RAPTOR tutorial 3: Customizing heating & current drive
In this tutorial we will add and customize auxiliary heating and current drive systems. We will have to specify the deposition location, as well as the power traces for each actuator.
This tutorial uses simple EC and NBI modules where the deposition is modeled by gaussian distributions. The EC current drive efficiency is scaled by Te/ne, while the NBI current drive efficiency is constant.
Contents
Example 1: Add 2 EC sources at fixed location
Preparation Start by repeating the first two steps of the previous tutorial
clear; close all hidden; run ../RAPTOR_path.m [config] = RAPTOR_config; % load default config
heating & current drive parameters To specify a heating and current drive actuator, we must choose a module
config.echcd = echcd('echcd_gaussian');
disp(config.echcd);
disp(config.echcd.params);
modeltype: 'echcd_gaussian'
params: [1x1 struct]
active: 0
rdep: [0 0.4000]
wdep: [0.3000 0.3500]
cd_eff: [0 1]
eta_eccd0: 7.0000e+14
cd_trap: 0
uindices: [2 3]
check: 0
Inspecting the result, we see that the config.echcd contains * the name of the module * the default parameter structure associated with the module
Now we can change the default module parameters
config.echcd.params.active = true; % activate the module, otherwise it does nothing. config.echcd.params.rdep = [0 0.4]; % two actuators, set rdep=0 for first, rdep=0.4 for second config.echcd.params.wdep = [0.35, 0.35]; % wdep =0.35 for each config.echcd.params.cd_eff = [0 1]; % current drive efficiency factor: pure ECH for first, co-ECCD for second config.echcd.params.uindices = [2 3]; % index of power for each actuator in input vector
Other modifications make some further modifications to the configuration structure, look in RAPTOR_config.m for exact parameter definitions
config.grid.tgrid = [0:0.001:0.1]; % time grid config.grid.rhogrid = linspace(0,1,21); % spatial grid config.debug.iterplot = 0; %10; % plot profiles every N iterations config.debug.iterdisp = 10; % display progress every N iterations % Create RAPTOR model,params and init structure with new parameters [model,params,init,g,v,U] = build_RAPTOR_model(config);
Define inputs We must now define more inputs than the plasma current alone
% plasma current U(1,:)= 200e3*ones(size(params.tgrid)); % input Ip trace: ramp from 40kA to 200kA U(1,params.tgrid<0.02) = linspace(80e3,200e3,sum(params.tgrid<0.02)); % first EC actautor: on-axis heating 1MW starting at 60ms U(2,:) = zeros(size(params.tgrid)); U(2,params.tgrid>0.06) = 1e6; % second EC actuator power: off-axis current drive, 1MW start at 40ms U(3,:) = zeros(size(params.tgrid)); U(3,params.tgrid>0.04) = 1e6;
Initial conditions and run model initial conditions
init.Ip0 = U(1,1); % Define the initial condition for state x0 = RAPTOR_initial_conditions(model,init,g,v); % run RAPTOR simres = RAPTOR_predictive(x0,g,v,U,model,params);
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 0.06 4 5.1e-10 0 1 80 0 1.41 78.6 15.4 5.59 5.59 3.4e+00 0.21 0.21 1.00 1.2e+01
