RAPTOR NTM simulation tutorial
NTMs can also be simulated, either by prescribing the time-evolution of the modes directly (affecting transport) or by solving MRE self-consistently.
Contents
RAPTOR Prescribed NTM time-evolution
This simulation also includes sawteeth, you will see the effect!
close all hidden; clear all; run('../RAPTOR_path.m'); [config] = RAPTOR_config; % load default params config.saw = saw('porcelli'); % load an ntm model. config.ntm = ntm('prescribed'); config.debug.iterdisp = 50; % build RAPTOR structure config.init.te0=100; config.grid.tgrid = [0.:0.001:1]; % generate model structure for these params. [model,params,init,g,v,U] = build_RAPTOR_model(config); % define input rampfun = @(t,tmin,ymin,tmax,ymax) ... max(ymin,min((ymax-ymin)/(tmax-tmin)*(t-tmin),ymax-ymin)+ymin); % anonymous function for ramps init.Ip0 = 80e3; U(1,:) = rampfun(config.grid.tgrid,0,init.Ip0,0.05,160e3); % define initial conditions x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); % Define the initial condition % Prescribe NTM evolution % make v0 vector time-varying nt = numel(params.tgrid); vtvar = v*ones(1,nt); % parameters params.saw.s1crit = 0.3; params.ntm.chiefact_A(:) = 2; % factor increase in chie % define NTM appearance times and width w43 = zeros(1,nt); w43(params.tgrid > 0.2 & params.tgrid<0.3) = 0.05; % 4/3 NTM w32 = zeros(1,nt); w32(params.tgrid > 0.4 & params.tgrid<0.5) = 0.05; % 3/2 NTM w21 = zeros(1,nt); w21(params.tgrid > 0.6 & params.tgrid<0.7) = 0.05; % 2/1 NTM w31 = zeros(1,nt); w31(params.tgrid > 0.8 & params.tgrid<0.9) = 0.05; % 3/1 NTM % assign to V % Make sure that the indices match with the m and n parameters vtvar(model.ntm.vind(1),:) = w21; vtvar(model.ntm.vind(2),:) = w32; vtvar(model.ntm.vind(3),:) = w43; vtvar(model.ntm.vind(4),:) = w31; % must turn these off for technical reasons params.neos.implicit = false; params.chi_e.implicit = false; simres = RAPTOR_predictive(x0,g,vtvar,U,model,params); out = RAPTOR_out(simres,model,params); % inspect result RAPTOR_plot_GUI(out,'overview'); plot(out.time,[out.w_32; out.w_43; out.w_31;out.w_21]);
it telaps newt res t[ s] dt[ s] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1 0.32 2 9.1e-16 0 0.001 80 0 0.532 79.4 15.3 4.89 4.89 6.7e+00 0.30 0.59 1.00 2.0e+01
51 1.1 2 2.5e-14 0.05 0.001 160 0 6.97 153 7.67 1.22 1.22 3.0e+00 0.75 1.51 1.00 6.8e+00
101 2.1 2 4.6e-14 0.1 0.001 160 0 7.24 153 7.67 0.837 0.837 1.7e+00 1.05 2.10 1.00 3.0e+00
151 3.1 2 5.3e-14 0.15 0.001 160 0 7.3 153 7.67 0.896 0.896 1.6e+00 1.08 2.16 1.00 4.2e+00
201 3.9 2 5.9e-14 0.2 0.001 160 0 7.29 153 7.66 0.978 0.978 1.6e+00 0.81 1.62 1.00 1.5e+01
251 4.7 2 6.0e-14 0.25 0.001 160 0 6.42 154 7.67 0.905 0.905 1.9e+00 0.68 1.36 1.00 9.2e-01
301 5.4 1 1.2e-11 0.3 0.001 160 0 6.53 153 7.67 0.978 0.978 1.9e+00 0.68 1.36 1.00 1.0e-02
351 6.2 2 4.5e-14 0.35 0.001 160 0 7.26 153 7.66 0.989 0.989 1.7e+00 0.85 1.70 1.00 1.3e+01
401 7.1 2 1.1e-13 0.4 0.001 160 0 7.31 153 7.67 0.896 0.896 1.5e+00 1.08 2.17 1.00 4.3e+00
451 7.9 2 9.5e-14 0.45 0.001 160 0 6.16 154 7.67 0.855 0.855 2.0e+00 0.67 1.34 1.00 1.4e+00
