1. D. McCune 1 Plasma State Representation XPLASMA – Tool for Representation of Equilibrium, Fields and Profiles Available at: http://w3.pppl.gov/NTCChttp://w3.pppl.gov/NTCC

2. D. McCune 2 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.

3. D. McCune 3 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 theta Sets 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.

4. D. McCune 4 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 1 theta grids from –pi to pi (or other domain of width 2*pi). R grids from Rmin to Rmax Z 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

5. D. McCune 5 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.

6. D. McCune 6 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.

7. D. McCune 7 Essential Interfaces Define grids, profiles, equilibria. Load equilibria from common tokamak experimental data sources: –EFIT (file or MDS+) (equilibrium only): call eqm_fromgeqdsk(,options…) –TRANSP (file or MDS+) (equilibrium and profiles): TRXPLIB NTCC module. Load odds and ends…

8. D. McCune 8 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

9. D. McCune 9 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.

10. D. McCune 10 Use of XPLASMA XPLASMA: Equilibrium Profiles Integrated Plasma Simulator RF or Neutral Beams Module Notice that: Each code sends data on its own grids. Each code receives data on its own grids.

11. D. McCune 11 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/NTCChttp://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)

12. D. McCune 12 Distributed Computing Entire XPLASMA contents can be saved or reloaded to/from NetCDF: –Call eq_save(, ) –Call eq_restore(, ) So far these files are reasonably small: –<~ 100MB –Read/write times ~ 1 second or less. Usable for process-to-process data transfer.

13. D. McCune 13 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 TRANSP Module 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.http://w3.pppl.gov/NTCC *viability of method depends on keeping files small. network

14. D. McCune 14 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!