M3D Stellarator Simulations


H.R. STRAUSS
New York University, New York, NY, USA
L.E. SUGIYAMA
Massachusetts Institute of Technology, Cambridge, MA, USA
G.Y. FU, W. PARK, J.BRESLAU, D. MONTICELLO
Princeton Plasma Physics Laboratory, Princeton, NJ, USA

M3D code

• Physics
  • MHD
  • 2 Fluid, neoclassical
  • hybrid
  • ``artificial sound" for parallel equilibration
• parallelization
  • shared memory, OMP
  • and distributed memory, MPI
• Mesh
  • unstructured mesh of triangles and quadrilaterals in poloidal pl anes
  • 4th order finite differencing or pseudo spectral in the toroidal direction

• initialization from the VMEC code (working on PIES)

Ideal and Resistive MHD

• Ideal MHD
  • ideal $n \sim \infty$ $\beta$ limit is too low.
• Resistive MHD
  • resistive ballooning modes unstable for all $\beta$.
  • Stellarators tend to be resistive interchange unstable, so the resistive modes are not stabilized at small resistivity, as in tokamaks.

Figure 1: Growth rate $\gamma$ of Ideal and Resistive Mode vs. $\beta$

Two fluid

• two fluid equations (Sugiyama and Park, PoP 2000)
• resistive modes are stabilized by diamagnetic drifts.
• realistic value of the Hall parameter
• Ideal modes can be stabilized, raising $\beta$ limit.

Hall parameter

$$H = {c \over \omega_{pi} R}$$

$$\omega_* R/v_A = H n ({\beta_p a \over 2 q L_p})$$

where $n$ is toroidal mode number. Ideal modes are stable if

$$\omega_* > \gamma_{MHD} \sim 0.1 v_A / R$$

can be stable, $\beta > 0.07, H = 0.02, n \ge 10$

Figure 2: Electrostatic potential for (a) MHD, $H=0$, (b) 2 Fluid $H=0.02$. In both cases, $\beta = 0.07, S=4 10^5, p_e = p_i,$ density = constant.

TAE Modes

• Hot particle kinetic effects can cause TAE modes in stellarators. TAE modes are confirmed by frequency and linear scaling of growth rate with hot particle $\beta$. The growth rate in a two period stellarator is lower than in a tokamak with the same profiles and average boundary shaping.

Growth rate $\gamma$ vs. hot particle $\beta$. Linear relation is characteristic of TAE.

M3D - PIES Comparison

• PIES restart file used to generate M3D input file
• compared vacuum case with islands

Figure 3: Poincare plots of a test case done with (a) PIES (b) M3D

Summary

• Two Fluid essential for equilibrium and stability
• Kinetic TAE calculations
• PIES - M3D Comparison
• need to include vacuum region for free boundary computations