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Turbulent Generation of Large Scale Magnetic Fields in Unmagnetized Plasma

Turbulent Generation of Large Scale Magnetic Fields in Unmagnetized Plasma. Vladimir P.Pavlenko Uppsala University, Uppsala, Sweden. Coworkers. Zhanna N.Andrushchenko Martin Jucker. Outline. Some notes from Fluid Mechanics Motivation Modeling Self-consistent description

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Turbulent Generation of Large Scale Magnetic Fields in Unmagnetized Plasma

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  1. Turbulent Generation of Large Scale Magnetic Fields in Unmagnetized Plasma Vladimir P.Pavlenko Uppsala University, Uppsala, Sweden

  2. Coworkers • Zhanna N.Andrushchenko • Martin Jucker Workshop ’Reconnection and Turbulence’ Uppsala

  3. Outline • Some notes from Fluid Mechanics • Motivation • Modeling • Self-consistent description • Non-linear dynamics • Conclusions Workshop ’Reconnection and Turbulence’ Uppsala

  4. Description of flows in a turbulent media Workshop ’Reconnection and Turbulence’ Uppsala

  5. Motivations Strong magnetic fields - Solar flares Magnetic field diffusivity Reconnection - Laser produced plasma Strong fields produced in unmagnetized plasma 70’s: Laser fusion experiments: Strong magnetic field observed in unmagnetized plasma Magnetic electron drift modes Workshop ’Reconnection and Turbulence’ Uppsala

  6. Modeling: Assumptions Workshop ’Reconnection and Turbulence’ Uppsala

  7. Modeling: Equations Workshop ’Reconnection and Turbulence’ Uppsala

  8. Model equations Workshop ’Reconnection and Turbulence’ Uppsala

  9. Linear approximation • - purely growing for • - no linear instability for • - largest increment for Workshop ’Reconnection and Turbulence’ Uppsala

  10. Comparison to electrostatic drift wave turbulence • Two-field vs. One-field model • Electron skin depthvs. Ion Larmor radius with electrontemperature • Direct andinversecascadevs.Inverse cascade Workshop ’Reconnection and Turbulence’ Uppsala

  11. Large scale structures: Definitions • Zonal magnetic fields • Magnetic streamers Workshop ’Reconnection and Turbulence’ Uppsala

  12. Large scale magnetic fields generation Workshop ’Reconnection and Turbulence’ Uppsala

  13. Large scale structures: Workshop ’Reconnection and Turbulence’ Uppsala

  14. Self-consistent description • Define ”action-like invariant” or wave spectrum • Wave kinetic equation (WKE) • Doppler shifted frequency Workshop ’Reconnection and Turbulence’ Uppsala

  15. Non-linear dynamics Large scale Drift-type wave Structures turbulence Workshop ’Reconnection and Turbulence’ Uppsala

  16. Large scale fields generation - Recipe • Model equations • Wave spectrum • Quasi-linear analysis, linearized WKE • Response function • Dispersion relation Workshop ’Reconnection and Turbulence’ Uppsala

  17. Large scale field generation – Hydrodynamic regime • Hydrodynamic regime - Monochromatic wave packet - Instability criterion - Explicit frequency Workshop ’Reconnection and Turbulence’ Uppsala

  18. Large scale field generation – Kinetic regime • Kinetic regime - Resonance (purely growing) - Instability criterion Contrary to Langmuir turbulence Workshop ’Reconnection and Turbulence’ Uppsala

  19. Large scale field generation – Modulation instability • Modulation instability - Restart from basic model equations - Pump wave and flows - Triad interactions sidebands - Explicit frequency - Well known Lighthill criterion Workshop ’Reconnection and Turbulence’ Uppsala

  20. Large scale field generation - Summary • Explicit increments -Hydrodynamic regime - Modulational instability - Note • Instability criteria - Hydrodynamic, modulational - Kinetic regime Workshop ’Reconnection and Turbulence’ Uppsala

  21. Non-linear dynamics Large scale Drift-type wave Structures turbulance Workshop ’Reconnection and Turbulence’ Uppsala

  22. Shearing • Quasi-linear analysis • Wave kinetic equation • Diffusion in k-space, i.e. shearing • Large k Small scales Dissipation Workshop ’Reconnection and Turbulence’ Uppsala

  23. Large scale pattern and predator-prey phenomena • Reduction of the basic equations minimaldynamical model (zero-dimensional approach) with two principal components: small-scale waves (prey) + ”zonal” magnetic pattern (predator) + Lotka-Volterra system Workshop ’Reconnection and Turbulence’ Uppsala

  24. Predator-prey dynamics of the system composed of zonal magnetic pattern and wave turbulence Results of the numerical analysis Workshop ’Reconnection and Turbulence’ Uppsala

  25. Conclusions • Magnetic electron drift mode turbulence – model equations • Separation of scales: waves + ”fields” • Self-consistent description – wave kinetic equation • Waves ”Fields”: Generation • ”Fields” Waves: Shearing • Long term dynamics Predator-prey dynamics Workshop ’Reconnection and Turbulence’ Uppsala

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