RAPTOR tutorial: ad-hoc transport model tuning
In this tutorial we will vary the parameters of the electron transport model to see their effect on the plasma.
We use the heating and current drive setup from tutorial 3 again, but modify some parmeters: in particular we choose a smaller time grid to handle the rapid rise of the pedestal.
Contents
close all hidden; clear; run('../RAPTOR_path.m'); [config] = RAPTOR_config; % load default config config.grid.tgrid = [0:0.001:0.2]; config.grid.rhogrid = linspace(0,1,21); % spatial grid config.debug.iterdisp = 20; % display progress every N iterations % set ECH/ECCD parameters config.echcd.params.active = true; config.echcd.params.rdep = [0.4]; % config.echcd.params.wdep = [0.35]; % deposition width config.echcd.params.cd_eff = [1]; % CD efficiency config.echcd.params.uindices = [2]; % index in input vector % set NBI parameters config.nbhcd.params.active = true; config.nbhcd.params.rdep = [0]; % config.nbhcd.params.wdep = [0.8]; % broad heating config.nbhcd.params.cd_eff = [0]; % no current drive config.nbhcd.params.uindices = [3]; % index in input vector % rerun the config file with the new parameter set [model,params,init,g,v,U] = build_RAPTOR_model(config); % plasma current U(1,:)= 200e3*ones(size(params.tgrid)); % input Ip trace: ramp from 80kA to 200kA U(1,params.tgrid<0.02) = linspace(80e3,200e3,sum(params.tgrid<0.02)); % first EC actuator power: 2MW start at 40ms U(2,:) = zeros(size(params.tgrid)); U(2,params.tgrid>0.04) = 2e6; U(3,:) = zeros(size(params.tgrid)); U(3,params.tgrid>0.04) = 1e6; % initial condition init.Ip0 = U(1,1); x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); % Run RAPTOR [simres] = RAPTOR_predictive(x0,g,v,U,model,params); out = RAPTOR_out(simres,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 0.08 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
21 0.77 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
41 1.5 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
61 2.2 2 1.8e-13 60 1 200 252 113 -165 6.16 1.46 1.46 5.7e-02 15.90 15.90 1.00 1.7e+00
81 2.9 2 5.6e-12 80 1 200 291 134 -225 6.16 1.56 1.56 2.9e-02 18.74 18.74 1.00 1.6e+00
101 3.5 2 8.0e-13 100 1 200 376 178 -353 6.16 1.52 1.67 1.0e-02 24.72 24.72 1.00 1.7e+00
121 4.2 2 9.0e-14 120 1 200 446 217 -463 6.16 1.44 1.8 -1.2e-02 28.99 28.99 1.00 1.5e+00
141 4.8 2 4.6e-14 140 1 200 467 234 -501 6.16 1.38 1.99 -2.6e-02 30.10 30.10 1.00 1.3e+00
161 5.5 2 6.5e-14 160 1 200 474 246 -520 6.16 1.35 2.22 -3.6e-02 30.53 30.53 1.00 1.1e+00
181 6.1 2 5.5e-14 180 1 200 479 260 -540 6.16 1.32 2.47 -4.5e-02 31.05 31.05 1.00 1.1e+00
201 6.8 2 2.8e-14 200 1 200 483 274 -556 6.16 1.31 2.57 -5.3e-02 31.19 31.19 1.00 1.0e+00
Changing parameters for the default ad-hoc transport model
RAPTOR includes an ad-hoc expression for \chi_e
where
and 
is an extra factor to reduce the transport at the edge to create an H-mode pedestal.
