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Magneto-acoustic waves in an asymmetric magnetic slab Progress in - - PowerPoint PPT Presentation
Magneto-acoustic waves in an asymmetric magnetic slab Progress in - - PowerPoint PPT Presentation
Magneto-acoustic waves in an asymmetric magnetic slab Progress in spatial magneto-seismology Matthew Allcock and Robertus Erd elyi Solar magneto-seismology Observations Solar magneto-seismology Wave parameters Observations Equilibrium
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Solar magneto-seismology
Observations Equilibrium parameters Wave parameters
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Solar magneto-seismology
Observations Equilibrium parameters Wave parameters Temporal parameters Spatial parameters
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models Eigenmodes
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models Eigenmodes Temporal magneto-seismology Spatial magneto-seismology
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models Eigenmodes Temporal magneto-seismology Spatial magneto-seismology
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models Eigenmodes Temporal magneto-seismology Spatial magneto-seismology
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Solar magneto-seismology
Observations Physical understanding Equilibrium parameters Wave parameters Temporal parameters Spatial parameters Equilibrium models Eigenmodes Temporal magneto-seismology Spatial magneto-seismology
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Motivation
Max Planck Institute for Solar System Research BBSO/NJIT
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Equilibrium conditions
−x0 x0 x z y
ρ1, p1, T1 ρ0, p0, T0 ρ2, p2, T2
Uniform magnetic field in the slab. Field-free plasma outside. Different density and pressure on each side.
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Governing equations
Ideal MHD equations: Conservation of: ρD✈ Dt = −∇p − 1 µ❇ × (∇ × ❇), momentum ∂ρ ∂t + ∇ · (ρ✈) = 0, mass D Dt p ργ
- = 0,
energy ∂❇ ∂t = ∇ × (✈ × ❇), magnetic flux
✈ = plasma velocity, ❇ = magnetic field strength, ρ = density, p = pressure, µ = magnetic permeability, γ = adiabatic index.
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Asymmetric slab modes
Dispersion relation:
ω4m02 k2vA2 − ω2 + ρ0 ρ1 m1 ρ0 ρ2 m2(k2vA2 − ω2) − 1 2m0ω2 ρ0 ρ1 m1 + ρ0 ρ2 m2
- (tanh m0x0 + coth m0x0) = 0,
m02 = (k2vA2 − ω2)(k2c2
0 − ω2)
(c2
0 + vA2)(k2cT 2 − ω2) ,
m1,22 = k2 − ω2 c1,22 , cT 2 = c2
0vA2
c2
0 + vA2 ,
vA = B0 √µρ0 , See Allcock and Erd´ elyi, 2017.
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Asymmetric slab modes
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Asymmetric slab modes
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Asymmetric slab modes
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Amplitude ratio
ˆ ξx(−x0) ˆ ξx(x0)
−x0 x0 x
Amplitude ratio
RA := ˆ ξx(x0) ˆ ξx(−x0) (
Top = quasi-kink Bottom = quasi-sausage)
= +
−
ρ1m2 ρ2m1 (k2vA2 − ω2)m1
ρ0 ρ1 − ω2m0
tanh
coth
- (m0x0)
(k2vA2 − ω2)m2
ρ0 ρ2 − ω2m0
tanh
coth
- (m0x0)
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Minimum perturbation shift
−x0 x0 x −x0 x0 x −x0 x0
- ξx
x ∆min −x0 x0
- ξx
x ∆min
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Minimum perturbation shift
−x0 x0 x −x0 x0 x
Quasi-kink: Quasi-sausage:
∆min = 1 m0 tanh−1(D) ∆min = 1 m0 tanh−1 1 D
- where
D = (k2vA2 − ω2)m2
ρ0 ρ2 tanh(m0x0) − ω2m0
(k2vA2 − ω2)m2
ρ0 ρ2 − ω2m0 tanh(m0x0)
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Solar magneto-seismology
Parameter inversion
Observe: ω, k, x0, Ti, and RA or ∆min. Solve to find: vA and hence B0.
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Further work
Generalise the model to a variety of structures:
−x0 x0 x z y
ρ1, p1, T1 ρ0, p0, T0 ρ2, p2, T2
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Further work
Generalise the model to a variety of structures: Add magnetic field outside the slab - coronal structures. See Zs´ amberger and Erd´ elyi, published soon.
−x0 x0 x z y
ρ1, p1, T1 ρ0, p0, T0 ρ2, p2, T2
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Further work
Generalise the model to a variety of structures: Add magnetic field outside the slab - coronal structures. See Zs´ amberger and Erd´ elyi, published soon. Add steady flow - dynamic structures e.g. solar wind. See Mihai Barbulescu’s poster.
−x0 x0 x z y
ρ1, p1, T1 ρ0, p0, T0 ρ2, p2, T2
U0
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Future work
Apply to observations of MHD waves in, for example: Elongated magnetic bright points,
Adaptation of Liu et al., 2017, by N. Zs´ amberger
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Future work
Apply to observations of MHD waves in, for example: Elongated magnetic bright points, Prominences,
NASA
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Future work
Apply to observations of MHD waves in, for example: Elongated magnetic bright points, Prominences, Sunspot light walls.
Max Planck Institute for Solar System Research
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