Global Simulations of Astrophysical Jets in Poynting Flux
Dominated Regime
Hui Li
S. Colgate, J. Finn, G. Lapenta, S. Li
Engine; Injection; Collimation; Propagation; Stability; Lobe Formation; Dissipation; Magnetization of IGM
Leahy et al.1996
I. Engine and Injection
Approach: Global Configuration Evolution without modeling the accretion disk physics. Replace accretion disk with a “magnetic engine” which pumps flux (mostly toroidal) and energy.
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Flux fn. (cylin.) Ψ = r2 exp(−r2 − k 2z2)
B =
Br = 2k 2z r exp(−r2 − k 2z2)
Bz = 2(1− r2) exp(−r2 − k 2z2)
Bφ =f (Ψ)
r = α r exp(−r2 − k 2z2)
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
q(r) = krBzBφ
= 2k(1− r2)
α
Mimicking BH-Accretion System? : Initial poloidal fields on “disk”, exponential drop-offf() : B profile, or disk rotation profile : toroidal/poloidal flux ratioJxB : radial pinching and vertical expansionJpxBp: rotation in direction, carrying angular momentum?
=5
=0.1
=3
Li et al.’05
Problems:No disk dynamicsFootpoints allowed to move, though could be in equilibriumNot precisely KeplerianMass loading?Dipole or Quadrupole
Injection
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∂B
∂t= B(r,z) γ(t)
1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:
3) Adding twists, self-consistently collimate and expand.
Impulsive Injection: Evolution of a highly wound and compressed magnetic “spring” Continuous Injection: Evolution of “magnetic tower” with continuous injected toroidal and/or poloidal fields
II. Collimation; Propagation
Run A: impulsive injection, =50 vinj >> vA > cs
Run B: continuous injection, =3, =3 vA > cs, scanning through (vinj)
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Run A
|B| at cross-section
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Run A
Total |B|
Current density
Run A Run A-2Kinetic KineticMagneti
cMagnetic
III. Stability and Lobe Formation
Dynamic: moving, q-profile changing
3D Kink unstable in part of helix: twist accumulation due to inertial/pressure confinement
Pressure profile: hollow
Velocity profile ?
radius
height
Pressure EvolutionIn Implusive
Injection Case
Azimuthally averaged
Poloidal Flux (n=0)
radius
height
3D Flux Conversion
Continuous Injection
radius
height
Azimuthally Averaged
Poloidal Flux
Run B: Continuous Injection
Injected toroidal flux vs time
Poloidal flux at disk surface
Z (height)
T=0
T=4 T=8 T=12
T=16
B flux
A Moving “Slinky”
T=0 T=3
T=5 T=10
pressure
height
HelixStability
radius
Lobe Formation
Continuous Injection
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∂B
∂t= Bφ(r,z) γ (t)
1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:
3) Adding twists, self-consistently collimate and expand.
Time
B flux
Kink unstable
High Injection Rate
Kink unstable
Conclusion: Lessons Learned
Field lines must “lean” on external pressure, concentrating twists to the central region --- collimation.
a) Static limit:
Expansion is fast, reducing the toroidal field per unit height. Velocity difference between the base and the head causes the head to undergo 3D kink, forming a fat head --- lobes (?).
b) Impulsive injection limit:
c) Continuous injection: Non-uniform twist distribution along height. Map out the dependence on injection rates.
In all cases, external pressure plays an important “confining” role, helping collimation and stability.