Magnetacoustic shock formation near
a magnetic null point
Marcin Gruszecki
S. Vasheghani Farahani, V. Nakariakov, T. Arber
Outline of my talk
1.Introduction,
2.Specific questions,
3.Numerical setup,
4. Numerical results,
5. Conclusions.
Introduction
Interaction MHD waves with magnetic null points is interesting in the context of flare
triggering and generation of quasi-periodic pulsations (e.g. through the generation of
current density spikes and hence anomalous resistivity)
1) Craig & Watson (1992) considered waves in the neighbourhood of X-point. They
showed that waves generate an exponentially large increase in the current density.
2) Ofman et al (1993) studied reconnection and relaxation of 2D X-point using resistive
MHD equations. They showed that the interaction between the plasma flow velocity
and the magnetic field is the important physical effect.
3) McLauglin & Hood in series of papers investigated behaviour of fast MHD waves
near X-point. They concluded that waves are refracted around and accumulated at
the null point.
Specific questions
1. Study the effect of nonlinear steepening of a fast magnetoacoustic wave near a
null point.
2. Find a distance of magnetoacoustic shock formation from the magnetic null point
as a function of initial wave length, amplitude.
3. What kind of pulses can reach the magnetic null point and ignite the magnetic
reconnection, i.e. seed the anomalous resistivity close enough to null point. Can
it explain the phenomenon of sympathetic flares.
4. Compare numerical results with the linear analytical solution.
Analitical model
 


   V  0
t



 
V
1

  V   V  p    B  B
t


 
B
  V  B
t




 V     p  V
t

B  0







p
 (  1)
Numerical result s were obtained with use LARE2D code (Arber T. et al. 2001)
Initial setup
B = B0 [x/L, -y/L, 0]
ρ [kg/m3]
B [T]
T [K]
cs [Mm/s]
VA [Mm/s]
β
10-12
10-3
6·105
0.129
0.9
0.025
Initial pulse
2
2

By
x

y
 r1 

Vx  A0  sin  
 2

 Bx  B y2
r0


2
2

x

y
 r1 
B

V y   A0  sin  
 2 x 2

 Bx  B y
r0


r1  x 2  y 2  r1  r0
c.f. McLaughlin et al. 2008
Comparison of numerical results with
linear analitical solution
A0=0.01
A0 = 0.1
A0 = 0.5
A0 =1
Analitical solution
Larger amplitude waves travel faster
Creation of shock
0.8s
0.6s 0.4s
1.4s
1.0s
0.7s
Paremetric studies
0.9·exp(-0.9·x)
0.35·ln(x)+0.91
Conclusions
1. We showed the creation of shock fast magnetoacoustic wave in vicinity of magnetic
X - point. The shock is accompanied with a spike of current density, hence anomalous
resistivity can be generated.
2. Small amplitudes pulse are coincide with the linear analytical
solution Craig and McClymont (1991).
3. Larger amplitude waves propagate faster.
4. We performed parametric studies by varying both width and strength of the initial
pulse. Only wider and small amplitude pulses can reach magnetic X - point before
overturning and ignite magnetic reconnection.
5. Narrower and high amplitude pulses overturn faster.
Thank you 