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neutral_rates.cxx
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neutral_rates.cxx
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/*!
Atomic processes
This code integrates atomic cross-sections over each grid cell
NOTE: Currently this only integrates in Y, but should integrate in 3D
******************
Copyright B.Dudson, J.Leddy, University of York, September 2016
email: [email protected]
This file is part of Hermes.
Hermes is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Hermes is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Hermes. If not, see <http://www.gnu.org/licenses/>.
*/
#include "hermes-1.hxx"
#include <bout/assert.hxx>
void Hermes::neutral_rates(const Field3D &Ne, const Field3D &Te,
const Field3D &Vi, // Plasma quantities
const Field3D &Nn, const Field3D &Tn,
const Field3D &Vnpar, // Neutral gas
Field3D &S, Field3D &F, Field3D &Q,
Field3D &R, // Transfer rates
Field3D &Riz, Field3D &Rrc, Field3D &Rcx) { // Rates
// Allocate output fields
S = 0.0;
F = 0.0;
Q = 0.0;
R = 0.0;
Riz = 0.0;
Rrc = 0.0;
Rcx = 0.0;
Cooordinates *coord = mesh->getCoordinates();
for (int i = mesh->xstart; i <= mesh->xend; i++)
for (int j = mesh->ystart; j <= mesh->yend; j++)
for (int k = 0; k < mesh->LocalNz; k++) {
// Integrate rates over each cell in Y
// NOTE: This should integrate over (x,y,z)
// Calculate cell centre (C), left (L) and right (R) values
BoutReal Te_C = Te(i, j, k),
Te_L = 0.5 * (Te(i, j - 1, k) + Te(i, j, k)),
Te_R = 0.5 * (Te(i, j, k) + Te(i, j + 1, k));
BoutReal Ne_C = Ne(i, j, k),
Ne_L = 0.5 * (Ne(i, j - 1, k) + Ne(i, j, k)),
Ne_R = 0.5 * (Ne(i, j, k) + Ne(i, j + 1, k));
BoutReal Vi_C = Vi(i, j, k),
Vi_L = 0.5 * (Vi(i, j - 1, k) + Vi(i, j, k)),
Vi_R = 0.5 * (Vi(i, j, k) + Vi(i, j + 1, k));
BoutReal Tn_C = Tn(i, j, k),
Tn_L = 0.5 * (Tn(i, j - 1, k) + Tn(i, j, k)),
Tn_R = 0.5 * (Tn(i, j, k) + Tn(i, j + 1, k));
BoutReal Nn_C = Nn(i, j, k),
Nn_L = 0.5 * (Nn(i, j - 1, k) + Nn(i, j, k)),
Nn_R = 0.5 * (Nn(i, j, k) + Nn(i, j + 1, k));
BoutReal Vn_C = Vnpar(i, j, k),
Vn_L = 0.5 * (Vnpar(i, j - 1, k) + Vnpar(i, j, k)),
Vn_R = 0.5 * (Vnpar(i, j, k) + Vnpar(i, j + 1, k));
if (Ne_C < 0.)
Ne_C = 0.0;
if (Ne_L < 0.)
Ne_L = 0.0;
if (Ne_R < 0.)
Ne_R = 0.0;
if (Nn_C < 0.)
Nn_C = 0.0;
if (Nn_L < 0.)
Nn_L = 0.0;
if (Nn_R < 0.)
