Recent Changes

Friday, August 11

  1. page STELLOPT Input Namelist edited ... TARGET_WP = 1.0E3 SIGMA_WP = 1.0 ! Stored Energy [J] TARGET_ASPECT = 5.0 S…
    ...
    TARGET_WP = 1.0E3 SIGMA_WP = 1.0 ! Stored Energy [J]
    TARGET_ASPECT = 5.0 SIGMA_ASPECT = 0.5 ! Aspect Ratio (R/a)
    !------------------------------------------------------------------------
    ! Equilibrium Elongation Targets
    ! KAPPA: Elongation defined by plasma minor radius.
    ! KAPPA_BOX: Elongation defined by box.
    ! KAPPA_AVG: Toroidal average of KAPPA.
    ! Note: KAPPA and KAPPA_BOX require a toroidal angle to be
    ! specified (defaults to 0.0).
    !------------------------------------------------------------------------
    TARGET_KAPPA = 2.0 SIGMA_KAPPA = 1.0 PHI_KAPPA = 0.0
    TARGET_KAPPA_BOX = 2.0 SIGMA_KAPPA_BOX = 1.0 PHI_KAPPA_BOX = 0.0
    TARGET_KAPPA_AVG = 2.0 SIGMA_KAPPA_AVG = 1.0

    !------------------------------------------------------------------------
    ! Boozer Coordinate Helicity
    (view changes)
    5:32 am

Monday, July 31

  1. page TERPSICHORE edited ... The TERPSICHORE code calculates ideal kink stability from VMEC equilibria. TheoryTheory ...…
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    The TERPSICHORE code calculates ideal kink stability from VMEC equilibria.
    TheoryTheory
    ...
    TERPSICHORE code utilizes utilizes an ideal
    \vec \xi = \vec \xi \left( {\xi ^s ,\eta ,\mu } \right) = \sqrt g \xi ^s \nabla \theta \times \nabla \varphi + \eta \frac{{\vec B \times \nabla s}}{{B^2 }} + \left[ {\frac{{J\left( s \right)}}{{\Phi '\left( s \right)B^2 }}\eta - \mu } \right]\vec B
    where the first component is normal to the flux tube. The perturbation is chosen to be divergence free eliminating the µ component. Stability is noted by an increase in potential energy for a given perturbation. Thus negative eigenvalues indicate unstable modes.
    ...
    Exponent governing transition towards the conducing wall from the PVI (>1)
    NOWALL
    ...
    conducting wall (recommended)-1(recommended) -1 : Conducting
    ...
    components by AWALL
    0
    AWALL0 : Conducting
    1 : Prescribed conducting wall, Drozdov Formula (GWALL, AWALL, EWALL, DWALL, DRWAL, DZWAL, NPWALL)
    AWALL
    ...
    Anderson D V, Cooper W A, Gruber R and Merazzi S 1990 TERPSICHORE: a three-dimensional ideal magnetohydrodynamic stability program //Scientific Computing on Supercomputers II
    Fu G Y, Cooper W A, Gruber R, Schwenn U and Anderson D V 1992 Fully three-dimensional ideal magnetohydrodynamic stability analysis of low-n modes and Mercier modes in stellarators //Phys. Fluids B// **4** 1401
    Redi, M. H., A. Diallo, W. A. Cooper, G. Y. Fu, C. Nührenberg, N. Pomphrey, A. H. Reiman, M. C. Zarnstorff, and NCSX Team 2000 Robustness and flexibility in compact quasiaxial stellarators: Global ideal magnetohydrodynamic stability and energetic particle transport //Physics of Plasmas// **7** 2508
    Turnbull A D, Cooper W A, Lao L L, and Ku L-P 2011 Ideal MHD spectrum calculations for the ARIES-CS configuration //Nucl. Fusion 51// 123011
    (view changes)
    12:13 pm

Tuesday, July 18

  1. page TERPSICHORE edited ... Exponent governing transition towards the conducing wall from the PVI (>1) NOWALL ... c…
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    Exponent governing transition towards the conducing wall from the PVI (>1)
    NOWALL
    ...
    conducting wall (recommended) -1(recommended)-1 : Conducting
    0 : Conducting wall extrapolated from PVI.
    1 : Prescribed conducting wall, Drozdov Formula (GWALL, AWALL, EWALL, DWALL, DRWAL, DZWAL, NPWALL)
    ...
    Vertical helical modulation of conducting wall.
    NPWALL
    ...
    conducting wall (ignored for NOWALL<1)
    RPLMIN
    Minimum absolute value of R, Z to reprint the active Boozer mode table (6 and 16 file, ~1E-5)
    (view changes)
    6:46 am