11 0.31 2 2.6e-10 10 1 143 0 4.06 139 8.61 3.19 3.19 5.3e+00 0.40 0.40 1.00 2.0e+01
21 0.55 3 9.0e-13 20 1 200 0 6.24 194 6.16 2.32 2.32 4.0e+00 0.64 0.64 1.00 1.6e+01
31 0.77 2 1.8e-11 30 1 200 0 6.75 193 6.16 1.79 1.79 2.7e+00 0.83 0.83 1.00 1.1e+01
41 1 2 9.2e-13 40 1 200 0 6.67 193 6.16 1.38 1.38 2.4e+00 0.95 0.95 1.00 8.4e+00
51 1.3 2 2.5e-10 50 1 200 36.1 25.1 139 6.16 1.29 1.29 5.3e-01 3.17 3.17 1.00 2.5e+00
61 1.5 4 4.3e-14 60 1 200 39 27.2 134 6.16 1.28 1.28 3.8e-01 6.54 6.54 1.00 2.2e+00
71 1.8 2 2.1e-11 70 1 200 86.8 81.9 31.2 6.16 1.33 1.33 1.2e-01 13.49 13.49 1.00 1.1e+00
81 2 2 4.9e-14 80 1 200 94.2 89.5 16.3 6.16 1.37 1.37 1.0e-01 14.61 14.61 1.00 1.0e+00
91 2.3 2 3.8e-14 90 1 200 96.9 93.4 9.66 6.16 1.4 1.4 9.1e-02 15.32 15.32 1.00 9.6e-01
101 2.5 2 4.4e-14 100 1 200 99.2 97.5 3.28 6.16 1.43 1.44 8.3e-02 16.11 16.11 1.00 9.4e-01
plot outputs
out=RAPTOR_out(simres,model,params); clf; subplot(211); surf(out.time,out.rho,out.pauxe); xlabel('t [s]');ylabel('\rho'); title('P_{aux,electrons} [W/m^3]'); shading flat; subplot(212); surf(out.time,out.rho,out.jaux); xlabel('t [s]');ylabel('\rho'); title('j_{aux} [A/m^2]'); shading flat;
The attentive reader will notice that the driven current increases then EC heating is added. This is due to the the ECCD current drive efficiency which increases with the higher temperature.
Example 2: Time-varying rdep and add NBI
We will now let the deposition locations be specified through the input vector. We also add NBI.
clear; close all; addpath(fullfile(pwd,'..','code'),'-end'); % add RAPTOR path [config] = RAPTOR_config; % load default config config.grid.tgrid = [0:0.001:0.1]; % time grid config.grid.rhogrid = linspace(0,1,21); % spatial grid config.debug.iterplot = 0; %10; % plot profiles every N iterations config.debug.iterdisp = 10; % display progress every N iterations % heating & current drive parameters
EC with time-varying deposition location To define the deposition location as time-varying, set rdep to -1. Then the actuator index assigning the deposition locations are appended to uindex.
% set ECH/ECCD parameters config.echcd.params.active = true; config.echcd.params.rdep = [-1 -1]; % -1 to indicate it is commanded extrernally config.echcd.params.wdep = [0.3, 0.35]; % deposition width config.echcd.params.cd_eff = [0 1]; % CD efficiency config.echcd.params.uindices = [2 3 4 5]; % index in input vector % 2,3 are for the two powers, 4,5 is for the deposition location
NBI Configure the NBI module like the EC module
config.nbhcd = nbhcd('nbhcd_gaussian'); % set NBI parameters config.nbhcd.params.active = true; config.nbhcd.params.rdep = [0 0.4]; % -1 to indicate commanded extrernally config.nbhcd.params.wdep = [0.8 0.4]; % broad heating config.nbhcd.params.wdep_out = [0.8 0.6]; % broad heating config.nbhcd.params.cd_eff = [0 0]; % no current drive config.nbhcd.params.uindices = [6 7]; % index in input vector
Create model rerun the config file with the new parameter set
[model,params,init,g,v] = build_RAPTOR_model(config);
Define inputs: Must define additional inputs for rdep and for the NBI power.