Nn_R = 0.0;
// Jacobian (Cross-sectional area)
BoutReal J_C = coord->J(i, j),
J_L = 0.5 * (coord->J(i, j - 1) + coord->J(i, j)),
J_R = 0.5 * (coord->J(i, j) + coord->J(i, j + 1));
///////////////////////////////////////////
// Charge exchange
BoutReal R_cx_L = Ne_L * Nn_L * hydrogen.chargeExchange(Te_L * Tnorm) *
(Nnorm / Omega_ci);
BoutReal R_cx_C = Ne_C * Nn_C * hydrogen.chargeExchange(Te_C * Tnorm) *
(Nnorm / Omega_ci);
BoutReal R_cx_R = Ne_R * Nn_R * hydrogen.chargeExchange(Te_R * Tnorm) *
(Nnorm / Omega_ci);
ASSERT2(finite(R_cx_L));
ASSERT2(finite(R_cx_C));
ASSERT2(finite(R_cx_R));
// Power transfer from plasma to neutrals
// Factor of 3/2 to convert temperature to energy
Q(i, j, k) = (3. / 2) * (J_L * (Te_L - Tn_L) * R_cx_L +
4. * J_C * (Te_C - Tn_C) * R_cx_C +
J_R * (Te_R - Tn_R) * R_cx_R) /
(6. * J_C);
// Plasma-neutral friction
F(i, j, k) =
(J_L * (Vi_L - Vn_L) * R_cx_L + 4. * J_C * (Vi_C - Vn_C) * R_cx_C +
J_R * (Vi_R - Vn_R) * R_cx_R) /
(6. * J_C);
// Cell-averaged rate
Rcx(i, j, k) =
(J_L * R_cx_L + 4. * J_C * R_cx_C + J_R * R_cx_R) / (6. * J_C);
// Check that the value is finite
ASSERT1(finite(Rcx(i, j, k)));
///////////////////////////////////////
// Recombination
BoutReal R_rc_L = hydrogen.recombination(Ne_L * Nnorm, Te_L * Tnorm) *
SQ(Ne_L) * Nnorm / Omega_ci;
BoutReal R_rc_C = hydrogen.recombination(Ne_C * Nnorm, Te_C * Tnorm) *
SQ(Ne_C) * Nnorm / Omega_ci;
BoutReal R_rc_R = hydrogen.recombination(Ne_R * Nnorm, Te_R * Tnorm) *
SQ(Ne_R) * Nnorm / Omega_ci;
ASSERT2(finite(R_rc_L));
ASSERT2(finite(R_rc_C));
ASSERT2(finite(R_rc_R));
// Radiated power from plasma
// Factor of 1.09 so that recombination becomes an energy source at
// 5.25eV
R(i, j, k) = (J_L * (1.09 * Te_L - 13.6 / Tnorm) * R_rc_L +
4. * J_C * (1.09 * Te_C - 13.6 / Tnorm) * R_rc_C +
J_R * (1.09 * Te_R - 13.6 / Tnorm) * R_rc_R) /
(6. * J_C);
// Plasma sink / neutral source
S(i, j, k) =
(J_L * R_rc_L + 4. * J_C * R_rc_C + J_R * R_rc_R) / (6. * J_C);
// Transfer of ion momentum to neutrals
F(i, j, k) += (J_L * Vi_L * R_rc_L + 4. * J_C * Vi_C * R_rc_C +
J_R * Vi_R * R_rc_R) /
(6. * J_C);
// Transfer of ion energy to neutrals
Q(i, j, k) += (3. / 2) *
(J_L * Te_L * R_rc_L + 4. * J_C * Te_C * R_rc_C +
J_R * Te_R * R_rc_R) /
(6. * J_C);
// Cell-averaged rate
Rrc(i, j, k) =
(J_L * R_rc_L + 4. * J_C * R_rc_C + J_R * R_rc_R) / (6. * J_C);
ASSERT1(finite(Rrc(i, j, k)));
///////////////////////////////////////
// Ionisation
BoutReal R_iz_L =
Ne_L * Nn_L * hydrogen.ionisation(Te_L * Tnorm) * Nnorm / Omega_ci;
BoutReal R_iz_C =
Ne_C * Nn_C * hydrogen.ionisation(Te_C * Tnorm) * Nnorm / Omega_ci;
BoutReal R_iz_R =
Ne_R * Nn_R * hydrogen.ionisation(Te_R * Tnorm) * Nnorm / Omega_ci;
ASSERT2(finite(R_iz_L));
ASSERT2(finite(R_iz_C));
ASSERT2(finite(R_iz_R));
// Neutral sink, plasma source
S(i, j, k) -=
(J_L * R_iz_L + 4. * J_C * R_iz_C + J_R * R_iz_R) / (6. * J_C);
// Transfer of neutral momentum to ions
F(i, j, k) -= (J_L * Vn_L * R_iz_L + 4. * J_C * Vn_C * R_iz_C +
J_R * Vn_R * R_iz_R) /
(6. * J_C);
// Transfer of neutral energy to ions
Q(i, j, k) -= (3. / 2) *
(J_L * Tn_L * R_iz_L + 4. * J_C * Tn_C * R_iz_C +
J_R * Tn_R * R_iz_R) /
(6. * J_C);
// Ionisation and electron excitation energy
R(i, j, k) += (Eionize / Tnorm) *
(J_L * R_iz_L + 4. * J_C * R_iz_C + J_R * R_iz_R) /
(6. * J_C);
// Cell-averaged rate
Riz(i, j, k) =
(J_L * R_iz_L + 4. * J_C * R_iz_C + J_R * R_iz_R) / (6. * J_C);
ASSERT1(finite(Riz(i, j, k)));
}
}