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Turbulent Generation of Large Scale Magnetic Fields in Unmagnetized Plasma

Explore the self-consistent modeling and non-linear dynamics of magnetic field generation in unmagnetized plasma through reconnection and turbulence phenomena. Includes comparisons to electrostatic drift wave turbulence and investigations into large-scale drift-type wave structures.

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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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