Marcin Gruszecki

1
Magnetacoustic shock formation near a magnetic
null point

• Marcin Gruszecki
• S. Vasheghani Farahani, V. Nakariakov, T. Arber

2
Outline of my talk

1. Introduction,
2. Specific questions,
3. Numerical setup,
4. Numerical results,
5. Conclusions.

3
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)
• Craig Watson (1992) considered waves in the
  neighbourhood of X-point. They showed that waves
  generate an exponentially large increase in the
  current density.
• 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.

4
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.

5
Analitical model
Numerical result s were obtained with use LARE2D
code (Arber T. et al. 2001)
6
Initial setup
B B0 x/L, -y/L, 0
? kg/m3 B T T K cs Mm/s VA Mm/s ß
10-12 10-3 6105 0.129 0.9 0.025
7
Initial pulse
c.f. McLaughlin et al. 2008
8
Comparison of numerical results with linear
analitical solution
A00.01
A0 0.1
A0 0.5
A0 1
Analitical solution
Larger amplitude waves travel faster
9
Creation of shock
0.8s
0.6s
0.4s
1.4s
1.0s
0.7s
10
Paremetric studies
0.9exp(-0.9x)
0.35ln(x)0.91
11
Conclusions

• 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.
• Small amplitudes pulse are coincide with the
  linear analytical
• solution Craig and McClymont (1991).
• 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.

12
Thank you ?