Tuesday, May 30

  1. 3:59 am

Monday, May 29

  1. page STELLOPT Input Namelist edited ... TARGET_PHIEDGE = 2.5 SIGMA_PHIEDGE = 0.025 ! Enclosed Toroidal Flux [Wb] TARGET_CURTOR …
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    TARGET_PHIEDGE = 2.5 SIGMA_PHIEDGE = 0.025 ! Enclosed Toroidal Flux [Wb]
    TARGET_CURTOR = 1.0E6 SIGMA_CURTOR = 1.0E3 ! Total Toroidal Current [A]
    TARGET_CURVATURE = 1.0E-3 SIGMA_CURVATURE = 1.0 ! Flux surface curvature
    TARGET_RBTOR = 7.2 SIGMA_RBTOR = 0.01 ! R*Btor [T-m]
    TARGET_R0 = 3.6 SIGMA_R0 = 0.01 ! Magnetic Axis R (phi=0) [m]
    (view changes)
    12:42 am

Wednesday, May 3

  1. page STELLOPT Input Namelist edited ... Number of workers to evaluate map (default: NPROCS) Variables ... values are only used …
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    Number of workers to evaluate map (default: NPROCS)
    Variables
    ...
    values are only used to bound the optimization (necessary for the global optimization techniques (GADE).searches: PSO,GADE; but optional for the Levenberg) . The scaling
    !------------------------------------------------------------------------
    ! Optimized Quantities
    (view changes)
    7:48 am

Monday, April 24

  1. page Bootstrap Calculation for NCSX-Like configuration edited ... MBUSE = 72 ! From Boozer Transformation NBUSE = 24 ! From Boozer Transformation ZEFF0 ZE…
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    MBUSE = 72 ! From Boozer Transformation
    NBUSE = 24 ! From Boozer Transformation
    ZEFF0ZEFF1 = 1.0
    DAMP_BS = 0.001
    TEMPRES = 1.0 ! Coefficient Te=P^TEMPRES
    (view changes)
    8:58 am

Monday, March 6

  1. page STELLOPT edited ... Boundary Representations Explained Optimization of an NCSX-like configuration Optimization …
    ...
    Boundary Representations Explained
    Optimization of an NCSX-like configuration
    Optimization of Iota using LMDIF
    STELLOPT Turbulent Transport
    STELLOPT Coil Optimization
    (view changes)
    8:02 am
  2. page Optimization of Iota using LMDIF edited ... . . ... the equilibrium.…
    ...
    .
    .
    ...
    the equilibrium. IfIf secondary codes
    ...
    as well. OnceOnce the code
    ...
    are printed. ForFor the OPT_TYPE="LMDIF"
    ...
    each minima. FirstFirst three numbers
    ...
    and chi-squared. TheseThese are the
    ...
    space jacobian. TheThe sign after
    ...
    downhill (-). AfterAfter which each
    ...
    Levenberg-Marquardt parameter. TheThe minimum value isis denoted by an asterisk. AA message regarding
    ...
    process repeats. ItIt is possible
    ...
    jacobian step. IfIf this occurs,
    Examine the output.
    The code outputs various 'temporary' files which can be removed at the end of a run. These files can easily be removed by the command 'rm *_opt*'. What remains are files for each minimum found by the VMEC (input, mercier, jxbout, and wout). In addition, STELLOPT outputs the fevals, jacobian, stellopt, var_labels, and xvec files. The STELLOPT file contains an ordered output of the various minima found.
    [[code format="BASH"]VERSION 2.49ITER 00000IOTAVERSION 2.49
    ITER 00000
    IOTA
    004 007R007
    R
    PHI Z
    ...
    SIGMA IOTA 0.000000000000E+000
    0.000000000000E+000
    0.000000000000E+000 0.000000000000E+000
    ...
    1.000000000000E-001 1.000000000000E-002 2.435819151485E-002 0.000000000000E+0002.43581915148
    5E-002
    0.000000000000E+000
    0.000000000000E+000 0.000000000000E+000
    ...
    1.000000000000E-001 1.000000000000E-002 3.002488050290E-002 0.000000000000E+0003.00248805029
    0E-002
    0.000000000000E+000
    0.000000000000E+000 0.000000000000E+000
    ...
    1.000000000000E-001 1.000000000000E-002 3.471811472812E-002 0.000000000000E+0003.47181147281
    2E-002
    0.000000000000E+000
    0.000000000000E+000 0.000000000000E+000
    ...
    1.000000000000E-001 1.000000000000E-002 4.480065323289E-002TARGETS4.48006532328
    9E-002
    TARGETS
    1 4TARGETS 1.000000000000E-001 1.000000000000E-001 1.000000000000E-001 1.000000000000E-001SIGMAS4
    TARGETS
    1.000000000000E-001
    1.000000000000E-001
    1.000000000000E-001
    1.000000000000E-001
    SIGMAS
    1 4SIGMAS 1.000000000000E-002 1.000000000000E-002 1.000000000000E-002 1.000000000000E-002VALS4
    SIGMAS
    1.000000000000E-002
    1.000000000000E-002
    1.000000000000E-002
    1.000000000000E-002
    VALS
    1 4VALUES 2.435819151485E-002 3.002488050290E-002 3.471811472812E-002 4.480065323289E-002[code]]
    >
    4
    VALUES
    2.435819151485E-002
    3.002488050290E-002
    3.471811472812E-002
    4.480065323289E-002
    Every iteration is stored in this file. Each chi-squared module outputs detailed information into the file and the full components of the chi-squared vector are output as well.

