**Santa Fe, NM, April 5, 2001**

ATTENDEES

*- Team Members:*

Dalton Schnack, Ming
Chu, Scott Parker, Jean-Noel Lebouf, Eric Held, John Wright, Jim Callen,
Rick Nebel, Charlson Kim, Tom Gianakon, Carl Sovinec, Alfonso Tarditi

*- DOE:*

Rostom Dagazian

*- Guests:*

Huo Tian (UW-Madison)

Giovanni Cone (UW-Madison)

Sangeeta Mahajan (UW-Madison)

Fatima Ebrahimi (UW-Madison)

*- Manpower/budget issues (Dalton Schnack)*

DOE is aware of the mighty challenges and
will do its best to alleviate problems that the team may be facing in the
near future.

*- 3D Linear System capabilities (Carl
Sovinec).*

Allowing for solutions that contain coupling along the toroidal direction has become a necessity. Examples are anisotropic thermal conduction problems or a 3D continuity equation, where the density r(r,z,j), for each toroidal mode, has still the full 3D dependence.

For this purpose a 3D CG solver has been added to NIMROD. 3D domain decomposition in layers is still allowed. Direct solve for quadrature points internal to the cell is not possible anymore, but impact on CPU time performance seems not significant (at least based on preliminary tests).

Other significant consequences are that now maintaining the efficiency of the FEM computations has become more important..

Data storage at quadrature points has changed and likely will need to be considered while making changes to the physics kernel of the code.

Tolerance input parameter needs to be reduced for problems with high thermal anisotropy.

A demonstration run for anisotropic thermal
conduction for a D3D problem was presented.

*- Vacuum Moving Interface (Scott Kruger)*

Original "step function" choice for the shape
variable caused problems: new formulation uses a smooth initial condition
for the shape variable that dramatically reduces the high-k noise. The
new coding is being ported to the latest release of NIMROD.

*- Particle Kinetic Closures (Charlson
Kim)*

A simple test with "tracing" particles trapped
in banana orbits (on a r-z grid) shows that the energy is fairly well conserved.
A version that tracks the particles (w/o self consistent effects) could
be made deliverable to the team quickly.

*- Visualization (Scott Parker)*

Experience was developed with Open-DX at
U. Colorado. Help for setting up Open DX based visualization will be provided
to team members by U. Colorado upon request.

*- Kinetic Closure of Parallel Ohm's Law
(Scott Parker)*

Theoretical work on the kinetic closure or
parallel Ohm's law was reported. This development interests electron transit
time scale (for passing particles, the time for an electron to go one poloidal
loop around). Electron inertia can be included. A slab tearing mode test
case was suggested.

*- Chapman-Enskog like kinetic equation
(Eric Held)*

In Chapman-Enskog like approach the electron distribution is written as sum of a Maxwellian and a distortion term. This term is then inserted and solved for in a drift kinetic equation. This model actually solves the gyro averaged drift kinetic equation for electron parallel dynamics.

In the calculation of parallel stress tensor
and heat flow moments time dependent closures retain free streaming and
collisional effects.

*- Neo-classical Tearing Modes (Tom Gianakon)*

Neoclassical effects through viscous stress tensor: a successful test case was completed.

Resistive MHD shows fast growing ballooning
instabilities: neo-classical enhancements of polarization current stabilize
medium-n ballooning modes. With extended MHD neo-classical tearing modes
(TM) are generated. A TM stabilization case was demonstrated with a customized
version of the code: slab geometry is considered and a source term for
an auxiliary current drive is added in the Ohm's law. A TM is loaded as
initial condition, the evolution of the island size is then observed for
different values of the source current width. It was shown that there is
lower limit that island size can reach.

*- High Beta Disruption in DIII-D (Dalton
Schnack)*

The DIII-D shot #87009 scenario is considered.
It was shown experimentally and theoretically that increasing beta through
the marginal stability threshold produces a mode growing faster than exponentially
(growth proportional to t^{3/2}).

For the NIMROD runs a normalized beta (b_{N}
) higher than in the experiment needs to be considered because the lack
of vacuum region. A run with high order finite elements (3^{rd}
order) was proven to be numerically stable with 65 poloidal mesh points
(previous efforts with linear elements required much higher poloidal resolution).
Linear growth of global modes for b_{N}
5 and 6 was observed with fair agreement with GATO linear results, as found
with earlier simulations with linear elements. For b_{N}=4,
below the stability threshold, a resistive interchange mode was also detected.
Results from nonlinear test runs were also shown.

*- GA Applications (Ming Chu)*

Several applications of the NIMROD code are being pursued at GA. Simulation of FRC formation through merging Spheromaks will be attempted to investigate the a suggested tilt stabilization effect due to the presence of a residual toroidal field.

Almost Ideal MHD physics is being investigated in a slab geometry simulation.

The problem of heat conduction in tokamaks will be investigated in connection with experimental results in ASDEX suggesting that neoclassical tearing modes appear to be stabilized by externally applied helical field in presence of magnetic island and other non-resonant harmonic components.

Another problem of interest is the Electron
Cyclotron Current Drive (ECCD) suppression of neoclassical tearing modes
(in connection with experimental result in DIII-D).

*- RFP Single Helicity modes (Carl Sovinec)*

Simulation of R/a=1.75 RFP for single helicity
modes were reported. Poincare plots of runs in periodic linear geometry
shows single helicity state while runs in toroidal geometry does not. An
example of a new diagnostic able to resolve modes in the poloidal direction
was shown.

*- Feasibility test of accretion disk simulation
with NIMROD (Carl Sovinec)*

A model of an accretion disk considers differential
rotation that in turn causes radial electric field. A NIMROD test case
was set where a dipole flux distribution expands as the differential rotation
is applied at the disk.

*- Last M3D-NIMROD meeting summary (Dalton
Schnack)*

NIMROD benchmark with M3D will include Wonchull
Park proposed ideal MHD case. Due to lacking efforts of the M3D team in
this area, no M3D run with same parameters as any NIMROD run was made available
yet.

*- Two-fluid comparison with M3D (Rick
Nebel)*

A test case for a M3D vs. analytic theory comparison has been made available. The test refers to a tokamak in a periodic cylinder, with m=1 ideal mode.

NIMROD runs two-fluid
runs (with Hall and diamagnetic terms only) were performed and linear eigenfunction
data were collected for the purpose of comparing with M3D recent results
by Linda Sujiama. The NIMROD two-fluid semi-implicit operator seems to
work satisfactory. Gyro-viscous terms and polarization drift need to be
included.

*- New version of the code (Dalton Schnack
and Carl Sovinec)*

A new version of the code with 3D linear system capabilities will be made available to the team members before Carl Sovinec's transfer to U. of Wisconsin - Madison. The new version of the code is expected to include also the vacuum region formulation and the full 3D continuity equation.

Linda Sujiama

An informal NIMROD
"code developer" workshop is tentatively planned for the late summer with
the purpose of transferring some of Carl Sovinec's code development and
maintenance expertise to other team members.