% plasma current U(1,:)= 200e3*ones(size(params.tgrid)); % input Ip trace: ramp from 40kA to 200kA U(1,params.tgrid<0.02) = linspace(80e3,200e3,sum(params.tgrid<0.02)); % first EC actautor: 1MW starting at 60ms U(2,:) = zeros(size(params.tgrid)); U(2,params.tgrid>0.06) = 1e6; % second EC actuator power: 1MW start at 40ms U(3,:) = zeros(size(params.tgrid)); U(3,params.tgrid>0.04) = 1e6; % deposition location for first EC actuator: on-axis with small movement U(4,:) = zeros(size(params.tgrid)); U(4,params.tgrid>0.08) = linspace(0,0.2,sum(params.tgrid>0.08)); % deposition location for first EC actuator: off-axis with sweep inward U(5,:) = 0.4*ones(size(params.tgrid)); U(5,params.tgrid>0.05) = linspace(0.4,0.2,sum(params.tgrid>0.05)); % NBI power: ramp slowly U(6,:) = 1e6*ones(size(params.tgrid)); U(6,params.tgrid<0.06) = linspace(0,500e3,sum(params.tgrid<0.06)); % Second NBI source: off U(7,:) = 0e6*ones(size(params.tgrid));
initial condition
init.Ip0 = U(1,1);
x0 = RAPTOR_initial_conditions(model,init,g,v);
% Run RAPTOR
simres = RAPTOR_predictive(x0,g,v,U,model,params);
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 0.058 4 5.1e-10 0 1 80 0 1.41 78.6 15.4 5.59 5.59 3.4e+00 0.21 0.21 1.00 1.2e+01
11 0.43 2 3.3e-09 10 1 143 0 5.38 138 8.61 3.12 3.12 5.0e+00 0.54 0.54 1.00 2.1e+01
21 0.7 3 8.5e-13 20 1 200 0 9.94 190 6.16 2.37 2.37 3.6e+00 1.09 1.09 1.00 1.7e+01
31 0.97 2 4.2e-11 30 1 200 0 12.9 187 6.16 1.91 2.02 2.0e+00 1.69 1.69 1.00 1.0e+01
41 1.2 2 2.9e-12 40 1 200 0 14.6 185 6.16 1.58 1.78 1.5e+00 2.20 2.20 1.00 7.3e+00
51 1.5 2 1.2e-10 50 1 200 51.1 40 109 6.16 1.57 1.74 3.2e-01 5.38 5.38 1.00 1.8e+00
61 1.8 4 4.0e-14 60 1 200 63.1 48.4 88.4 6.16 1.54 1.76 2.0e-01 10.92 10.92 1.00 1.7e+00
71 2.1 2 2.9e-11 70 1 200 163 140 -103 6.16 1.5 1.9 4.6e-02 22.50 22.50 1.00 1.2e+00
81 2.3 2 1.2e-12 80 1 200 207 162 -168 6.16 1.46 2.09 4.3e-02 26.01 26.01 1.00 1.2e+00
91 2.6 2 9.7e-13 90 1 200 250 176 -226 6.16 1.41 2.36 4.3e-02 28.10 28.10 1.00 1.3e+00
101 2.8 2 1.0e-11 100 1 200 289 184 -273 6.16 1.37 2.9 4.0e-02 29.07 29.07 1.00 1.3e+00
plot results
out = RAPTOR_out(simres,model,params); subplot(321); plot(out.time,out.U(1,:)); title('Ip'); subplot(322); plot(out.time,out.U([2:3,6],:)); title('P_{aux}') subplot(323); plot(out.time,out.U([4:5],:)); title('\rho_{dep}'); set(gca,'Ylim',[0,1]); subplot(324); pcolor(out.time,out.rho,bsxfun(@times,out.Vp,out.pec)); shading flat; title('p_{EC}*dV/d\rho') subplot(325); [cs,h] = contour(out.time,out.rho,out.q,[1 2 3 4],'color','k'); clabel(cs,h,'labelspacing',72); title('rational q locations'); xlabel('t [s]'); ylabel('\rho'); subplot(326); [cs,h] = contour(out.time,out.rho,out.te/1e3,[0.5 1 2 4 8],'color','k'); clabel(cs,h,'labelspacing',72); title('T_e contours [keV]') xlabel('t [s]'); ylabel('\rho');
Example 3: Add gaussian central ICRH
clear; close all; [config] = RAPTOR_config; % load default config config.grid.tgrid = [0:0.001:0.1]; % time grid config.grid.rhogrid = linspace(0,1,21); % spatial grid config.debug.iterplot = 0; %10; % plot profiles every N iterations config.debug.iterdisp = 10; % display progress every N iterations
Heating & current drive parameters *keep default EC and NBI, add IC Configure the IC module similarly to EC module
config.ichcd = ichcd('ichcd_gaussian'); % set NBI parameters config.ichcd.params.active = true; config.ichcd.params.rdep = [0]; config.ichcd.params.wdep = [0.4]; % broad heating config.ichcd.params.wdep_out = [0.4]; % broad heating config.ichcd.params.cd_eff = [0]; % no current drive config.ichcd.params.uindices = [5]; % index in input vector (after NBH = 4 by default)
Create model rerun the config file with the new parameter set
[model,params,init,g,v,U] = build_RAPTOR_model(config);
Define inputs: Must define additional inputs for rdep and for the NBI power.
