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Enhancing Linear Stability Analysis with MARS-F and CarMa Codes

Explore the fusion of MARS-F and CarMa codes for Resistive Wall Mode analysis, with practical applications for plasma stability, controller design, and time domain simulations. Gain insights on coupling matrices, self-consistent CarMa block creation, and ongoing bug fixes.

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Enhancing Linear Stability Analysis with MARS-F and CarMa Codes

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  1. Status of MARS-F and CarMa codes on ITM D. Yadykin,Y.Q. Liu, F. Villone, R. Paccagnella

  2. MARS-F and CarMa codes are used to calculate the linear stability of Resistive Wall Mode (RWM) MARS-F computes the complex RWM eigenvalue for the uniform wall(s) with the possibility of active control system (coils, amplifiers) inclusion CarMa code is the combination of MARS-F and CARIDDI codes. It computes complex RWM eigenvalue including realistic (3D) conducting structures MARS-F and CarMa codes

  3. MARS-F and CARIDDI codes were imported to the ITM gateway. The modules were created allowing reading and writing data in CPO format Initial XML files with esential code parameters were created for both codes Interface files between MARS-F and CARIDDI were transfered from MATLAB to FORTRAN Status 2009

  4. Merge MARS-F and CARIDDI codes (create self-consistent CarMa block) Change the method of input/output of the data to/from the codes (read/write data from/to the ITM data base instead of data files) Create Kepler actor corresponding to one of the codes (MARS-F or CarMa) Goals for 2010

  5. plasma S Resistive wall CarMa code Realization • The plasma/wall interaction is decoupled via a suitable surface S in between • - Inside S, MHD equations (MARS-F) • - Outside S, eddy currents equations (CARIDDI) • - On S suitable matching conditions (coupling matrices) Several possible uses • Growth rate calculation • Unstable eigenvalue of the dynamical matrix • Standard routines (e.g. Matlab) or ad hoc computations • Beta limit with 3D structures (when the system gets fictitiously stable) • Controller design • state-space model (although with large dimensions and with many unstable modes) • Time domain simulations • Controller validation • Inclusion of non-ideal power supplies (voltage/current limitations, time delays, etc.)

  6. plasma S S S Resistive wall Resistive wall Resistive wall CarMa code (forward coupling scheme) • The plasma response to a given magnetic flux density perturbation on S is computed as a plasma response matrix, solving MHD equations inside S. • Using such plasma response matrix, the effect of 3D structures on plasma is evaluated by computing the magnetic flux density on S due to 3D currents. • The currents induced in the 3D structures by plasma are computed via an equivalent surface current distribution on S providing the same magnetic field as plasma outside S.

  7. CarMa code (benchmark results) n=1 kink instability Three dimentional view of the mesh used to represent the axisymmetric resistive wall and a typical current pattern corresponding to the unstable eigenvalue Eigenvalue comparison S1 – rS=1.1a S2 – rS=1.2a

  8. MARS-F and CARIDDI codes are merged together (self-consistent CarMa block is created). Interface between the codes (coupling matrices) is created in one run (new feature) Tests are ongoing to fix various bugs appeared during merging process Work Performed (CarMa)

  9. Work Performed (CarMa) Present Before MARS-F MARS-F MARS-F MARS-F Coupling Matrix Coupling Matrix Coupling Matrix Coupling Matrix Coupling Matrix Coupling Matrix CARIDDI CARIDDI rwm rwm

  10. Combine essential code parameters of MARS-F and CARIDDI in one block Decide the format of the wall(s) information input (at present it is given via data file with wall(s)coordinates and physical parameters – thickness and conductivity). Additional CPO block is needed with such information Perform normalization of the quantities read from CPO Create Kepler actor Work to Do (CarMa)

  11. Modules are created to allow reading of the input data from CPO (and not from the data files as it is usually done) Normalization factors are introduced to be able to use CPO read data in the code and to meet the requirements of the existing ITM conventions Tests are ongoing for verification of the normalization factors Work Performed (MARS-F)

  12. Work Performed (MARS-F) ITM convensions MARS-F Toroidal coordinate system (R,Z,) (R,,Z) Btor>0 Ip<0 q>0 Btor>0 Ip>0 q>0 Flux coordinates Straight field lines coordinates (at the moment) • - poloidal flux • - polidal angle  - toroidal angle (corresponds to - on the picture above) • s - normalized poloidal flux • - poloidal angle  - toroidal angle

  13. Work Performed (MARS-F) Normalization factors Metric factors Physical quantities Bold – additional normalization factors

  14. Vacuum region description. Discussions on the vacuum region description are ongoing (possibilities are: include the vacuum region into the stability code or introduce additional CPO block). Final form is not agreed. Create Kepler actor Work to Do (MARS-F)

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