组会记录 PSC code PWSO model baldur discussion

14th week group meeting record

normal speed

Posted by JXLIU on April 7, 2022

第十四周组会记录

1. 平衡

修改文章

PWSO 0D 模型

由PWSO 0D 模型推出的密度极限与 Greenwald 密度极限的对比

PWSO 0D 模型推出的密度极限

\[n_{c}=\frac{2 D_{\perp}}{f \lambda \operatorname{Rad}[T(r)]} \frac{T_{t}}{I\left(T_{t}\right) a} \propto \frac{T_{t}}{I\left(T_{t}\right) a}\]

垂直扩散系数：

  • Bohm diffusion [stangeby 2000 Eq. (4.8); D. Bohm, in The characteristics of electrical discharges in magnetic fields Eq. (8)] $q\approx \frac{aB_\phi}{RB_p}, 2\pi aB_p=\mu_0I_0$, \(D_\perp\propto Te/B\propto\frac{a^2T}{qRI_0}\)

    \[n_{c}=\frac{2 D_{\perp}}{f \lambda \operatorname{Rad}[T(r)]} \frac{T_{t}}{I\left(T_{t}\right) a} \propto \frac{T_{t}}{I\left(T_{t}\right)}\frac{aT}{qRI_0f\lambda \text{Rad}}\]

  • Classical diffusion [stangeby 2000 Eq. (4.9); Goldston R. J. Introduction to plasma physics 1997, p196] $\rho_|^{\text{spitzer}}\approx 8\times 10^{-4}/T_e^{3/2}, D_\perp^{\text{classical}}=2\rho_|^{\text{spitzer}}nk(T_e+T_i)/B^2\propto nT/B^2$

  • Neoclassical diffusion

中性粒子电离位置 $\lambda$ 与输运系数、温度有关，需要找到相应模型进行描述。

2. 辐射

将目前的 ignitor 算例对照着 baldur 文献中程序结构图运行了一遍。列了一个大致的程序修改计划。

3. GPU

PSC with CPU only 在 mhd, hust, 北京并行超算上都可以成功编译、运行。

PSC with CUDA 在 mhd, hust, 北京并行超算上的编译有各种没解决的问题。

下周计划

  • 修改文章
  • 继续查找根据 PWSO 0D 模型推导出的 $n_c$ 中 $D_\perp,~\lambda$ 与磁场、电流、温度的关系，从而与 Greenwald 密度极限对比。 可以查找 EMC3 程序文献 [Y. Feng 1999] 中的扩散系数做参考。
  • 开始修改 baldur 程序，以 PPT 形式讲 baldur 参考文献。
  • 学习 OpenACC；安装 heq 系统。

Program BALDUR

按照如下流程，可以将程序大致分为 30 步，大致一周一步

Outer calling structure

  1. Set up I/O units (except for ripple input data file).
  2. Call BLOCKDTA Store fundamental constants.
  3. Call MASTER
    1. Call BASIC Initialize OLYMPUS variables. Call MODIFY, which reads input deck header cord used for restart switches (not implemented in present revision of BALDUR).
    2. Print date and time.
    3. Call COTROL
      1. Call LABRUN Store BALDUR version number. Read runs labels from input deck. Work revision number, labels, “PROGRAM BALDUR”.
      2. Call CLEAR Clear common blocks. Includes calls to ACLEAR, GCLEAR, HCLEAR, ZCLEAR.
      3. If run is not a restart Call PRESET Set default values for NAMELIST input variables ($\leftarrow$ appendix D).
      4. If run is a restart Call RESUME Restart capability is not implemented in present version of BALDUR. Do not use this branch.
      5. Call DATA Read and write NAMELIST input.
      6. Call AUXVAL
        1. Call ERRCHK Check for obvious mistakes in input deck.
        2. Call UNITS Computer units conversion factors.
        3. Set auxiliary values based on input data. This includes code flags, the radial grid, time dependent conditions, plasma conditions variables not defined in INITIAL or START, etc. ($\leftarrow$ section 4).
        4. If scrape-off model is on, output sheath limited current densities ($\leftarrow$ section 2.8).
        5. Call **IMPRAD(1)**
          1. Initialize neutral impurity influx parameters ($\leftarrow$ section 2.9.13).
          2. If scrape-off model is on Call PDX Initialize and compute scrape-off losses ($\leftarrow$ section 2.9.5).
          3. Initialize coronal radiation package. Read atomic data file FOR22 ($\leftarrow$ section 7.3).
        6. Call **BEAMS(1)**

          Initialize neutral beam package ($\leftarrow$ section 2.9.2).

        7. If run is not a restart Call INITAL
          1. Call **IMPRAD(2)**
            1. If scrapeoff model is on Call PDX Initialize and compute scrapeoff losses ($\leftarrow$ section 2.9.5).
            2. Compute initial radiation terms, impurity charge states. Call coronal radiation package if selected ($\leftarrow$ section 2.9.4).
          2. Define physical initial conditions for $\chi$ ($\leftarrow$ section 5.2.3), $B_\theta$. Note that the electron density is redefined in START (~section 4).
        8. Call START
          1. Set initial $\Delta t$, boundary conditions, volume integrals. Unlock neutral impurity influx flag.
          2. Call GETCHI(2)
            1. Call **IMPRAD(2)**

              Same as above, plus compute neutral impurity and He influxes. Includes call to PDX.

