D. McCune

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Plasma State Representation

XPLASMA – Tool for Representation of Equilibrium,

Fields and Profiles

Available at: http://w3.pppl.gov/NTCC

D. McCune

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Definition of Plasma State• A plasma geometry and field configuration

represented over “standard” coordinates

• A collection of profiles (such as plasma temperatures and densities) defined over the same coordinates.

• XPLASMA is a tool for gathering and sharing such a collection of data.

• XPLASMA created for purpose of inter-module communication in NTCC project.

D. McCune

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Mathematical Description

Grid variables: x – normalized radial magnetic flux coordinate (sqrt(phi/philim))

0 at magnetic axis, 1 at plasma boundary. theta – poloidal angle coordinate. phi – toroidal angle coordinate. R – major radius coordinate. Z – vertical coordinate.

R

Z

phi x

thetaSets of Labeled Profile Objects: F: {f_i(x); fname(i), i = 1 to Nf } G: {g_i(x,theta); gname(i), I = 1 to Ng } H: {h_i(R,Z); hname(i), I = 1 to Nh }Sets of profiles vs. (R,phi,Z) and (x,phi,theta) could also be defined. Lookup map M:name => integer – tool for finding named profiles.

RED means not yet in XPLASMA

[Rmin,Rmax]x

[Zmin,Zmax]Rectangle encloses plasma.

D. McCune

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Math Description (2).

A Profile Object consists of:• Gridded data covering a prescribed range AND• An interpolation method (see NTCC PSPLINE module):

• C0 – piecewise linear;• C1 – Hermite spline with boundary conditions.• C2 – Cubic spline with boundary conditions.

Grids are strict ascending sequences covering a prescribed range:x grids from 0 to 1theta grids from –pi to pi (or other domain of width 2*pi).R grids from Rmin to RmaxZ grids from Zmin to Zmax

There can be multiple grids for each grid variable (x,theta,R,Z,phi); all must cover the same range.

Adaptive or Unstructured Grids (Meshes) could be defined.

RED means not yet in XPLASMA

D. McCune

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Math Description (3)Axisymmetric MHD equilibrium, “direct” representation: B_phi = [sign]*g(x)/R – toroidal magnetic field. [B_R,B_Z] = [sign]*grad(Psi(R,Z))/R – poloidal magnetic field. Psi(R,Z) profile and g(x) are given; Psi(x) is given only to locate the boundary Psi(1).

Axisymmetric MHD equilibrium, “inverse” representation: B_phi = [sign]*g(x)/R – toroidal magnetic field. {R(x,theta),Z(x,theta)} (bicubic splines) describe flux surface locations. [B_R,B_Z] = [sign]*grad(Psi(x))/R – poloidal magnetic field. g(x), R(x,theta), Z(x,theta), Psi(x) are given.

A direct MHD equilibrium representation defines an inverse representation via interpolation.

Extrapolation can “extend” an inverse representation to cover an [R,Z] region (mimic a direct equilibrium) but the extrapolation is unstable!

Non-axisymmetric equilibria exist.

D. McCune

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Odds and Ends (XPLASMA)• MKS units; sign conventions for fields–

– d[Psi]/dx > 0, g(x) > 0; nsnccwb = 1 if B_phi is “counter-clockwise” (ccw) looking down from above; nsnccwj = 1 if J_phi is ccw from above.

• A closed sequence {(R[j],Z[j])} defines a “vacuum vessel wall / limiter structure”.

• A “list object” is available:– Define sets of related profiles.– Provide additional labeling.– Define other data like plasma species lists.

D. McCune

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Essential Interfaces

• Define grids, profiles, equilibria.

• Load equilibria from common tokamak experimental data sources:– EFIT (file or MDS+) (equilibrium only):

• call eqm_fromgeqdsk(<data path>,options…)

– TRANSP (file or MDS+) (equilibrium and profiles):

• TRXPLIB NTCC module.

• Load odds and ends…

D. McCune

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Essential Interfaces• Coordinate mappings (x,theta) (R,Z).

• Interpolate magnetic field values.

• Locate profiles; interpolate profile values.

• Geometrical information:– Distance (R,Z) to plasma flux surface.– Distance (R,Z) to limiter or vacuum vessel.– Flux surface averages; surface areas,

volumes enclosed in flux surfaces.• http://w3.pppl.gov/~pshare/help/xplasma.htm

D. McCune

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Additional Interfaces

• XPLASMA supports an “irregular” (x,theta) mesh for NUBEAM outputs:– Neutron emissivity profiles Sn(x,theta).– Neutral sources and sink rate profiles.– Fast ion distribution functions f(x,theta,E,vpll/v).

• Number of theta “bins” varies radially; increases linearly with x.

• Other specialized structures could easily be added to XPLASMA.

D. McCune

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Use of XPLASMA

XPLASMA:• Equilibrium• Profiles

IntegratedPlasma

Simulator

RF or NeutralBeams Module

Notice that:• Each code sends data on its own grids.• Each code receives data on its own grids.

D. McCune

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XPLASMA for Intermodule Communication – Example.

XPLASMA is an NTCC* tool for communication of

axisymmetric MHD equilibria and profiles

portably and conveniently between modules.

• It supports numerous mapping and interpolation methods.• Example: accurate, conservative rebinning of heating profiles (as shown).• Planned for use in Fusion Simulation Project.

* http://w3.pppl.gov/NTCC Beam electron heating (small # of MC ptcls)

Total power is conserved.

Integrated power: original and as interpolated.

Power density: original and as interpolated.

(difference is negligible)

D. McCune

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Distributed Computing

• Entire XPLASMA contents can be saved or reloaded to/from NetCDF:– Call eq_save(<filename>,<return_status>)– Call eq_restore(<filename>,<return_status>)

• So far these files are reasonably small:– <~ 100MB– Read/write times ~ 1 second or less.

• Usable for process-to-process data transfer.

D. McCune

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MPI-Parallel Module Server

Serial TRANSP Run (Client #1)

Serial TRANSP Run (Client #2)

Serial TRANSP Run (Client #N)

Serial TRANSP Run (Client #3)

…

Input File* Package, e.g.XPLASMA** NetCDF state.

Output File* Package, e.g.XPLASMA** NetCDF state.

Server Queue

MPI-Parallel TRANSPModule Server(s):

•NUBEAM monte carlo•TORIC5 full wave•GenRAY ray tracing•CQL3D fokker planck•GCNM transp. solver• ... … …

**NTCC container module for equilibrium, profiles, distribution functions, etc. (http://w3.pppl.gov/NTCC) to be used for Fusion Simulation Project prototype and tested in TRANSP deployment.

*viability of method depends on keeping files small.

network

D. McCune

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Assessment• XPLASMA was developed for intermodule

communication in the NTCC project.

• Fusion Simulation Project use is feasible.

• But:– This is essentially a data model for the project.– “Old fasioned” f77-style interface; mixed

language compatible but not modern.– The physics content is quite small.– I would like to get Computer Science help!