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 ��J ~ ��[B���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)?