            2. Compute boundary-centered densities and temperatures, zone-centered $B_\theta$ and $J$ ($\leftarrow$ section 5.2.2). Compute Z-effective, electron density.
            3. Initialize packages for remaining source terms: call **HEAT(1)** (lower hybrid and input profile heating), **ECRH(1)** (electron cyclotron resonance heating), and either **ALFINI(alphas)** or **HE3(1)** (D-D fusion) as selected by input.
        9. Call OUTPUT(1) Initial alphanumeric output (call MPRINT, GPRINT, HPRINT, IPRINT, APRINT **or **FPRINT, RPRINT, SPRINT). Initial graphics output (call TGRAF(1), GRAFIX(1)).
        10. Call STEPON Do a time step of main computations. See ext. chart.
        11. Call OUTPUT(2) Control output flags. At times or time steps selected by input, do main alphanumeric output (call MPRINT, NCFPRT, GPRINT, HETPRT, HPRINT, IPRINT and either APRINT, FPRINT, as selected by input), short alphanumeric output (call SPRING, GPRINT), and/or graphics output (call TGRAF(2), GRAFIX(2)).
        12. CALL TSEND Test for completion of run.
        13. If run is not yet completed, do next time step: go to #10.
        14. Call OUTPUT(3) Do main alphanumeric output for final time step if this has not been done already (same calls as in #11). Do final graphics output and close graphics (call TGRAF(3), GRAFIX(3).
        15. Call ENDRUN Terminate run. Print final message, STOP.

Inner calling structure

  1. Call STEPON
    1. Do short teletype output at appropriate time steps. Zero the iteration counter. CALL SAWMIX
    2. Call RESOLV(1) Initialize flags and store values for predictor-corrector, extrapolation.
    3. Unlock neutral impurity influx flag.
    4. Call COEF
      1. Call GETCHI(2)
        1. Call **IMPRAD(2)**
          1. If scrapeoff model is on, Call PDX Compute scrapeoff losses Call DIVER.
          2. Compute radiation terms, impurity $\left<Z\right>$ and $\left<Z^2\right>$, calling coronal radiation package if selected by input.
          3. Compute neutral impurity and its influxes.
        2. Compute boundary-centered densities and temperatures, zone-centered $B_\theta$ and $J$ ($\leftarrow$ section 5.2.2). Compute $Z_{\text{eff}}$, electron density.
      2. Call TRCOEF Compute transport coefficients. This may include calls to EMPIRC, XSCALE, INIGRL. On initial call if ripple input data file is being used, open and read this file and call AVERAGE.
      3. If this is a repeated time step, or the corrector portion of a predictor-corrector time step, or a $\Delta t/2$ minor time step of an extrapolation time step, skip to #10.
      4. Call **NEUGAS**

        Compute sources due to neutral gas. This includes calls to PDX if scrapeoff model is on, and to the Monte Carlo neutral gas package at appropriate time steps. Compute neutral hydrogen influxes, either by prescription or by density monitor.

      5. Call **BEAMS(2)**

        Compute sources due to neutral beam injection. This includes Fokker-Planck calculation of beam fast ion distribution, and every so often includes call to Monte Carlo computation of beam deposition profile.

      6. Call **HEAT(2)**

        Compute sources due to lower hybrid heating or input profile heating.

      7. Call **ECRH(1)**

        Compute sources due to electron cyclotron resonance heating.

      8. If D-T fusion has been selected by input,

        Call ALPHAS(2) Compute sources due to D-T fusion. This includes calculation of alpha-particle distribution, and includes call to Monte Carlo computation of alpha-particle orbits.

      9. If D-D fusion has been selected by input,

        Call HE3(2) Compute sources due to D-T fusion.

      10. Call CONVRT
        1. If nearly exact neoclassical transport model has been selected, compute transport coefficients for this model. This includes call to NCFLUX.
        2. Compute A, B, C, D ($\leftarrow$ appendix A).
      11. Call CNVCOF Convert A, B, C, D ($\leftarrow$ appendix A) from standard to interval units.
    5. Call SOLVEB Solve $B_\theta$ equation. Compute source due to ohmic heating.
    6. Call BOUNDS Compute boundary condition coefficients.
    7. Call REDUCE Compute P, Q, R, S ($\leftarrow$ eq. 5.2.3g). Reduce equations to first order.
    8. Call SOLVE Solve transport equations for new $\chi$
    9. Call RESOLV Time-step control. Set next $\Delta t$. Control flags and store values for predictor-corrector. extrapolation, time step repetition.
    10. Increment iteration counter. Check that maximum number of iterations has not been exceeded.
    11. If time step is to be repeated, or the predictor portion of a predictor-corrector time step has just finished, or the first $\Delta t/2$ minor time step of an extrapolation time step has just finished, go to #4.
    12. If the $\Delta t$ minor time step of an extrapolation time step has just finished, go to #5.
    13. Call CMPRES
      1. Compress the plasma: adjust $\chi$, $B_\theta$ radial grid.
      2. Call other routines which may need to compress: BEAMS(3), HEAT(3) and either ALPHAS(3) or HE3(3) as selected by input.
    14. Call **PDRIVE** Compute sources due to pellet injection.
    15. Call GETCHI(1) Update quantities based on $\chi$: densities in standard units, ion and electron temperatures. Also update $B_\theta$ $B_Z$ in standard units. Note that electron density (but not electron temperature) is recomputed in GETCHI(2).
    16. Lock neutral impurity influx flag

      .

    17. Call **GETCHI(2)**

      Almost same as COEF#1, but new $\chi$ values were used, and there is no neutral impurity or He influx computation when IMPRAD(2) is called.

    18. Advance the time. Time step is completed.
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