Tutorial explaining how to simulate density evolution
The default setting in RAPTOR is to simulate only flux diffusion and electron temperature evolution. Here we explain how to add also an equation for evolving electron density.
Contents
% First, add the relevant paths close all hidden; run(fullfile(pwd,'..','RAPTOR_path.m')); % add RAPTOR path
Solve for ne with manual transport coefficients, fix ni/ne fraction
Load the default configuration structure.
[config] = RAPTOR_config; % load default params config.equi.mode = 'free'; % required to solve for ne % To solve ne equation, set these options: config.ne.method = 'state'; % Set boundary condition type (Dirichlet, specify ne directly) and value config.ne.BCtype = 'ne'; config.ne.BCval = 0.1e19; config.ni.method = 'nescal'; % also specify ion density method: scale w.r.t. ne init.ni0scal = 0.9; init.niescal = 1; % set core ni to be 90% of core ne and edge ni=ne; [model,params,init,g,v,U] = build_RAPTOR_model(config); % inspect transport model used for ne; disp(model.vpdn_e); % manual model disp(params.vpdn_e); x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); % Run RAPTOR simres = RAPTOR_predictive(x0,g,v,U,model,params); % To compute some physical outputs, we run the RAPTOR_out function. out = RAPTOR_out(simres,model,params); % Plots hf=figure(1); set(hf,'position',[50 50 700 300]); clf(hf); subplot(131); plot(out.time,out.ne/1e19); xlabel('time [s]'); title('n_e at various rho [10^{19}m^{-3}]'); subplot(132); plot(out.rho,out.ne(:,1:5:end)/1e19); xlabel('\rho_{tor}'); title('n_e profiles [10^{19}m^{-3}]'); subplot(133); plot(out.time,out.ne(1,:)/1e19,'b',out.time,out.ni(1,:)/1e19,'r--'); xlabel('time [s]'); title('ne(-),ni(--)');
manual
dne_pr: 1
vpe_pr: -5
it telaps newt res t[ms] dt[ms] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1 0.063 4 3.0e-09 0 1 80 0 1.5 78.5 15.3 5.68 5.68 3.1e+00 0.21 0.21 1.16 8.8e+00
11 0.38 2 3.9e-12 10 1 80 0 3.33 76.6 15.3 3.27 3.27 2.4e+00 0.35 0.35 1.05 4.4e+00
21 0.67 2 3.5e-13 20 1 80 0 3.32 76.6 15.3 2.35 2.35 2.1e+00 0.46 0.46 0.80 3.2e+00
31 0.95 2 1.2e-13 30 1 80 0 3.16 76.8 15.3 1.88 1.88 1.8e+00 0.57 0.57 0.64 2.6e+00
41 1.2 2 4.2e-14 40 1 80 0 2.98 77 15.3 1.6 1.6 1.7e+00 0.67 0.67 0.54 2.2e+00
51 1.5 2 1.8e-14 50 1 80 0 2.84 77.1 15.3 1.41 1.41 1.5e+00 0.75 0.75 0.48 1.8e+00
Solve for ne with manual transport coefficients, compute ni from Zeff and quasineutrality
To solve for ni via Zeff and quasineutrality, we need to introduce one impurity species (since we have two constraints).
% Change the method for ne to 'qnze' (quasi-neutrality and Z-effective). config.ni.method = 'qnze'; config.n1.method = 'qnze'; % solve for one impurity species as wel. config.atom.Z1 = 6; config.atom.A1 = 12; % choose carbon impurity [model,params,init,g,v,U] = build_RAPTOR_model(config); init.ze0 = 2.0; init.zee = 3.0; % set Zeff at axis and edge. v = build_kinetic_profiles(model,init); % update Zeff in v x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); % Run RAPTOR simres = RAPTOR_predictive(x0,g,v,U,model,params); % To compute some physical outputs, we run the RAPTOR_out function. out = RAPTOR_out(simres,model,params); hf=figure(1); set(hf,'position',[50 50 700 300]); clf(hf); subplot(131); plot(out.rho,[out.ne(:,end),out.ni(:,end)]/1e19); xlabel('\rho_{tor}'); title('n_e,n_i [10^{19}m^{-3}]'); subplot(132); plot(out.rho,out.ze,'r',out.rho,out.ne(:,end)./out.ni(:,end)); xlabel('\rho_{tor}'); title('Z_{eff}, n_i/n_e'); subplot(133); plot(out.time,out.ne(1,:)/1e19,'b',out.time,out.ni(1,:)/1e19,'r--'); xlabel('time [s]'); title('ne(-),ni(--)');
