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Simulations of Princeton Gallium Experiment

Simulations of Princeton Gallium Experiment. Wei Liu Jeremy Goodman Hantao Ji Jim Stone Michael J. Burin Ethan Schartman CMSO Plasma Physics Laboratory Princeton University, Princeton NJ, 08543.

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Simulations of Princeton Gallium Experiment

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  1. Simulations of Princeton Gallium Experiment Wei Liu Jeremy Goodman Hantao Ji Jim Stone Michael J. Burin Ethan Schartman CMSO Plasma Physics Laboratory Princeton University, Princeton NJ, 08543 Research supported by the US Department of Energy, NASA under grant ATP03-0084-0106 and APRA04-0000-0152 and also by the National Science Foundation under grant AST-0205903

  2. Outline • Introduction • Linear Simulations of MRI • Nonlinear Saturation of MRI • Conclusions

  3. Diagram and Parameters Physical Parameters Material Properties (Liquid Gallium) • Control Dimensionless Parameters • Reynolds Number • Magnetic Reynolds Number • Lundquist Number • Mach Number

  4. Main Features and modifications of ZEUS ZEUS: An explicit, compressible astrophysical MHD code* Modified for non-ideal MHD: Add viscous term into Euler Equation with azimuthal viscous term in flux-conservation form Add resistive term to Induction Equation by defining equivalent electromotive force Boundary condition: Magnetic Field: Vertically Periodic, Horizontally Conducting Velocity Field: Vertically Periodic, Horizontally NO-SLIP Benchmarks against Wendl’s Low Reynolds Number Test** and Magnetic Gauss Diffusion Test * Ref. J. Stone and M. Norman, ApJS. 80, 753 (1992) J. Stone and M. Norman, ApJS, 80, 791 (1992) **Ref. M.C.Wendl, Phys. Rev. E. 60, 6192 (1999)

  5. Comparison with Incompressible Code Re=1600 Compressible Code Incompressible Code* • Low Mach Number ( ) with NO-SLIP boundary condition on cylinders and end-caps • Error *Ref. A. Kageyama, H. Ji, J. Goodman, F. Chen, and E. Shoshan, J. Phys. Soc. Japan. 73, 2424 (2004)

  6. Linear MRI Simulation Comparison with Local Linear Analysis* *Ref. H. Ji, J. Goodman and A. Kageyama, Mon. Not. R. Astron. Soc. 325, L1 (2001)

  7. Linear MRI Simulation Comparison with Global Linear Analysis* *Ref. J. Goodman and H. Ji Fluid Mech. 462, 365 (2002)

  8. Nonlinear Saturation Rotating Speed Profile ( )

  9. Nonlinear Saturation (Re=400,Rm=400,M=1/4,S=4) Flux Function Stream Function

  10. Rapid outward Jet and Current Sheet (Re=400,Rm=400,M=1/4,S=4) Rapid Jet Current Sheet

  11. Speed and Width of outward jet From the theory* From the simulation And roughly, From Mass Conservation Thus * Ref. E. Knobloch and K. Julien, Mon. Not. R. Astron. Soc. 000, 1-6 (2005)

  12. Z-Average torques versus R Re=400 Rm=400 Initial State Final State

  13. Increase of Total Torque on cylinders

  14. Conclusions about Nonlinear Saturation M=1/4,S=4 These conclusions apply at large Rm ( ). • At final state, the rotating profile is flattened somewhat, uniform rotation results*. • The width of the “jet” is almost independent of resistivity, but it does decrease with increasing Re; the speed of the “jet” scales as*: • At final state the total torque integrated over cylinders depends somewhat upon viscosity but hardly upon resistivity. • The smaller the resistivity, the longer is required to reach the final state. Oscillations appear to persist indefinitely if Rm>800*. • The ratio of the poloidal flow speed to the poloidal field strength is proportional to resistivity**. * Ref. E. Knobloch and K. Julien, Mon. Not. R. Astron. Soc. 000, 1-6 (2005) **Ref. F. Militelo and F. Porcelli, Phys. Plasmas 11, L13 (2004)

  15. The END Thanks

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