Callen:  NTM Physics Discussion (Nov 14, 2000)



Electrons:  bootstrap current (w<ne)

Ions:  poloidal ion flow damping (/t < ni )

            Neo-enhanced polarization flow

             (from Ń·J ~ Ń·[B´Ń·P_parallel/B2] )

            Longer-term … kinetic-based closures (/t > ni , kparallel vT> w)


                        Temperature cparallel >> cperp , diffusive to “free-streaming”

                        Pressure, density (sound waves) evolution

?  need Landau-type closure to limit mode interactions to

Dx < (Ls/rp)ri ~10ri

                        need gyroviscosity to obtain correct nonlinear behavior


Possible physics tests of NTM simulations:


Level 0

Level 1

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/nc) 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)?