it telaps newt res t[ms] dt[ms] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1 0.081 4 2.0e-10 0 1 80 0 1.64 78.3 15.3 5.56 5.56 2.7e+00 0.20 0.20 1.16 9.2e+00
11 0.43 2 3.2e-12 10 1 80 0 3.06 76.9 15.3 3.07 3.07 2.2e+00 0.31 0.31 1.05 4.7e+00
21 0.77 2 3.1e-13 20 1 80 0 3.02 76.9 15.3 2.15 2.15 1.9e+00 0.41 0.41 0.80 3.4e+00
31 1.1 2 1.3e-13 30 1 80 0 2.84 77.1 15.3 1.69 1.69 1.6e+00 0.51 0.51 0.64 2.7e+00
41 1.4 2 4.5e-14 40 1 80 0 2.66 77.3 15.3 1.43 1.43 1.5e+00 0.60 0.60 0.54 2.3e+00
51 1.8 2 1.7e-14 50 1 80 0 2.51 77.5 15.3 1.26 1.26 1.4e+00 0.68 0.68 0.48 1.9e+00
ITPA-IOS benchmark coordinated by Y.S. Na [paper in preparation]
[config] = RAPTOR_config('ITER'); % load default params config.grid.tgrid = [0:.1:10]; config.grid.rhogrid = linspace(0,1,41); config.equi.mode = 'free'; config.ne.method = 'state'; config.ne.scal = 1e19; config.ne.BCtype = 'ne'; config.ne.BCval = 4.6e19; config.ni.method = 'nescal'; config.init.ne0 = 6e19; config.init.ni0 = 6e19; % Transport and sources config.vpdn_e = vpdn_e('benchmark'); config.sn_e = sn_e('benchmark'); [model,params,init,g,v,U] = build_RAPTOR_model(config); x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); simres = RAPTOR_predictive(x0,g,v,U,model,params); out = RAPTOR_out(simres,model,params); % plots hf=figure(1); set(hf,'position',[50 50 700 300]); clf(hf); subplot(131); plot(out.rho,out.ne(:,end)/1e19,'b',out.rho,out.ni(:,end)/1e19,'r--'); legend({'ne','ni'},'location','southwest'); xlabel('\rho_{tor}'); title('Final n_e,n_i profiles'); ylabel('m^{-3}'); subplot(132); plot(out.sne(:,end)/1e19,'b'); title('Source'); ylabel('m^{-3}/s'); xlabel('\rho_{tor}'); set(gca,'ylim',[0,5]); subplot(133); plot(out.rho,out.dne(:,end),'r',out.rho,out.vne(:,end),'b'); legend({'D_{ne} [m^2/s]','V_{ne} [m/s]'},'location','northwest'); title('diffusion, pinch')
it telaps newt res t[ s] dt[ s] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1 0.14 5 6.3e-12 0 0.1 4 0 0.724 3.28 14.9 2.63 2.63 5.1e-02 3.60 3.60 6.01 3.3e+00
11 1.1 3 3.7e-12 1 0.1 4 0 0.163 3.84 14.9 2.54 2.54 2.9e-01 1.45 1.45 6.54 4.3e+00
21 1.9 3 4.0e-12 2 0.1 4 0 0.106 3.89 14.9 2.46 2.46 4.1e-01 1.08 1.08 7.50 4.3e+00
31 2.7 2 4.5e-09 3 0.1 4 0 0.0951 3.9 14.9 2.38 2.38 4.9e-01 1.00 1.00 8.24 3.9e+00
41 3.4 2 1.4e-09 4 0.1 4 0 0.0905 3.91 14.9 2.31 2.31 5.4e-01 0.97 0.97 8.74 3.5e+00
51 4 2 4.8e-10 5 0.1 4 0 0.0871 3.91 14.9 2.26 2.26 5.9e-01 0.94 0.94 9.06 3.2e+00
61 4.6 2 1.7e-10 6 0.1 4 0 0.0842 3.92 14.9 2.24 2.24 6.2e-01 0.92 0.92 9.26 3.1e+00
71 5.3 2 6.6e-11 7 0.1 4 0 0.0815 3.92 14.9 2.25 2.25 6.5e-01 0.89 0.89 9.40 3.0e+00
81 6 2 2.5e-11 8 0.1 4 0 0.079 3.92 14.9 2.3 2.3 6.7e-01 0.87 0.87 9.48 3.0e+00
91 6.6 2 1.1e-11 9 0.1 4 0 0.0767 3.92 14.9 2.37 2.37 7.0e-01 0.84 0.84 9.54 2.9e+00
101 7.3 2 5.1e-12 10 0.1 4 0 0.0745 3.93 14.9 2.47 2.47 7.1e-01 0.81 0.81 9.57 2.9e+00