501 8.5 1 3.9e-10 0.5 0.001 160 0 6.32 154 7.67 0.995 0.995 2.0e+00 0.64 1.29 1.00 1.2e-01
551 9.4 2 6.7e-14 0.55 0.001 160 0 7.25 153 7.67 0.837 0.837 1.7e+00 1.07 2.13 1.00 3.2e+00
601 10 2 2.2e-13 0.6 0.001 160 0 7.3 153 7.67 0.94 0.94 1.6e+00 1.00 2.01 1.00 7.1e+00
651 11 2 1.5e-13 0.65 0.001 160 0 5.57 154 7.66 1 1.02 2.2e+00 0.65 1.30 1.00 8.6e+00
701 12 2 1.9e-13 0.7 0.001 160 0 5.58 154 7.67 0.86 0.86 2.2e+00 0.79 1.57 1.00 4.5e+00
751 13 2 3.2e-13 0.75 0.001 160 0 7.28 153 7.67 0.895 0.895 1.6e+00 1.07 2.14 1.00 4.1e+00
801 14 2 1.3e-13 0.8 0.001 160 0 7.31 153 7.67 0.896 0.896 1.5e+00 1.09 2.17 1.00 4.4e+00
851 15 2 2.5e-13 0.85 0.001 160 0 5.49 155 7.66 1 1.01 2.1e+00 0.60 1.20 1.00 1.4e+01
901 16 2 9.7e-14 0.9 0.001 160 0 5.5 155 7.66 1 1.01 2.0e+00 0.61 1.21 1.00 1.4e+01
951 17 2 2.1e-13 0.95 0.001 160 0 7.32 153 7.67 0.94 0.94 1.5e+00 1.01 2.01 1.00 7.5e+00
it telaps newt res t[ s] dt[ s] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1001 18 2 3.0e-13 1 0.001 160 0 7.18 153 7.67 0.865 0.865 1.5e+00 1.11 2.21 1.00 4.3e+00
NTM simulation using Modified Rutherford equation
Includes ECRH power to stabilise the mode
close all hidden; run('../RAPTOR_path.m'); [config] = RAPTOR_config; % load default params % load the Modified Rutherford Equation ntm model. config.ntm = ntm('mre'); config.ntm.params.m=[2 3]; config.ntm.params.n=[1 2]; config.ntm.params.chiefact_A=[2 1]; % factor increase in chie config.ntm.params.chiefact_w=2*ones(1,config.ntm.n_ntm); config.ntm.params.w_d_e=0.01*ones(1,config.ntm.n_ntm); config.ntm.params.w_d_i=0.01*ones(1,config.ntm.n_ntm); config.ntm.params.a2_bs=0.1*ones(1,config.ntm.n_ntm); config.ntm.params.a_ggj=ones(1,config.ntm.n_ntm); config.ntm.params.conf_deg=zeros(1,config.ntm.n_ntm); config.ntm.params.w_cd_ntm=0.01*ones(1,config.ntm.n_ntm); config.ntm.params.rhodeltap_cl0=-config.ntm.params.m; % Specify the ECRH launcher, make sure that the last NTM launcher can be % moved config.echcd.params.active=true; config.echcd.params.rdep=[0 0.4100 -1]; config.echcd.params.wdep=[0.3000 0.3500 0.35]; config.echcd.params.cd_eff=[0 1 1]; config.echcd.params.eta_eccd0=7.0000e+14; config.echcd.params.uindices=[2 3 4 5]; config.nbhcd.params.uindices=max(config.echcd.params.uindices)+1; % build RAPTOR structure config.debug.iterdisp = 50; config.init.te0=100; config.grid.tgrid = 0.:0.001:1; % generate model structure for these params. [model,params,init,g,v,U] = build_RAPTOR_model(config);
define input
nt = numel(params.tgrid); rampfun = @(t,tmin,ymin,tmax,ymax) ... max(ymin,min((ymax-ymin)/(tmax-tmin)*(t-tmin),ymax-ymin)+ymin); % anonymous function for ramps init.Ip0 = 80e3; P_central1 = zeros(1,size(config.grid.tgrid,2)); P_central1(:,params.tgrid >= 0.05 & params.tgrid <= 1.1) = 1.0e6; NTM_stabpow2=zeros(1,size(config.grid.tgrid,2)); NTM_stabpow2(params.tgrid >= 0.5 & params.tgrid <= 0.6) = 0.1e6; NTM_stabpow3=zeros(1,size(config.grid.tgrid,2)); rhodep3 = 0.45*ones(1,size(config.grid.tgrid,2)); U(1:5,:) = ... [rampfun(config.grid.tgrid,0,init.Ip0,0.05,160e3); ... P_central1;... NTM_stabpow2;... NTM_stabpow3;... rhodep3]; % rho dep % Define the initial condition for state x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); % ntm % make v0 vector time-varying vtvar = v*ones(1,nt);
