Callen: NTM Physics Discussion (Nov 14, 2000)

• Key NTM physics issues involve poloidal flow damping:

Electrons: bootstrap current (w<n_e)

Ions: poloidal ion flow damping (¶/¶t < n_i )

Neo-enhanced polarization flow

(from Ñ·J ~ Ñ·[B´Ñ·P_parallel/B²] )

Longer-term … kinetic-based closures (¶/¶t > n_i , k_parallel v_T> w)

• Related Physics Issues (Mainly 2-fluid effects)
• Equilibration of plasma properties along B₀ + B₁

Temperature c_parallel >> c_perp , diffusive to “free-streaming”

Pressure, density (sound waves) evolution

• Diamagnetic flow, frequency (w*) effects:

? need Landau-type closure to limit mode interactions to

Dx < (L_s/r_p)r_i ~10r_i

need gyroviscosity to obtain correct nonlinear behavior

Possible physics tests of NTM simulations:

Level 0

• Demonstrate NTM Nonlinear (Rutherford regime) growth and saturation…compare with 0D dW/dt equation

Level 1

• Explore NTM Physics Effects:

o Seed island threshold…due to Chi_parallel, classical and neoclassical ion polarization effects

o Flow effects…diamagnetic flows, toroidal flow, island rotation

o Stabilization by localized current (ECCD), heating (ECH)

o Error field, helical perturbation effects ?

Level 2

· Explore NTM Nonlinear Physics:

o NTM excitation via mode coupling … sawtooth crash, ELMs, …(need flow differences on different rational surfaces)

o Why does only one NTM mode occur at a time?

o Why does 2/1 NTM mode in DIII-D evolve to a disruption?

o NTM interactions with resistive wall modes (RWMs)

o What happens when NTM islands get large ?

…toroidal mode coupling, island hits “limiter”?

Hegna (Presented at Oct APS) Issues for NTM modeling

Physics Elements:

· Neoclassical flow damping – damping of flows within magnetic surfaces (bootstrap current/poloidal ion flow damping)

Current implementation of the flow damping forms encapsulates this physics – produces bootstrap current drive for NTM’s – damping of flows along perturbed surfaces. Analytic forms used are based on long-timescale asymptotics (t >> 1/n_c) and quasi-equilibrium structure of helically distorted magnetic surfaces -> time and space issues for theorists to ponder.

· Anisotropic heat and particle flux-transport along field lines >> transport across field lines.

Local diffusion coefficients with disparate scales present in NIMROD. Wave-like physics to equilibrate along field lines in M3D – mocks up free streaming physics – long mean free part regime equilibration along B is nonlocal (Held’99) – implementation ?

· Ion polarization threshold requires 2-fluid drift effects (w*) – differential flow between ion and electron fluids.

In two-fluid formulation, what is the natural frequency of a nonlinear island? Depends parametrically on viscosity ? ion flow damping ? neoclassical elements? Other dissipation processes ? Island width?

· Seed island formation requires another MHD event (sawtooth crash, ELM). Differential rotation between geometrically coupled magnetic surfaces.

Self-consistent edquilibrium with sheared flow. Accurate description of sawteeth? ELM’s?

· Ultimate nonlinear evolution – isolated small island dynamics explained by Rutherford-like theory- what happens when islands gets big ? – little theoretical insight.

Disruption phenomenology ? Coupled island dynamics ? Nonlinear NTM sawtooth interaction ? NTM coupled to free boundary modes (RWM)?