![Page 1: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/1.jpg)
Current Formation DuringMagnetic Field Relaxation
Simon Candelaresi, David Pontin, Gunnar Hornig
![Page 2: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/2.jpg)
Force-Free Magnetic Fields
2
Parker: Equilibrium with the same topology exists onlyif the twist varies uniformly along the field lines.Strongly braided fields → topological dissipation.
Braided fields from foot point motion complex enough.
NASASolar corona: low plasma beta and magnetic resistivity
Force-free magnetic fields
Minimum energy state
(Parker 1972)
(Parker 1983)
Solutions possible with filamentary current structures (sheets).(Mikic 1989, Low 2010)
![Page 3: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/3.jpg)
Methods
3
Own GPU code GLEMuR: (https://github.com/SimonCan/glemur)
Preserves topology and divergence-freeness.
Magneto-frictional term:
(Craig and Sneyd 1986)
Frozen in magnetic field(Batchelor, 1950)
(Hyman, Shashkov 1997)
Ideal (non-resistive) evolutionuse Lagrangian method
Fluid with pressure:
Fluid with inertia:
For use mimetic numerical operators.
(Candelaresi et al. 2014)
![Page 4: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/4.jpg)
4
Simply Twisted Fields
Magnetic streamlines:
(Candelaresi et al. 2014)
![Page 5: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/5.jpg)
Highly Braided FieldsSufficiently highly braided according to Parker.
Force-free state is not reached.
Current layers well resolved.
5(Candelaresi et al. 2015)
![Page 6: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/6.jpg)
6
Distorted Magnetic Fields
(Longbottom 1998)
resolved current concentrations
shear leads to strong currents
(Candelaresi et al. 2015)
![Page 7: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/7.jpg)
7
Magnetic Nulls
(Syrovatskiĭ 1971; Pontin & Craig 2005; Fuentes-Fernández & Parnell 2012, 2013; Craig & Pontin 2014)
Singular current sheets observed at magnetic nulls (B = 0)
singular current sheets at magnetic nulls
Pressure cannot balance singularity.
![Page 8: Current Formation During Magnetic Field Relaxation](https://reader036.vdocuments.us/reader036/viewer/2022062406/55b3a786bb61eba40a8b458b/html5/thumbnails/8.jpg)
Conclusions
● Topology preserving relaxation of magnetic fields.
● Current concentrations not singular.
● Current increases strongly with field complexity.
● Singular currents at magnetic nulls.