define NTM appearance times and width
% Seed the 3/2 to 5 cm which provides a lower bound between 0.4 s and 0.5 s w32 = zeros(1,nt); w32(params.tgrid >= 0.4 & params.tgrid <= 0.45) = 0.05; % 3/2 NTM, island held for some time % Seed the 2/1 at 0.1 s to 15 cm w21 = zeros(1,nt); w21(params.tgrid == 0.1) = 0.15; % 2/1 NTM % assign to V % Make sure that the indices match with the m and n parameters vtvar(model.ntm.vind(1),:) = w21; vtvar(model.ntm.vind(2),:) = w32; % run RAPTOR params.neos.implicit = false; params.chi_e.implicit = false; params.ntm.doplot = false; simres = RAPTOR_predictive(x0,g,vtvar,U,model,params); % generate output structure out = RAPTOR_out(simres,model,params);
it telaps newt res t[ s] dt[ s] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1 0.075 2 9.1e-16 0 0.001 80 0 0.532 79.4 15.3 4.89 4.89 6.7e+00 0.30 0.59 1.00 2.0e+01
51 0.97 2 3.0e-14 0.05 0.001 160 0 6.97 153 7.67 1.22 1.22 3.0e+00 3.97 7.95 1.00 6.8e+00
101 1.7 1 3.1e-09 0.1 0.001 160 0 65.8 94.1 7.67 1.31 1.41 2.7e-01 10.07 20.14 1.00 1.4e+00
151 2.6 2 1.9e-14 0.15 0.001 160 0 54.6 105 7.67 0.908 1.21 2.2e-01 10.45 20.91 1.00 9.3e-01
201 3.3 1 1.3e-10 0.2 0.001 160 0 54 106 7.67 0.843 1.05 1.4e-01 10.50 21.00 1.00 5.2e-01
251 3.8 1 1.9e-11 0.25 0.001 160 0 52.8 107 7.67 0.797 0.881 1.2e-01 10.52 21.04 1.00 4.3e-01
301 4.4 1 8.2e-12 0.3 0.001 160 0 52 108 7.67 0.76 0.764 1.1e-01 10.54 21.08 1.00 3.6e-01
351 5 1 5.0e-12 0.35 0.001 160 0 51.3 109 7.67 0.685 0.685 1.1e-01 10.55 21.11 1.00 3.0e-01
401 5.6 1 3.3e-12 0.4 0.001 160 0 50.8 109 7.67 0.63 0.63 1.0e-01 10.57 21.14 1.00 2.5e-01
451 6.3 1 2.9e-10 0.45 0.001 160 0 34.8 125 7.67 0.556 0.556 1.9e-01 7.83 15.67 1.00 6.2e-01
501 7.1 2 4.6e-14 0.5 0.001 160 0 49.2 111 7.67 0.518 0.518 1.1e-01 10.64 21.28 1.00 2.8e-01
551 7.7 1 1.1e-11 0.55 0.001 160 4.86 52.1 103 7.67 0.495 0.495 7.0e-02 10.84 21.68 1.00 1.1e-01
601 8.3 1 1.7e-12 0.6 0.001 160 4.86 52.2 103 7.67 0.481 0.481 7.0e-02 10.81 21.62 1.00 6.7e-02
651 9 1 4.1e-12 0.65 0.001 160 0 49.3 111 7.67 0.474 0.474 9.7e-02 10.58 21.16 1.00 8.4e-02
701 9.5 1 1.1e-12 0.7 0.001 160 0 49.2 111 7.67 0.47 0.47 9.4e-02 10.61 21.22 1.00 6.6e-02
751 10 1 4.4e-13 0.75 0.001 160 0 49.2 111 7.67 0.468 0.468 9.2e-02 10.63 21.26 1.00 5.5e-02
801 11 1 2.1e-13 0.8 0.001 160 0 49.1 111 7.67 0.466 0.466 9.1e-02 10.64 21.28 1.00 4.7e-02
851 11 1 1.3e-13 0.85 0.001 160 0 49.1 111 7.67 0.464 0.464 9.0e-02 10.65 21.30 1.00 4.1e-02
901 12 1 8.3e-14 0.9 0.001 160 0 49 111 7.67 0.461 0.461 8.9e-02 10.66 21.32 1.00 3.5e-02
951 13 1 1.1e-13 0.95 0.001 160 0 49 111 7.67 0.459 0.459 8.8e-02 10.66 21.33 1.00 3.0e-02
it telaps newt res t[ s] dt[ s] Ip[kA] Icd[kA] Ibs[kA] Ioh[kA] qe qmin q0 Vl[V] Te0[keV] Ti0[keV] ne0[e19] f_ss
1001 13 1 7.0e-14 1 0.001 160 0 48.9 111 7.67 0.457 0.457 8.8e-02 10.67 21.33 1.00 2.5e-02
Inspect result
RAPTOR_plot_GUI(out,'overview'); figure hold on plot(out.time,out.w_21,'x') plot(out.time,out.w_32,'or') xlabel('Time t [s]') ylabel('Island width w [m]') legend('2/1','3/2')
