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