suzuki.c

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#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "ascot5.h"
#include "consts.h"
#include "error.h"
#include "suzuki.h"
 
#define N_IMPURITY_DATA 7

real A_highE[3][10] = {
{12.7, 1.25, 0.452, 0.0105, 0.547, -0.102,   0.360, -0.0298, -0.0959, 4.21e-3},
{14.1, 1.11, 0.408, 0.0105, 0.547, -0.0403,  0.345, -0.0288, -0.0971, 4.74e-3},
{12.7, 1.26, 0.449, 0.0105, 0.547, -0.00577, 0.336, -0.0282, -0.0974, 4.87e-3}
};

real A_lowE[3][10] = {
{-52.9, -1.36, 0.0719, 0.0137, 0.454, 0.403, -0.220, 0.0666, -0.0677, -1.48e-3},
{-67.9, -1.22, 0.0814, 0.0139, 0.454, 0.465, -0.273, 0.0751, -0.0630, -5.08e-4},
{-74.2, -1.18, 0.0843, 0.0139, 0.453, 0.491, -0.294, 0.0788, -0.0612, -1.85e-4}
};

integer Z_imp[]    = {   2,   6,   6,   8,   7,   5,  26 };

real Zeffmin_imp[] = { 1.0, 1.0, 5.0, 1.0, 1.0, 1.0, 1.0 };

real Zeffmax_imp[] = { 2.1, 5.0, 6.0, 5.0, 5.0, 5.0, 5.0 };

real B_highE[N_IMPURITY_DATA][12] = {
    {  0.231,     0.343,    -0.185,    -0.162e-1,  0.105,    -0.703e-1,
       0.531e-1,  0.342e-2, -0.838e-2,  0.415e-2, -0.335e-2, -0.221e-3 },
    { -0.101e1,  -0.865e-2, -0.124,    -0.145e-1,  0.391,     0.161e-1,
       0.298e-1,  0.332e-2, -0.248e-1, -0.104e-2, -0.152e-2, -0.189e-3 },
    { -0.100e1,  -0.255e-1, -0.125,    -0.142e-1,  0.388,     0.206e-1,
       0.297e-1,  0.326e-2, -0.246e-1, -0.131e-2, -0.148e-2, -0.180e-3 },
    //{ -0.613,     0.552e-1, -0.167,    -0.159e-1,  0.304,     0.154e-2,
    //   0.436e-1,  0.378e-2, -0.201e-1, -0.216e-3, -0.251e-2, -0.227e-3 },
    { -0.102e1,  -0.148e-1, -0.674e-1, -0.917e-2,  0.359,     0.143e-1,
       0.139e-1,  0.184e-2, -0.209e-1, -0.732e-3, -0.502e-3, -0.949e-4 },
    { -0.102e1,  -0.139e-1, -0.979e-1, -0.117e-1,  0.375,     0.156e-1,
       0.224e-1,  0.254e-2, -0.226e-1, -0.889e-3, -0.104e-2, -0.139e-3 },
    //{ -0.441,     0.129,    -0.170,    -0.162e-1,  0.277,    -0.156e-1,
    //   0.466e-1,  0.379e-2, -0.193e-1,  0.753e-3, -0.286e-2, -0.239e-3 },
    { -0.732,     0.183e-1, -0.155,    -0.172e-1,  0.321,     0.946e-2,
       0.397e-1,  0.420e-2, -0.204e-1, -0.619e-3, -0.224e-2, -0.254e-3 },
    { -0.820,    -0.636e-2,  0.542e-1,  0.395e-2,  0.202,     0.806e-3,
      -0.200e-2, -0.178e-2, -0.610e-2,  0.651e-3,  0.175e-2,  0.146e-3 }
};

real B_lowE[N_IMPURITY_DATA][12] = {
    { -0.792,     0.420e-1,  0.530e-1,  -0.139e-1,  0.301,    -0.264e-1,
      -0.299e-1,  0.607e-2,  0.272e-3,   0.611e-2,  0.347e-2, -0.919e-3 },
    {  0.161,     0.598e-1, -0.336e-2,  -0.426e-2, -0.157,    -0.396e-1,
       0.460e-2,  0.219e-2,  0.391e-1,   0.711e-2, -0.144e-2, -0.385e-3 },
    {  0.158,     0.554e-1, -0.431e-2,  -0.335e-2, -0.155,    -0.374e-1,
       0.537e-2,  0.174e-2,  0.388e-1,   0.683e-2, -0.160e-2, -0.322e-3 },
    //{  0.112,     0.495e-1,  0.116e-1,  -0.286e-2, -0.149,    -0.331e-1,
    //  -0.426e-2,  0.980e-3,  0.447e-1,   0.652e-2, -0.356e-3, -0.203e-3 },
    {  0.111,     0.541e-1, -0.346e-3,  -0.368e-2, -0.108,    -0.347e-1,
       0.193e-2,  0.181e-2,  0.280e-1,   0.604e-2, -0.841e-3, -0.317e-3 },
    {  0.139,     0.606e-1, -0.306e-2,  -0.455e-2, -0.133,    -0.394e-1,
       0.399e-2,  0.236e-2,  0.335e-1,   0.690e-2, -0.124e-2, -0.405e-3 },
    //{  0.112,     0.495e-1,  0.116e-1,  -0.286e-2, -0.149,    -0.331e-1,
    //  -0.426e-2,  0.980e-3,  0.447e-1,   0.652e-2, -0.356e-3, -0.203e-3 },
    {  0.122,     0.527e-1, -0.430e-3,  -0.318e-2, -0.151,    -0.364e-1,
       0.343e-2,  0.151e-2,  0.420e-1,   0.692e-2, -0.141e-2, -0.290e-3 },
    { -0.110e-1,  0.202e-1,  0.946e-3,  -0.409e-2, -0.666e-2, -0.117e-1,
      -0.236e-3,  0.202e-2,  0.408e-2,   0.185e-2, -0.648e-4, -0.313e-3 }
};