This model is written as
![$H = a_{LH}[1-1/(1+\exp(w_{LH}(d_{LH}-LH_{crit}))]\chi_{prof}(\rho)$](RAPTOR_tutorial_transport_eq02129109952163232118.png)
The relevant parameters can be set from the params structure
params.chi_e
ans =
cneo: 0.5000
cano: 7
witb: 3
aitb: 1
ditb: 0
chi_csawtooth: 0
chi_wsawtooth: 10
te_constant: 0
aTeterm: 0
arhoterm: 1
apsiterm: 1
chiecentral: 10
deltacentral: 0.1500
chiiscal: 1
implicit: 1
check: 0
For example, to remove the confinement enhancement at low shear we can set 
params.chi_e.aitb = 0; % simulate [simres_noenhance] = RAPTOR_predictive(x0,g,v,U,model,params); out_noenhance = RAPTOR_out(simres_noenhance,model,params); RAPTOR_plot_GUI({out,out_noenhance},'overview')
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 0.064 4 4.4e-10 0 1 80 0 1.41 78.6 15.4 5.57 5.57 3.3e+00 0.19 0.19 1.00 1.1e+01
21 0.64 3 8.1e-13 20 1 200 0 5.66 194 6.16 2.42 2.42 4.1e+00 0.56 0.56 1.00 1.6e+01
41 1.1 2 8.3e-13 40 1 200 0 6.27 194 6.16 1.42 1.42 2.4e+00 0.83 0.83 1.00 7.8e+00
61 1.7 2 3.3e-14 60 1 200 215 93.8 -108 6.16 1.52 1.52 7.0e-02 11.77 11.77 1.00 1.7e+00
81 2.3 2 4.4e-14 80 1 200 220 95.6 -115 6.16 1.62 1.62 3.7e-02 11.78 11.78 1.00 1.4e+00
101 2.8 2 3.7e-14 100 1 200 223 97.2 -120 6.16 1.65 1.73 1.5e-02 11.74 11.74 1.00 1.2e+00
121 3.3 2 4.9e-14 120 1 200 226 98.9 -125 6.16 1.6 1.87 -3.1e-04 11.69 11.69 1.00 1.0e+00
141 3.8 2 4.4e-14 140 1 200 228 101 -129 6.16 1.57 2.06 -1.1e-02 11.62 11.62 1.00 8.9e-01
161 4.3 1 9.1e-09 160 1 200 230 103 -132 6.16 1.54 2.35 -1.9e-02 11.55 11.55 1.00 8.0e-01
181 4.7 1 5.7e-09 180 1 200 231 105 -136 6.16 1.52 2.81 -2.6e-02 11.47 11.47 1.00 7.2e-01
201 5 1 3.8e-09 200 1 200 232 108 -140 6.16 1.5 3.64 -3.1e-02 11.38 11.38 1.00 6.5e-01
ans =
Figure (1: RAPTOR output) with properties:
Number: 1
Name: 'RAPTOR output'
Color: [0.9400 0.9400 0.9400]
Position: [0.0490 0.1983 0.9010 0.7058]
Units: 'normalized'
Use GET to show all properties
Simple H-mode model
rampfun = @(t,tmin,ymin,tmax,ymax) max(ymin,min((ymax-ymin)/(tmax-tmin)*(t-tmin),ymax-ymin)+ymin); % anonymous function for ramps Hmode_indicator = rampfun(params.tgrid,0.08,0,0.1,1) - rampfun(params.tgrid,0.18,0,0.19,1); plot(params.tgrid,Hmode_indicator); nt = numel(params.tgrid); x0 = RAPTOR_initial_conditions(model,init,g(:,1),v(:,1)); [model,params,init,g,v,~] = build_RAPTOR_model(config); v = v*ones(size(params.tgrid)); v(model.hmode.vind,:) = Hmode_indicator; params.hmode.active = true; [simres_Hmode] = RAPTOR_predictive(x0,g,v,U,model,params); out_Hmode = RAPTOR_out(simres_Hmode,model,params); RAPTOR_plot_GUI({out_noenhance,out_Hmode},'overview')
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 0.052 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