    (view changes)
    8:01 am
  3. page Optimization of Iota using LMDIF edited Tutorial: Optimization of iota using Levenberg-Marquardt {ncsx_fieldlines.jpg} This tutorial w…

    Tutorial: Optimization of iota using Levenberg-Marquardt {ncsx_fieldlines.jpg}
    This tutorial walks the user through using STELLOPT to optimize a simple configuration throught fixed boundary shaping.
    Edit the input namelist text file.
    The input namelist (input.STELLOPT_IOTA_LMDIF) contains the VMEC INDATA name list for a simple rotating ellipse equilibrium. And the STELLOPT OPTIMUM name which optimizes this equilibrium (varying the boundary harmonics and targeting the rotational transform).
    &INDATA
    !----- Runtime Parameters -----
    DELT = 0.9000000000000E+000
    NSTEP = 200
    TCON0 = 1.000000000000E+000
    NS_ARRAY = 16 25 36
    FTOL_ARRAY = 1.000000E-06 1.000000E-09 1.000000E-13
    NITER_ARRAY = 1000 1000 10000
    PRECON_TYPE = 'none'
    PREC2D_THRESHOLD = 1.000000E-19
    !----- Grid Parameters -----
    LASYM = F
    NFP = 0001
    MPOL = 005
    NTOR = 001
    PHIEDGE = 1.0
    !----- Free Boundary Parameters -----
    LFREEB = F
    !----- Pressure Parameters -----
    GAMMA = 0.000000000000E+000
    BLOAT = 1.000000000000E+000
    SPRES_PED = 1.000000000000E+000
    PRES_SCALE = 0.000000000000E+000
    PMASS_TYPE = 'power_series'
    AM = 0.00000000000000E+00
    !----- Current/Iota Parameters -----
    CURTOR = 0.0
    NCURR = 1
    PCURR_TYPE = 'power_series'
    AC = 0.0
    !----- Axis Parameters -----
    RAXIS = 1.0
    ZAXIS = 0.0
    !----- Boundary Parameters -----
    RBC( 00,00) = 1.00 ZBS( 00,00) = 0.00
    RBC( 00,01) = 0.10 ZBS( 00,01) = 0.10
    RBC( 01,01) = 0.01 ZBS( 01,01) =-0.01
    RBC( 01,03) = 0.01 ZBS( 01,03) = 0.01
    /
    &OPTIMUM
    !-----------------------------------------------------------------------
    ! OPTIMIZER RUN CONTROL PARAMETERS
    !-----------------------------------------------------------------------
    NFUNC_MAX = 1000
    EQUIL_TYPE = 'VMEC2000'
    OPT_TYPE = 'LMDIF'
    FTOL = 1.00E-06
    XTOL = 1.00E-06
    GTOL = 1.00E-30
    FACTOR = 10.0
    EPSFCN = 1.00E-06
    MODE = 1
    LKEEP_MINS = T
    !-----------------------------------------------------------------------
    ! OPTIMIZED QUANTITIES
    !-----------------------------------------------------------------------
    LBOUND_OPT(001,001) = T
    LBOUND_OPT(001,003) = T
    !------------------------------------------------------------------------
    ! IOTA PROFILE TARGETS
    !------------------------------------------------------------------------
    TARGET_IOTA(001) = 0.1000 SIGMA_IOTA(001) = 0.0100 S_IOTA(001) = 0.0000
    TARGET_IOTA(002) = 0.1000 SIGMA_IOTA(002) = 0.0100 S_IOTA(002) = 0.25
    TARGET_IOTA(003) = 0.1000 SIGMA_IOTA(003) = 0.0100 S_IOTA(003) = 0.50
    TARGET_IOTA(004) = 0.1000 SIGMA_IOTA(004) = 0.0100 S_IOTA(004) = 1.0
    /
    Execute the code.
    The STELLOPT code is executed by passing the input file as an argument to the STELLOPT code. Note that since STELLOPT is a parallel code, it should be executed using a wrapper (such as mpirun, mpiexec, srun, etc.)
    >mpirun -np 8 ~/bin/xstelloptv2 input.STELLOPT_IOTA_LMDIF
    STELLOPT Version 2.49
    Equilibrium calculation provided by:
    =================================================================================
    ========= Variational Moments Equilibrium Code (v 8.52) =========
