMU

February 2014 SDO AIA 171 Å

Bart, Igor, Chip, Rona, Gabor, Meng, Ofer, Noé, Zhenguang,

Darren, Rich, Lars, and Tamas

Thank you!

February 2014 SDO AIA 171 Å

Introduction• The formation and disruption of current sheets • Applies to many domains and problems in heliophysics• Coronal loops are bright structures in EUV and X ray images

– A variety of observations indicate that both loops and the diffuse emission between loops are heated by impulsive bursts of energy, called nanoflares

3

• What are the critical onset conditions for current sheet disruption, and are they different in the chromosphere and corona?

• How does the coupling between the chromosphere and corona affect the disruption?

• At what height in the atmosphere is the disruption likely to occur?

Rebekah M. Evans October 14, 2014 SWMF User Meeting

July 2012 SDO/AIA

Approach: leverage experience and existing problem type

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REGIONAL Flux Emergence Model (ModUserEe)

Rebekah M. Evans October 14, 2014 SWMF User Meeting

GLOBAL Solar Corona Model (ModUserScChromo)

REGIONAL Coronal Loop Model with Chromosphere (ModUserTbd)

Fang et al. 2012

g

Schematic of a semicircular loop, straightened out with a modified profile for

gravity.

Simulation Set Up

5

Base of Chromosphere

Loop Top

Base of Corona

Rebekah M. Evans October 14, 2014 SWMF User Meeting

€

Z Gravitational acceleration

New Initial Conditions

6

€

Z

Rebekah M. Evans October 14, 2014 SWMF User Meeting

Tchromo

Tcorona

Lchromo

Lcorona

Specify:Bz

New Initial Conditions

7

€

Z

Rebekah M. Evans October 14, 2014 SWMF User Meeting

Steady State Atmosphere

Calculate Q* and Ncorona using static equilibrium

loop scaling laws;ρcorona from ideal gas law

Calculate Q* and Ncorona using static equilibrium

loop scaling laws;ρcorona from ideal gas law

Hydrostatic extrapolation using Pcorona and Tchromo

(H~500 km) to find base pressure Pchromo

Hydrostatic extrapolation using Pcorona and Tchromo

(H~500 km) to find base pressure Pchromo

*Q is the background volumetric heating. We use density-

dependent heating for T<Tchromo

Tchromo

Tcorona

Specify:Bz

Lchromo

Lcorona

Existing capabilitiesModEquationMhd (single fluid)

• Optically thin radiative energy loss

User-defined

loss function

• Field-aligned collisional heat flux

• User-defined source terms to energy, momentum equations– Gravity and Volumetric heating function

• AMR – Static atmosphere and Current sheet formation

8Rebekah M. Evans October 14, 2014 SWMF User Meeting

Radiative loss function Radiative loss function

Rad

iati

ve

Lo

ss F

un

ctio

n

Klim

chuk

, R

aym

ond

€

Qrad = ni neΛ Te( ) = n2Λ Te( )

€

qe = −κ 0Te5

2∇Te Simulation time increases significantly

Temperature

Challenge: Boundary conditions IDesired features for top/bottom plasma BCs: force

balance across the boundary (no mass flow)

• BATSRUS options for BCs base of chromosphere:– ‘reflect’, ‘float’, ‘fixed’, ‘linetied’

• Implemented user BC– Hydrostatic extrapolation of pressure into ghost cells using

Temp. in first internal cell. Density calculated from p, Temp

– As the simulation approaches SS, pressure increases somewhat at the boundary and total mass of system increases

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k=-1

Rebekah M. Evans October 14, 2014 SWMF User Meeting

k=1

k=0

k=2

€

Z

• Future – solve for the actual force balance (may be too complicated)

€

∇p

€

ρg

€

p−1 = p0 = p1

€

p0 = p1 exp zH −1( )

€

ρUz( )0

= − ρUz( )1

€

ρUz( )0

= − ρUz( )1

€

p−1 = p0 = PressBase Sides are periodic

Challenge: Boundary conditions II

10Rebekah M. Evans October 14, 2014 SWMF User Meeting

Desired features for top/bottom BCs: create a current sheet by adding energy into the system via a shear flow at the boundary

• BATSRUS options for shearing BCs:

– ‘shear’: instructions to only use for specific problem type (shock tube) – Eruptive event, breakout - not clear how to easily work into generic ModUser

• Implemented BC:

• No magnetic flux transport through boundary

€

Uy (x,z = ±LZ 2 ) = ±U0 cosπx

Lx

⎛

⎝ ⎜

⎞

⎠ ⎟tanh

x

w

⎛

⎝ ⎜

⎞

⎠ ⎟

- Shearing speed U0=0.01vA,corona

- Current sheet half width w=0.001Ly

- Ramp up time - Apply in both ghost cells

w/Ly=0.01w/Ly=0.001

X [km]U

y [k

m/s

]

€

Bx( )0

=ρ 0

ρ1

Bx( )1

€

Bz( )−1,0

= Bz,input

€

By( )0

=ρ 0

ρ1

By( )1

Simulation at the end of the ramp up (t=10 minutes)

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w ~200 kmw ~200 km

UyUy

ByBy

JzJz

At the lower boundary: Velocity and magnetic shear, and the resulting current sheet

At the lower boundary: Shear profile and resulting magnetic field

Rebekah M. Evans October 14, 2014 SWMF User Meeting

Required feature - AMR• Currently using:

– Static atmosphere (4 AMR levels)

• dz= 24 km in TR

• ~4 million cells

– Current sheet (5 AMR levels)• > 10 million cells

12Rebekah M. Evans October 14, 2014 SWMF User Meeting

Using AMR to refine TR

Cell Number

€

J 2

€

gradlogρ

Z (km)

Cel

l S

ize

(km

)C

ell

Siz

e (k

m) corona

corona

TR

TR 24 km

375 km

Required feature - AMR• Currently using:

– Static atmosphere (4 AMR levels)

• dz= 24 km in TR

• ~4 million cells

– Current sheet (5 AMR levels)• > 10 million cells

• Desire – flexible AMR criteria to give length scales for any quantity

13Rebekah M. Evans October 14, 2014 SWMF User Meeting

• Desire – AMR criteria selection in PARAM.in normalized to the maximum value in the simulation

Using AMR to refine TR

Cell Number

€

BydBy

dx

€

J 2

€

gradlogρ

Z (km)

Cel

l S

ize

(km

)C

ell

Siz

e (k

m) corona

corona

TR

TR

Challenge: Grid Optimization• Direction-specific

AMR– Current capability: one

direction, must be specified during configure – we are still thinking about how to take advantage of this

– Desire: variable during runtime

• Aspect ratio of cells – Current capability: can

be stretched, but fixed from grid initialization

– Desire: variable in time, and in the domain

14Rebekah M. Evans October 14, 2014 SWMF User Meeting

CoronaTRChromo.

Early times

As current sheet forms

As current sheet disrupts

€

Z

€

X

Needs for the future• Short term:

– 3d file saving issue (Tecplot) may be resolved• Field lines, domain

– Energy balance issue (Jim will discuss more)

– Need S>10,000, CS aspect ratio >100

– Assistance w/ higher order schemes (spatially fifth-order MP5 limiter)

– Subcycling and Part-Steady scheme may be useful

• Long term:– Neutrals (multi-fluid) – Jim will discuss more

– Resistivity: T-dependent, B-dependent, Pederson (cross-field)

• General feedback– Tecplot output is used

– Easier way to make user-defined plot variables (ex: source terms in En. Eq)

– Making the code run faster is always good

15Rebekah M. Evans October 14, 2014 SWMF User Meeting