1) Simulations were conducted of the decay of various helical and non-helical magnetic knot configurations, including trefoil knots, IUCAA knots, and Borromean rings. 2) The decay was slower for configurations with higher magnetic helicity, as these knots were more strongly packed. This led to different decay slopes for different configurations. 3) Reconnection events transformed magnetic self-linking into twisting, approximately conserving magnetic helicity over time. Isolated helical structures that formed also inhibited energy decay.

1. Decay of helical and non-helical
magnetic knots
Simon Candelaresi and Axel Brandenburg
Submitted to Phys. Rev. E

2. Magnetic Helicity
Realizability condition:
Magnetic energy is bound from twisted field
below by magnetic helicity.
magnetic helicity
conservation
trefoil knot

3. Helical and non-helical setups
Trefoil knot IUCAA knot Borromean rings
Compare with
(Del Sordo et al. 2010):

4. Simulations
● mesh point
● Isothermal compressible gas
● Viscous medium
● Periodic boundaries

5. Helicity of n-foil knots

6. Linking number
Number of crossings
increases like
Sign of the crossings
for the 4-foil knot

7. Magnetic energy decay
Slower decay for higher .

8. Realizability condition
Realizability condition more important for high .

9. Helicity vs. energy
Knot is more strongly
packed with increasing .
Magnetic energy is closer to
its lower limit for high .

10. Magnetic helicity conservation
Magnetic helicity is approximately conserved.
Self-linking is transformed into twisting after reconnection.

11. IUCAA knot
Parametrization:
Asymmetry due to parametrization

12. Field ejection

13. Field ejection
Magnetic field ejection Isolated helical structures

14. Decay comparison

15. Reconnection characteristics
Conversion of linking into twisting
Ruzmaikin and Akhmetiev (1994)

16. Reconnection characteristics
3 rings Twisted ring + 2 twisted rings
interlocked rings

17. Conclusions
● Stronger packing for high leads to different decay slopes.
● Higher order invariants?
● Non-forced ejection of magnetic field
● Isolated helical structures inhibit energy decay
● Reconsider realizability condition

18. References
Del Sordo et al. 2010
Fabio Del Sordo, Simon Candelaresi, and Axel Brandenburg.
Magnetic-field decay of three interlocked flux rings with zero linking number.
Phys. Rev. E, 81:036401, Mar 2010.
Ruzmaikin and Akhmetiev 1994
A. Ruzmaikin and P. Akhmetiev.
Topological invariants of magnetic fields, and the effect of reconnections.
Phys. Plasmas, vol. 1, pp. 331–336, 1994.