    ========= (S. Hirshman, J. Whitson) =========
    ========= http://vmecwiki.pppl.wikispaces.net/VMEC =========
    =================================================================================
    ----- Optimization -----
    =======VARS=======
    RBC( 001, 001): Radial Boundary Specification (COS)
    ZBS( 001, 001): Vertical Boundary Specification (SIN)
    RBC( 001, 003): Radial Boundary Specification (COS)
    ZBS( 001, 003): Vertical Boundary Specification (SIN)
    ======TARGETS=====
    Rotational Transform
    ==================
    Number of Processors: 8
    Number of Parameters: 4
    Number of Targets: 4
    !!!! EQUILIBRIUM RESTARTING NOT UTILIZED !!!!
    ========Parallel Code Execution Info=======
    Number of Processors: 8
    Number of Optimization Threads: -1
    Workers per optimizer thread: -8
    Number of Optimizer Threads: 8
    OPTIMIZER: Levenberg-Mardquardt
    NFUNC_MAX: 1000
    FTOL: 1.0000E-06
    XTOL: 1.0000E-06
    GTOL: 1.0000E-30
    EPSFCN: 1.0000E-06
    MODE: 1
    FACTOR: 10.000000000000000
    Warning: more processors have been requested than the maximum (nvar) required = 4
    --------------------------- EQUILIBRIUM CALCULATION ------------------------
    NS = 16 NO. FOURIER MODES = 14 FTOLV = 1.000E-06 NITER = 1000
    ITER FSQR FSQZ FSQL RAX(v=0) DELT WMHD
    1 7.45E-01 5.05E-01 2.30E-01 1.000E+00 9.00E-01 1.0432E+02
    118 4.48E-07 2.85E-07 3.90E-08 9.970E-01 7.08E-01 9.7789E+01
    NS = 25 NO. FOURIER MODES = 14 FTOLV = 1.000E-09 NITER = 1000
    ITER FSQR FSQZ FSQL RAX(v=0) DELT WMHD
    1 4.11E-04 2.18E-04 9.80E-07 9.970E-01 9.00E-01 9.7789E+01
    200 4.61E-09 1.42E-09 1.09E-09 9.972E-01 6.37E-01 9.7789E+01
    289 9.75E-10 1.73E-10 1.74E-10 9.976E-01 6.37E-01 9.7789E+01
    NS = 36 NO. FOURIER MODES = 14 FTOLV = 1.000E-13 NITER = 10000
    ITER FSQR FSQZ FSQL RAX(v=0) DELT WMHD
    1 1.82E-04 1.18E-04 2.26E-07 9.976E-01 9.00E-01 9.7789E+01
    200 1.51E-08 6.31E-09 4.71E-09 9.971E-01 6.18E-01 9.7789E+01
    400 8.50E-10 2.78E-10 1.41E-10 9.983E-01 6.18E-01 9.7789E+01
    600 1.82E-10 5.17E-11 3.50E-11 1.000E+00 6.18E-01 9.7789E+01
    800 4.25E-11 1.19E-11 6.84E-12 1.002E+00 6.18E-01 9.7789E+01
    1000 1.82E-11 2.92E-12 1.87E-12 1.003E+00 6.18E-01 9.7789E+01
    1200 5.39E-12 7.38E-13 6.01E-13 1.004E+00 6.18E-01 9.7789E+01
    1400 1.04E-12 3.08E-13 1.45E-13 1.004E+00 6.18E-01 9.7789E+01
    1600 2.17E-13 1.01E-13 2.43E-14 1.004E+00 6.18E-01 9.7789E+01
    1660 9.57E-14 2.98E-14 1.54E-14 1.004E+00 6.18E-01 9.7789E+01
    EXECUTION TERMINATED NORMALLY
    FILE : reset_file
    NUMBER OF JACOBIAN RESETS = 3
    TOTAL COMPUTATIONAL TIME 4.09 SECONDS
    TIME TO READ IN DATA 0.00 SECONDS
    TIME TO WRITE DATA TO WOUT 0.01 SECONDS
    TIME IN EQFORCE 0.14 SECONDS
    TIME IN FOURIER TRANSFORM 1.04 SECONDS
    TIME IN INVERSE FOURIER XFORM 0.78 SECONDS
    TIME IN FORCES + SYMFORCES 0.85 SECONDS
    TIME IN BCOVAR 0.76 SECONDS
    TIME IN RESIDUE 0.09 SECONDS
    TIME (REMAINDER) IN FUNCT3D 0.35 SECONDS
    --------------------------- VMEC CALCULATION DONE -------------------------
    ASPECT RATIO: 9.901
    BETA: 0.000 (total)
    0.000 (poloidal)
    0.000 (toroidal)
    TORIDAL CURRENT: 0.803664860355E-10
    TORIDAL FLUX: 1.000
    VOLUME: 0.201
    MAJOR RADIUS: 1.000
    MINOR_RADIUS: 0.101
    STORED ENERGY: 0.000000000000E+00
    Beginning Levenberg-Marquardt Iterations
