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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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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