Initiation of Alfvénicturbulence by Alfvén wave

collisions: a numerical study

Sergei Shestov1,3, Yuriy Voitenko2, Andrei Zhukov1,41 – Royal Observatory of Belgium; 2 – Royal Belgian Institute for Space Aeronomy;

3 – Lebedev Physical Institute, Moscow, Russia; 4 – Skobeltsyn Institute of Nuclear Physics, Moscow, Russia

Solar-Terrestrial Centre of ExcellenceSIDC, Royal Observatory of Belgium

Outline

• Alfvénic turbulence• Physical conditions• Numerical setup• Analysis:

• Spatial distribution of v;• Fourier components;

• Conclusions

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Alfvénic turbulence in plasma

Iroshnikov (1963), Kraichnan (1965)

and followers … Ng&Battacharge 1996Howes&Nielson 2013 …

• Interaction between counter-propagating AWs;

• 𝒛− = 𝒖 − 𝒃4πρ

• 𝒛+ = 𝒖 + 𝒃4πρ

• Transfer of energy to smaller ⊥ scales – larger 𝒌Ʇ ;

incompr. MHD

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Alfvénic turbulence in plasma

Necessary conditions:

𝒛− = 𝒖 − 𝒃4πρ

• 𝒌‖ towards B0• 𝒌Ʇ ̶ nonunif. along y-axis• zx-polarization

𝒛+ = 𝒖 + 𝒃4πρ

• 𝒌‖ anti B0• 𝒌Ʇ ̶ nonunif. along x-axis• zy-polarization

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Alfvénic turbulence in plasma

𝒛+ = 𝒖 + 𝒃4πρ 𝒛− = 𝒖 − 𝒃

4πρ

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Animation

Alfvénic turbulence in plasmaIroshnikov (1963), Kraichnan (1965) and followers

• Interaction between counter-propagating AWs;• 𝒛− = 𝒖 − 𝒃

4πρ

• 𝒛+ = 𝒖 + 𝒃4πρ

• Transfer of energy to smaller ⊥ scales – larger 𝒌Ʇ ;

incompr. MHD

MHD eqs. -> Elsasser form𝜕𝑧±

𝜕𝑡 ∓ 𝒗𝐴 ∙ 𝛻 𝑧± + 𝑧∓ ∙ 𝛻 𝑧± = −𝛻𝑃𝜌0

…𝑘⊥+ + 𝑘⊥− = 𝑘2

(0)

𝑘⊥±+𝑘2

(0)=𝑘⊥3±

Efficiency should depend on:• Relative scales λ‖ and λ⊥;• Amplitudes 𝑧+ and 𝑧−;

From Howes & Nielson 2013

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Numerical setup

• MPI-AMRVAC, 3D MHD- B0 =20 Gauss- ne=109 cm-3

- T = 1 MK;- vA = 1 380 km/s;- 𝛽 = 0.017;

Lz=50 Mm; Lx,Ly = 2λ⊥;Sensitive to grid size (256x256x512), method (tvdlf, woodward).

• Perturbations:u = 0.1vA; b = 0.1B0;λ‖=10 Mm;λ⊥=0.3, 0.75, 1.5, 7.5, 37.5 Mm;

z+ wave

z- wave

z+ wave

z- wave

B0

Early phase Late phase

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Expected results and possibilities for analysis

Waves with new 𝒌Ʇ are produced. They propagate with vA together with mother waves;

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Perturbation of vx profiles

λ⊥=1.5 Mm; λ⊥=0.75 Mm; λ⊥=0.3 Mm;

λ‖=10 Mm;

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Perturbation of vx and vy profiles

λ⊥=0.75 Mm;

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Perturbation of vx and vy profiles

λ⊥=0.75 Mm;

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Spectral components

kx

ky

Fourier space No variation 1 period 2 periods

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Spectral componentskx

ky

Fourier space No variation 1 period 2 periods

𝑣𝑦 (simul.)𝑣𝑥 (simul.)

case

1 –

larg

eλ ⊥

case

2 –

smal

lλ ⊥

Single wave (no z+)

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Conclusions

• Alfvén wave collisions – interaction of counter-propagating Alfvén waves in MHD;

• Necessary conditions – ⊥ wavefrontnonuniformities (𝒌Ʇ);

• New waves with smaller ⊥ scales are generated (higher 𝒌Ʇ);

• Efficiency depends on ⊥/‖ scales;

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Thank you for attention!