    Number of Processors: 8
    ======================================================================
    Iteration Processor Chi-Sq LM Parameter Delta Tol
    ======================================================================
    0 0 1.7927E+02
    1 1 1.7917E+02 -
    3 3 1.7920E+02 -
    4 4 1.7921E+02 -
    2 2 1.7937E+02 +
    5 1 1.0000E+12 1.8158E-05 6.9004E+01
    6 2 7.5974E+00* 9.5200E-01 5.4202E+00
    7 3 1.5923E+02 5.2374E+01 4.2575E-01
    8 4 1.7770E+02 7.0796E+02 3.3442E-02
    9 5 1.7914E+02 9.0542E+03 2.6269E-03
    10 6 1.7926E+02 1.1208E+05 2.0634E-04
    11 7 1.7927E+02 1.4678E+06 1.6208E-05
    12 8 1.7927E+02 1.8690E+07 1.2731E-06
    new minimum = 7.597E+00 lm-par = 4.760E-01 delta-tol = 1.138E+01
    .
    .
    .
    The screen output begins with basic information about the input parameters and how STELLOPT will be run. Then for the first iteration, the full VMEC screen output is shown along with information about the equilibrium. If secondary codes had been run, their output would be printed to the screen as well. Once the code enters the full optimization loop, only the values relevant to optimization are printed. For the OPT_TYPE="LMDIF" there are two phases for each minima. First three numbers are output: iteration number, processor number and chi-squared. These are the forward finite difference of the parameter space jacobian. The sign after each evaluation indicates if the resulting finite difference is uphill (+) or downhill (-). After which each processor evaluates a point along the descent direction, varying the Levenberg-Marquardt parameter. The minimum value is denoted by an asterisk. A message regarding the discovery of the new minima is then printed (if found) and the process repeats. It is possible that this step will fail to find a minima with smaller chi-squared than found during the parameter space jacobian step. If this occurs, a routine which searches finite difference combinations of the jacobian evaluation is executed.
    Examine the output.
    The code outputs various 'temporary' files which can be removed at the end of a run. These files can easily be removed by the command 'rm *_opt*'. What remains are files for each minimum found by the VMEC (input, mercier, jxbout, and wout). In addition, STELLOPT outputs the fevals, jacobian, stellopt, var_labels, and xvec files. The STELLOPT file contains an ordered output of the various minima found.
    [[code format="BASH"]VERSION 2.49ITER 00000IOTA 004 007R PHI Z S TARGET SIGMA IOTA 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 1.000000000000E-001 1.000000000000E-002 2.435819151485E-002 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 2.500000000000E-001 1.000000000000E-001 1.000000000000E-002 3.002488050290E-002 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 5.000000000000E-001 1.000000000000E-001 1.000000000000E-002 3.471811472812E-002 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 1.000000000000E+000 1.000000000000E-001 1.000000000000E-002 4.480065323289E-002TARGETS 1 4TARGETS 1.000000000000E-001 1.000000000000E-001 1.000000000000E-001 1.000000000000E-001SIGMAS 1 4SIGMAS 1.000000000000E-002 1.000000000000E-002 1.000000000000E-002 1.000000000000E-002VALS 1 4VALUES 2.435819151485E-002 3.002488050290E-002 3.471811472812E-002 4.480065323289E-002[code]]
    >

    (view changes)
    7:59 am

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