% plasma current U(1,:)= 200e3*ones(size(params.tgrid)); % input Ip trace: ramp from 40kA to 200kA U(1,params.tgrid<0.02) = linspace(init.Ip0,200e3,sum(params.tgrid<0.02)); % IC power U(5,:) = 1e6*ones(size(params.tgrid)); U(5,params.tgrid<0.06) = linspace(0,1e6,sum(params.tgrid<0.06));
initial condition
x0 = RAPTOR_initial_conditions(model,init,g,v);
% Run RAPTOR
simres = RAPTOR_predictive(x0,g,v,U,model,params);
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 0.05 4 5.1e-10 0 1 80 0 1.41 78.6 15.4 5.59 5.59 3.4e+00 0.21 0.21 1.00 1.2e+01
11 0.41 3 6.0e-15 10 1 143 0 6.98 136 8.61 3.17 3.17 4.7e+00 0.70 0.70 1.00 2.1e+01
21 0.65 3 6.8e-13 20 1 200 0 14.8 185 6.16 2.53 2.61 3.1e+00 1.62 1.62 1.00 1.6e+01
31 0.9 2 7.1e-11 30 1 200 0 22.4 178 6.16 1.99 2.46 1.5e+00 2.84 2.84 1.00 8.5e+00
41 1.2 2 3.4e-12 40 1 200 0 29.2 171 6.16 1.71 2.43 9.8e-01 4.11 4.11 1.00 5.5e+00
51 1.4 2 3.1e-13 50 1 200 0 35.2 165 6.16 1.56 2.43 6.7e-01 5.30 5.30 1.00 3.8e+00
61 1.7 2 1.5e-10 60 1 200 0 40.8 159 6.16 1.45 2.44 4.8e-01 6.37 6.37 1.00 2.8e+00
71 1.9 2 6.3e-14 70 1 200 0 41.6 158 6.16 1.38 2.44 4.2e-01 6.65 6.65 1.00 2.4e+00
81 2.2 2 3.0e-14 80 1 200 0 40.2 160 6.16 1.32 2.4 3.9e-01 6.62 6.62 1.00 2.2e+00
91 2.4 2 3.0e-14 90 1 200 0 38.6 161 6.16 1.27 2.33 3.7e-01 6.55 6.55 1.00 2.1e+00
101 2.7 2 6.2e-14 100 1 200 0 37.3 163 6.16 1.23 2.24 3.5e-01 6.47 6.47 1.00 1.9e+00
plot results
out = RAPTOR_out(simres,model,params); subplot(311); plot(out.time,out.U(1,:)); title('Ip'); subplot(312); plot(out.time,out.U([5],:)); title('P_{ic}') subplot(325); [cs,h] = contour(out.time,out.rho,out.te/1e3,[0.5 1 2 4 8],'color','k'); clabel(cs,h,'labelspacing',72); title('T_e contours [keV]') subplot(326); [cs,h] = contour(out.time,out.rho,out.pice/1e3); clabel(cs,h,'labelspacing',72); title('p_{ic} contours [W/m^3]') xlabel('t [s]'); ylabel('\rho');
Example 4: Completely manual specification of heating & current drive
clear; close all; [config] = RAPTOR_config; % load default config config.grid.tgrid = [0:0.001:0.1]; % time grid config.grid.rhogrid = linspace(0,1,21); % spatial grid config.debug.iterplot = 0; %10; % plot profiles every N iterations config.debug.iterdisp = 10; % display progress every N iterations % Manual heating and current drive specification config.echcd = echcd('none'); config.nbhcd = nbhcd('nbhcd_manual'); % define the manual module rho = linspace(0,1,21); % arbitrary rho grid % disp(nbhcd_manual)
active: 1
rho: [21x1 double]
pnbe: [21x1 double]
pnbi: [21x1 double]
jnb: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
uindices: 2
