1. Code Name: Cbesc (Equilibrium and stability code)
2. The scope: Equilibrium (2-D), MHD, Particle gyro- and full- orbits.
3. Developer: Leonid E. Zakharov.
4. Users: LEZ, Users of ASTRA.
5. Description: Fix/free boundary equilibria, reconstruction, etc.
6. Language: C/CodeBuilder (Cb).
7. CodeControl: Real time interactive (organized by Cb).
8. Communications:Distributed over sections and organized by Cb (I/O file system, X-Window graphics, shared memory). In addition, is lnked to the JET data base, generates the Equilibrium Spline Interface (ESI) files for stability, transport, gyro-kinetic and particle orbit codes.
9. Postprocessors: Other Cb-codes can read files from I/O database (the structure of records is common), esi.c file is provided for external use of ESI output.
10. Docs: Online-Help and code maintenance documentation is organized by Cb.
11. Web: w3.pppl.gov/~zakharov
12. Versions: No needs in keeping versions were experienced.
13. NumModel: Fix boundary routines solve the Grad-Shafranov equation in flux coordinates using linearization. Solution is represented by Fourier harmonics with radial coefficients in the form of splines. Free-boundary routines use the r-z grid. Time is a parameter.
14. OperModel Non-linear.
15. Reference: L. Zakharov, A. Pletzer. Physics of Plasmas, v.6, 4693 (1999).
16. Uniqueness: (a) Fix-boundary solver: 4 choices of radial coordinate system, simplest regular poloidal coordinate, broad set of input radial profiles, 2 choices of ODE solvers (Runge-Kutta, lsode()), generates eigen-functions of n=0 MHD modes, special Fourier representation of a boundary layer near separatrix, current hole option, the fastest among known analogs (J/Q-SOLVERs, VMEC, EFIT), called in ASTRA at every time step; (b) Link between fix- and free- boundary solvers; (c) Free-boundary solver: broad database of magnetic diagnostics of existing tokamaks, direct, reconstruction modes, and reconstruction with response functions of eddy currents are implemented; (d) CHI reconstruction with open field lines; (e) Variance analysis of equilibrium reconstruction.
17. Verification: Self-verified in radial direction by lsode() (ibid).
18. Tangible results: First current hole reconstruction on JET, reconstruction of the energy confinement time on CDX-U in the high eddy-current case, design of LTX, assessment of performance MSE-LP, MSE-LS, Faraday rotation diagnostics for equilibrium reconstruction in ITER, design of burning plasma regime for FFRF and Sts.
19. Limitations: Reasonably covers all basic needs of tokamak fusion in 2-D equilibrium simulations.
20. Externals: CodeBuilder, lsode().
21. Scalability: Not an issue. The approach relies on optimal representation rather than on the number of mesh points (with 10 radial intervals ESC has better accuracy than JSOLVER with 512x256 grid and orders of magnitude higher speed).
22. Bottlenecks: Fix boundary separatrix model is limited by a single null case.
23. Composition: The code is structured by communication sections (rather than by modules or smaller codes) in consistency with Cb.
24. Portability: Not an issue. Any unix system.
25. Performance: Characteristic time is 0.1 sec/equilibrium.

Cbesc1. Code Name: Cbesc (Equilibrium and stability code)

2. The scope: Equilibrium (2-D), MHD, Particle gyro- and full- orbits.

3. Developer: Leonid E. Zakharov.

4. Users: LEZ, Users of ASTRA.

5. Description: Fix/free boundary equilibria, reconstruction, etc.

6. Language: C/CodeBuilder (Cb).

7. CodeControl: Real time interactive (organized by Cb).

8. Communications:Distributed over sections and organized by Cb (I/O file system, X-Window graphics, shared memory). In addition, is lnked to the JET data base, generates the Equilibrium Spline Interface (ESI) files for stability, transport, gyro-kinetic and particle orbit codes.

9. Postprocessors: Other Cb-codes can read files from I/O database (the structure of records is common), esi.c file is provided for external use of ESI output.

10. Docs: Online-Help and code maintenance documentation is organized by Cb.

11. Web: w3.pppl.gov/~zakharov

12. Versions: No needs in keeping versions were experienced.

13. NumModel: Fix boundary routines solve the Grad-Shafranov equation in flux coordinates using linearization. Solution is represented by Fourier harmonics with radial coefficients in the form of splines. Free-boundary routines use the r-z grid. Time is a parameter.

14. OperModel Non-linear.

15. Reference: L. Zakharov, A. Pletzer. Physics of Plasmas, v.6, 4693 (1999).

16. Uniqueness: (a) Fix-boundary solver: 4 choices of radial coordinate system, simplest regular poloidal coordinate, broad set of input radial profiles, 2 choices of ODE solvers (Runge-Kutta, lsode()), generates eigen-functions of n=0 MHD modes, special Fourier representation of a boundary layer near separatrix, current hole option, the fastest among known analogs (J/Q-SOLVERs, VMEC, EFIT), called in ASTRA at every time step; (b) Link between fix- and free- boundary solvers; (c) Free-boundary solver: broad database of magnetic diagnostics of existing tokamaks, direct, reconstruction modes, and reconstruction with response functions of eddy currents are implemented; (d) CHI reconstruction with open field lines; (e) Variance analysis of equilibrium reconstruction.

17. Verification: Self-verified in radial direction by lsode() (ibid).

18. Tangible results: First current hole reconstruction on JET, reconstruction of the energy confinement time on CDX-U in the high eddy-current case, design of LTX, assessment of performance MSE-LP, MSE-LS, Faraday rotation diagnostics for equilibrium reconstruction in ITER, design of burning plasma regime for FFRF and Sts.

19. Limitations: Reasonably covers all basic needs of tokamak fusion in 2-D equilibrium simulations.

20. Externals: CodeBuilder, lsode().

21. Scalability: Not an issue. The approach relies on optimal representation rather than on the number of mesh points (with 10 radial intervals ESC has better accuracy than JSOLVER with 512x256 grid and orders of magnitude higher speed).

22. Bottlenecks: Fix boundary separatrix model is limited by a single null case.

23. Composition: The code is structured by communication sections (rather than by modules or smaller codes) in consistency with Cb.

24. Portability: Not an issue. Any unix system.

25. Performance: Characteristic time is 0.1 sec/equilibrium.