2. Contents Introduction Force-Free Approximation Analytical Solutions
Simulations
Conclusions
Future Goals

3. Introduction Jets are plasma outflows extended for large distances.
They stay collimated for many Mpc in some cases.
Are observed in active galactic nuclei (AGN), neutron stars , young stellar object (YSO) etc.
Relativistic (AGN, Pulsar etc)
Non Relativistic (YSO, u~ Km/s)
The first jet observed was from the galaxy M87 in by Curtis.
Center for Magnetic Self Organization
in Laboratory and Astrophysical Plasmas

4. Active Galactic Nuclei
3C273(earthsky.org)
Cygnus A(NRAO)

5. Herbig-Haro
Carina Nebula(nasa.gov)
HH47(esa)

6. Most Important Papers
Tsinganos K.. Magnetohydrodynamic equilibrium. I - Exact solutions of the equations. 1981, ApJ, 245, 764.
Blandford R. D. and Payne D. G.. Hydromagnetic ows from accretion discs and the production of radio jets , MNRAS, 199, 883.
Contopoulos J., Lovelace R. V. E. Magnetically driven jets and winds: Exact solutions , ApJ, 429, 139
Bodo G., Massaglia S., Ferrari A., and Trussoni E.. Kelvin-Helmholtz instability of hydrodynamics supersonic jets , A&A, 283, 655.
Matsakos T., Tsinganos K., Vlahakis N., Massaglia, Mignone A., Trussoni E. Two-component jet simulations I:Topological stability of analytical MHD out-flow solutions , A&A, 477, 52.
Mizuno Y., Jose L. Gomez et al. Recollimation shock in magnetized relativistic jets , ApJ, 809, 38.

8. Force-Free (1) - - Ε<<B Force-Free momentum equation:
Relativistic momentum equation
In the force-free limit: -
- Ε<<B
Force-Free momentum equation:

9. Force-Free (2) We apply . We define Ρ as magnetic flux. Magnetic field
Ampere law
Transfield:
Where β(Ρ) is the current in a cross section at a height Z

10. Force-Free (3) Non linear equation. The function β(Ρ) is unknown.
No critical points.
Boundary conditions Ρ(0,z)=P(R,z)=0

11. Dunce's Cap Model Spherical coordinates Transfield:
We consider solutions as , where μ=cosθ and
Finally:
Solutions:

12. Results (1) We consider small angles Magnetic Fields: -
C4 is calculated from the pressure balance

13. Results (2)
Bφ Βθ
Lynden-Bell 2006 Br
Lynden-Bell 2006

14. Simulations All the simulations were executed with the pluto code.
The purpose of the simulation is to create magnetic towers based in Lynden-Bell’s idea.
We consider:
- Cylindrical coordinates with axial symmetry
- Ideal magnetohydrodynamics in 2 dimensions and 3 components
- Negligible gravity
- Polytropic gas with γ=5/3
- Non relativistic fluid
- Vφ=0 initially

15. Problem Set Up
We are based in Dunce's Cap model as an initial condition.
We consider
Magnetic fields: -
Where Ζο=0.5, wo=10^(-3), C4=2π

16. Problem Set Up (2) All variables are non dimensional.
Jet pressure Pj=0.0001
Environment pressure Pa=1/8π
Characteristic velocity Alfven

17. ρj=10, ρa=0.1, Vz=1

18. Recollimation

19. Magnetic Fields

20. Velocities

21. Mach
The
We consider k // Vp
We define

22. For β<1 the magnetic field dominates
Plasma β(1)
The
For β<1 the magnetic field dominates
For β>1 the thermal pressure dominates.

23. Plasma β(2)

24. Energies (1) Kinetic energy flux: Thermal energy flux: Poynting flux:
Kinetic to thermal ratio gives
Kinetic to Poynting ratio gives
Thermal to Poynting ratio gives plasma β

25. Energies(2)

26. ρj=0.1, ρa=1, Vz=5

27. Recollimation

28. Magnetic Fields

29. Velocities

30. Mach

31. Plasma β

32. Energies

33. Conclusions
In all simulations with subfast initial velocities the outflow couldn’t reach superfast velocities.
In the case with η=100 density ratio and superfast initial velocity
recollimation shocks appeared.
In the case with η=0.1 and η=1 density ratio and superfast initial velocities Kelvin-Helmholtz instabilities appeared.
In all simulations the initial magnetic energy is converted to thermal energy.
In all simulation the outflow became hydrodynamic.
The Dunce's Cap model is unsuitable to accelerate the outflows in superfast velocities and create magnetic towers. Very interesting solutions for jet propagation - Possible magnetic reconnection.

34. Future Goals Test the Bessel function solutions.
Make simulations with relativistic velocities.
Use non ideal MHD in order to test the magnetic reconnection hypothesis.

35. Thank you!