a5err suzuki_sigmav(real* sigmav, real EperAmu, real vnorm, real ne, real te,
                    integer nion, real* ni, const int* anum, const int* znum) {
    a5err err = 0;
    /* Convert eperamu to keV and te to eV */
    EperAmu /= (1e3*CONST_E);
    te /= CONST_E;
 
    int ind_H[3]; /* Indices of possible hydrogen species H, D, and T */
    int n_H = 0;  /* Total number of hydrogen species (max 3)         */
    int ind_Z[MAX_SPECIES]; /* Indices of impurity species            */
    int n_Z = 0;  /* Total number of impurity species                 */
 
    /* Separate ions into hydrogen species and impurities and calculate
     * their total densities and Zeff */
    real dens_H = 0.0, dens_Z = 0.0;
    real Zeff_sum1 = 0.0, Zeff_sum2 = 0.0;
    for(int i = 0; i < nion; i++) {
        if(znum[i] == 1) {
            ind_H[n_H] = i;
            dens_H += ni[i];
            n_H++;
        } else {
            ind_Z[n_Z] = i;
            dens_Z += ni[i];
            n_Z++;
        }
 
        Zeff_sum1 += ni[i] * znum[i] * znum[i];
        Zeff_sum2 += ni[i] * znum[i];
    }
    real Zeff = Zeff_sum1 / Zeff_sum2;
 
    if(n_H == 0) {
        /* No hydrogen species present */
        err = error_raise( ERR_INPUT_EVALUATION, __LINE__, EF_SUZUKI );
    }
 
    /* Select low- or high-energy coefficient tables */
    real (*A)[10];
    real (*B)[12];
    if(EperAmu >= 9.0 && EperAmu < 100.0) {
        A = A_lowE;
        B = B_lowE;
    } else if(EperAmu < 10000.0) {
        A = A_highE;
        B = B_highE;
    } else {
        /* Outside energy range, just put some data to avoid segfaults */
        A = A_lowE;
        B = B_lowE;
        err = error_raise( ERR_INPUT_EVALUATION, __LINE__, EF_SUZUKI );
    }
 
    real logE = log(EperAmu);
    real N    = ne * 1.0e-19;
    real logN = log(N);
    real U    = log(te * 1.0e-3);
 
    /* Equation 28 for sigma_H */
    real sigma_H = 0.0;
    for(int i = 0; i < n_H; i++) {
        real* Aijk = A[anum[ind_H[i]]-1];
        /* Weight with density in case we have multiple hydrogen species */
        sigma_H += ni[ind_H[i]]
            * ( Aijk[0] * 1.e-16 / EperAmu )
            * ( 1.0 + Aijk[1] * logE + Aijk[2] * logE * logE )
            * ( 1.0 + pow( 1.0 - exp( -Aijk[3] * N ), Aijk[4] )
                * (Aijk[5] + Aijk[6] * logE + Aijk[7] * logE * logE) )
            * ( 1.0 + Aijk[8] * U + Aijk[9] * U * U );
    }
    sigma_H /= dens_H;
 
    /* Equations 26 & 27 for Sz with Rui's correction for the sum */
    real sigma_Z = 0, numerator = 0, denominator = 0;
    for(int i = 0; i < n_Z; i++) {
        int ind_B = -1;
        for(int j = 0; j < N_IMPURITY_DATA; j++) {
            if(Z_imp[j] == znum[ind_Z[i]] && Zeff > Zeffmin_imp[j]
               && Zeff < Zeffmax_imp[j]) {
                ind_B = j;
            }
        }
        if(ind_B < 0 && !err) {
            /* Data for the input species not tabulated */
            err = error_raise( ERR_INPUT_EVALUATION, __LINE__, EF_SUZUKI );
        }
        denominator += znum[ind_Z[i]] * (znum[ind_Z[i]] - 1) * ni[ind_Z[i]];
        numerator += znum[ind_Z[i]] * (znum[ind_Z[i]] - 1) * ni[ind_Z[i]]
            * (B[ind_B][0]
               + B[ind_B][1]  * U
               + B[ind_B][2]  * logN
               + B[ind_B][3]  * logN * U
               + B[ind_B][4]  * logE
               + B[ind_B][5]  * logE * U
               + B[ind_B][6]  * logE * logN
               + B[ind_B][7]  * logE * logN * U
               + B[ind_B][8]  * logE * logE
               + B[ind_B][9]  * logE * logE * U
               + B[ind_B][10] * logE * logE * logN
               + B[ind_B][11] * logE * logE * logN * U);
    }
    if(denominator > 0)
        sigma_Z = numerator / denominator;
 
    /* Equation 24 and convert cm^2 to m^2*/
    *sigmav = sigma_H * (1 + (Zeff - 1) * sigma_Z) * 1e-4;
    /* Multiply with velocity to get correct units */
    *sigmav *= vnorm;
 
    if(err) { *sigmav = 0.0; }
    return err;
}
 
#undef N_IMPURITY_DATA