Waves generated by
rapid reconnection
Alan Hood,
Eric Priest,
Kuan Tam
University of St Andrews
18 November 2010
Reconnection Waves
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Rapid dissipation of J sheet.
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Rapid dissipation of line J.
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Taylor relaxation and
avalanches.
Alan Hood University of St Andrews
18 November 2010
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Longcope and Priest, 2007
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Initial state: finite current sheet in potential field
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Enhanced resistivity
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Current sheet disappears
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Outward linear wave triggered
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Leaves reconnection flows
Reconnection Waves
Alan Hood University of St Andrews
18 November 2010
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Initial magnetic field
Reconnection Waves
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18 November 2010
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Initial current sheet
Reconnection Waves
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Linear equations
∂U
∂t
∂2C
∂t2
∂C
,
∂r ∂C
∂ 1 ∂2C
2 ∂
= ωA r
r
+ ηr
.
∂r
∂r
∂r r ∂r∂t
2
= ωA
r
U is perpendicular velocity. C = rBφ = −∂A1 /∂r is total current
inside radius r.
Diffusion region near r = 0, then fast mode.
How does it evolve non-linearly?
Reconnection Waves
Alan Hood University of St Andrews
18 November 2010
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Non-linear equations
ρ
Dv
Dt
∂ρ
+ ∇ · (ρv)
∂t
∂B
∂t
p
ργ D
γ − 1 Dt ργ
p
= −∇p + j × B,
(1)
= 0,
(2)
= ∇ × (v × B) − ∇ × (η∇ × B),
(3)
= ηj 2 + Qvisc ,
(4)
= ρRT.
(5)
Note if p is zero initially, it can’t remain zero due to Ohmic
heating. In fact need p inside current sheet!
Reconnection Waves
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18 November 2010
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Pressure
(2Dpressure.mpeg)
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18 November 2010
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Current
(2Dcurrent.mpeg)
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Velocity
(2DmodV.mpeg)
Reconnection Waves
Alan Hood University of St Andrews
18 November 2010
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Try a finite line current
Take a cylindrical field.
◮
Assume axial current (goes smoothly to zero at r = a.)
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Calculate Bθ (r) and p(r) for equilibrium.
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Note assume rapid diffusion of J.
◮
Pressure gradient generates an outflow.
Reconnection Waves
Alan Hood University of St Andrews
18 November 2010
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Initial pressure gradient
Reconnection Waves
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Velocity profiles at two times
Reconnection Waves
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Velocity profile and estimate
Check ”LineVelocity magnitude”.
Reconnection Waves
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18 November 2010
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Line current: Velocity cut
(Velocity.mov)
Reconnection Waves
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18 November 2010
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Perpendicular fast shock
Reconnection Waves
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18 November 2010
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Shock: Internal structure
Reconnection Waves
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18 November 2010
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Taylor Relaxation: Two loops
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Taylor relaxation can heat coronal loops.
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Ideal MHD kink instability gives reconnection and heat.
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This models a nanoflare.
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High temperature and field restructuring.
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Can one event trigger another in nearby stressed loop?
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Start with two loops.
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First instability sends out fast waves to destabilise second
loop?
Reconnection Waves
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18 November 2010
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Taylor relaxation: Temperature
(Case8temperature.mpg)
Reconnection Waves
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18 November 2010
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Taylor relaxation: Fieldlines
(Case3fieldlines.mpeg)
Reconnection Waves
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18 November 2010
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Reconnection Waves
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Reconnection Waves
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Reconnection Waves
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Reconnection Waves
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Reconnection Waves
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18 November 2010
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Magnetic, kinetic and internal energies
Reconnection Waves
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18 November 2010
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Taylor relaxation: Two loops
(newcase1cd.mp4)
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18 November 2010
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Taylor relaxation: Two loops and velocity cut
(vx.mpg)
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