Marcin Gruszecki S. Vasheghani Farahani, V. Nakariakov, T. Arber Magnetacoustic shock formation near...
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Transcript of Marcin Gruszecki S. Vasheghani Farahani, V. Nakariakov, T. Arber Magnetacoustic shock formation near...
Marcin GruszeckiMarcin Gruszecki
S. Vasheghani Farahani, V. Nakariakov, S. Vasheghani Farahani, V. Nakariakov, T. Arber T. Arber
Magnetacoustic shock Magnetacoustic shock formation near a magnetic formation near a magnetic
null pointnull point
Outline of my talkOutline of my talk
1.Introduction,
2.Specific questions,
3.Numerical setup,
4. Numerical results,
5. Conclusions.
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.
IntroductionIntroduction
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.
Specific questionsSpecific questions
Analitical modelAnalitical model
)1(
0
1
0
p
B
VpVt
BVt
B
BBpVVt
V
Vt
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
0122
1
220
122
0
220
122
0
sin
sin
rryxr
BB
B
r
ryxAV
BB
B
r
ryxAV
yx
xy
yx
yx
c.f. McLaughlin et al. 2008
Comparison of numerical results with linear analitical solution
Analitical solution
A0 =1
A0=0.01
A0 = 0.1
A0 = 0.5
Larger amplitude waves travel faster
Creation of shock
0.7s
1.0s
1.4s
0.4s0.6s0.8s
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