check: 0
We now set the nbh deposition parameters manually
config.nbhcd.params.active = 1; config.nbhcd.params.rho = rho; config.nbhcd.params.pnbe = 1*(1-linspace(0,1,21).^2)'; % heating profile to electrons config.nbhcd.params.pnbi = 0.8*(1-linspace(0,1,21).^2)'; % heating profile to ions (ignored anyway since we don't solve for ions now) config.nbhcd.params.jnb = 0.1*config.nbhcd.params.pnbe; % current drive profile config.nbhcd.params.uindices = 2; % index of U to be used for scaling the prescribed power deposition profiles % *Create model* % rerun the config file with the new parameter set [model,params,init,g,v] = build_RAPTOR_model(config); init.te0 = 300; % define inputs U(1,:)= 200e3*ones(size(params.tgrid)); % input Ip trace: ramp from 40kA to 200kA U(1,params.tgrid<0.02) = linspace(80e3,200e3,sum(params.tgrid<0.02)); % first EC actautor: on-axis heating 1MW starting at 60ms U(2,:) = zeros(size(params.tgrid)); U(2,params.tgrid>0.06) = 1e6; % initial conditions init.Ip0 = U(1,1); x0 = RAPTOR_initial_conditions(model,init,g,v); % run RAPTOR simres = RAPTOR_predictive(x0,g,v,U,model,params); % *plot outputs* out = RAPTOR_out(simres,model,params); figure; subplot(221); surf(out.time,out.rho,out.pauxe); xlabel('t [s]');ylabel('\rho'); title('P_{aux,electrons} from NBI [W/m^3]'); shading flat; subplot(222); surf(out.time,out.rho,out.jaux); xlabel('t [s]');ylabel('\rho'); title('j_{aux} NBI [A/m^2]'); shading flat; subplot(223); plot(out.time,[out.Pnbe;out.Pnbi]/1e6); xlabel('t [s]');ylabel('[MW]'); title('Total power to electrons (-), ions (--)'); return
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 0.075 4 8.7e-15 0 1 80 0 2.9 77.1 15.4 5.61 5.62 3.2e+00 0.26 0.26 1.00 1.3e+01
11 0.4 2 2.7e-10 10 1 143 0 4.06 139 8.61 3.16 3.16 5.3e+00 0.40 0.40 1.00 2.0e+01
21 0.71 3 9.1e-13 20 1 200 0 6.24 194 6.16 2.3 2.3 4.0e+00 0.64 0.64 1.00 1.6e+01
31 0.99 2 1.8e-11 30 1 200 0 6.75 193 6.16 1.78 1.78 2.7e+00 0.83 0.83 1.00 1.1e+01
41 1.3 2 9.2e-13 40 1 200 0 6.66 193 6.16 1.37 1.37 2.3e+00 0.95 0.95 1.00 8.3e+00
51 1.6 2 1.5e-13 50 1 200 0 6.56 193 6.16 1.09 1.09 2.1e+00 1.05 1.05 1.00 6.7e+00
61 1.9 4 1.5e-11 60 1 200 0 6.49 193 6.16 0.917 0.917 1.1e+00 1.46 1.46 1.00 2.6e+00
71 2.2 2 2.7e-11 70 1 200 13.2 15.7 171 6.16 0.862 0.862 6.0e-01 2.46 2.46 1.00 1.4e+00
81 2.5 2 4.6e-14 80 1 200 13.2 16 171 6.16 0.828 0.828 5.7e-01 2.52 2.52 1.00 1.2e+00
91 2.8 2 2.5e-14 90 1 200 13.2 15.9 171 6.16 0.799 0.799 5.5e-01 2.54 2.54 1.00 1.1e+00
101 3 1 6.9e-09 100 1 200 13.2 15.8 171 6.16 0.775 0.775 5.4e-01 2.56 2.56 1.00 1.0e+00
