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MagnetoHydroDynamics: Numerical Simulation for Feedback Control of the Resistive Wall ModeRWM

22.012 Fusion and Plasma Physics Seminar. MHD. Dynamics of electrically conducting fluidsConcern specific to plasma is that the equations give equilibrium and stability conditionsMotivation: Avoid major disruptionsNavier-Stokes equations: Fluid DynamicsMaxwell's equations: Electromagnetism. 22.012 Fusion and Plasma Physics Seminar.

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MagnetoHydroDynamics: Numerical Simulation for Feedback Control of the Resistive Wall ModeRWM

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    1. 22.012 Fusion and Plasma Physics Seminar MagnetoHydroDynamics: Numerical Simulation for Feedback Control of the Resistive Wall Mode(RWM) Kevin Durand May 17,2007

    2. 22.012 Fusion and Plasma Physics Seminar MHD Dynamics of electrically conducting fluids Concern specific to plasma is that the equations give equilibrium and stability conditions Motivation: Avoid major disruptions Navier-Stokes equations: Fluid Dynamics Maxwell’s equations: Electromagnetism

    3. 22.012 Fusion and Plasma Physics Seminar MHD Complications Resistive Wall Mode (RWM) Edge Localized Mode (ELM) Neoclassical Tearing Mode (NTM)

    4. 22.012 Fusion and Plasma Physics Seminar Resistive MHD Ideal MHD vs. Resistive MHD Resistive MHD is of concern to numerically simulate the Resistive Wall Mode (RWM) in advanced tokamaks Resistive Wall Mode slowly grows to create instability in steady-state operation Resistive MHD Extended model This includes an extra term in Ampere's Law which models the collisional resistivity Resistivity of the plasma serves as a diffusion constant

    5. 22.012 Fusion and Plasma Physics Seminar Computational MHD and Computation Fluid Dynamics(CFD) CFD and MHD related: Both use Navier-Stokes but differ in other necessary state variables CFD started in 60’s for NASA and military aircraft development Both involve solving non-linear, 3-dimensional, complex differential equations simultaneously

    6. 22.012 Fusion and Plasma Physics Seminar Numerical Methods Finite Volume Method (Most Popular) Also can use Finite Element or Finite Difference Discretize control volumes Break up into a 2-dimensional grid or 3-dimensional mesh State variables remain conservative via Finite Volume Method Governing equations (Q) and fluxes leaving control volumes (F)

    7. 22.012 Fusion and Plasma Physics Seminar Simple CFD Example: Flow over an Airfoil Matlab implementation of Navier-Stokes equations for a NACA 0012 airfoil at 10 degrees angle of attack Simulation Example

    8. 22.012 Fusion and Plasma Physics Seminar Simulation of RWM in an Advanced Tokamak Much harder than previous CFD example 3-D mesh + Resistive MHD model In order to achieve high Beta plasmas in advanced tokamaks, we need to characterize system dynamics via simulation of unstable wall modes Use Computational MHD

    9. 22.012 Fusion and Plasma Physics Seminar

    10. 22.012 Fusion and Plasma Physics Seminar Feedback Control of the RWM Instability Stability achieved using dynamic compensation (feedback control) of active coils

    11. 22.012 Fusion and Plasma Physics Seminar System Dynamics Model

    12. 22.012 Fusion and Plasma Physics Seminar Problems Sensor Noise at low frequency Time delay of sensors Minimize using internal poloidal and toroidal sensors Control unstable modes and hopefully never enter modes unreachable using the controller Propotional+Derivative Control (PID) K_RWM= K+ (K_i)/s

    13. 22.012 Fusion and Plasma Physics Seminar Acknowledgments Professor Molvig Professor Friedberg Professor Hutchinson

    14. 22.012 Fusion and Plasma Physics Seminar Sources “Feedback control of resistive wall modes in torodial devices”. Nucler Fustion, 44, pg 77-86, Dec. 2003. “Active control of resistive wall modes in the large-aspect-ratio tokamak”. Nuclear Fusion, 42, pg 768-779, June 2002 . http://www.elmagn.chalmers.se/elmagn/CEMgroup/MHD/ http://flash.uchicago.edu/~emonet/astro/mhd/index.html http://en.wikipedia.org/wiki/Magnetohydrodynamics http://en.wikipedia.org/wiki/Computational_fluid_dynamics

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