21 0.6 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
41 1.1 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
61 1.7 2 1.8e-13 60 1 200 252 113 -165 6.16 1.46 1.46 5.7e-02 15.90 15.90 1.00 1.7e+00
81 2.3 2 5.6e-12 80 1 200 291 134 -225 6.16 1.56 1.56 2.9e-02 18.74 18.74 1.00 1.6e+00
101 2.9 2 5.1e-12 100 1 200 382 181 -363 6.16 1.53 1.67 3.8e-03 24.75 24.75 1.00 1.7e+00
121 3.5 2 7.9e-14 120 1 200 453 220 -473 6.16 1.45 1.8 -1.6e-02 29.10 29.10 1.00 1.5e+00
141 4 2 6.1e-14 140 1 200 475 238 -513 6.16 1.39 1.98 -2.7e-02 30.28 30.28 1.00 1.3e+00
161 4.5 2 7.2e-14 160 1 200 482 250 -533 6.16 1.36 2.21 -3.6e-02 30.71 30.71 1.00 1.1e+00
181 5.1 2 5.8e-14 180 1 200 487 265 -553 6.16 1.33 2.46 -4.3e-02 31.23 31.23 1.00 1.1e+00
201 5.7 2 5.6e-14 200 1 200 485 276 -561 6.16 1.32 2.6 -4.0e-02 31.40 31.40 1.00 1.0e+00
ans =
Figure (1: RAPTOR output) with properties:
Number: 1
Name: 'RAPTOR output'
Color: [0.9400 0.9400 0.9400]
Position: [0.0490 0.1983 0.9010 0.7058]
Units: 'normalized'
Use GET to show all properties
Bohm Gyrobohm
We can also use the Bohm-gyroBohm model first initialize new default parameters
config.chi_e = chi_e('BgB'); % % we now have a new set of parameters to change, but leave them fixed for now config.chi_e.params % make new model and parameters [model,params,init,g,v,U] = build_RAPTOR_model(config); % run simulation with new model params.debug.iterdisp = 10; % plot progress to see pedestal growing [simres_Hmode] = RAPTOR_predictive(x0,g,v,U,model,params); out_BgB = RAPTOR_out(simres_Hmode,model,params); RAPTOR_plot_GUI({out_noenhance,out_BgB},'overview')
ans =
aeb: 8.0000e-05
aegb: 0.0700
aib: 1.6000e-04
aigb: 0.0175
cneo: 1.0000e-03
chi_csawtooth: 0
chi_wsawtooth: 5
chimax: 20
a1: 2
z1: 1
implicit: 1
check: 0
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 0.072 5 1.5e-09 0 1 80 0 1.41 78.6 15.4 5.67 5.67 2.3e+00 0.25 0.25 1.00 6.3e+00
11 0.39 2 7.0e-12 10 1 80 0 6.76 73.2 15.4 3.99 3.99 1.4e+00 0.48 0.48 1.00 3.6e+00
21 0.66 2 3.8e-14 20 1 80 0 7.27 72.7 15.4 3.02 3.02 1.3e+00 0.57 0.57 1.00 2.5e+00
31 0.94 2 6.2e-15 30 1 80 0 7.51 72.5 15.4 2.48 2.48 1.2e+00 0.63 0.63 1.00 1.8e+00
41 1.2 2 5.6e-15 40 1 80 0 7.66 72.3 15.4 2.17 2.17 1.1e+00 0.68 0.68 1.00 1.3e+00
51 1.5 2 6.9e-15 50 1 80 0 7.76 72.2 15.4 1.98 1.98 1.0e+00 0.71 0.71 1.00 9.4e-01
61 1.7 2 6.3e-15 60 1 80 0 7.82 72.2 15.4 1.85 1.85 1.0e+00 0.74 0.74 1.00 6.8e-01
71 1.9 1 7.7e-09 70 1 80 0 7.87 72.1 15.4 1.77 1.77 1.0e+00 0.75 0.75 1.00 5.0e-01
81 2.1 1 4.0e-09 80 1 80 0 7.9 72.1 15.4 1.71 1.71 9.8e-01 0.77 0.77 1.00 3.6e-01
91 2.3 1 2.1e-09 90 1 80 0 7.92 72.1 15.4 1.67 1.67 9.7e-01 0.77 0.77 1.00 2.6e-01
101 2.5 1 1.1e-09 100 1 80 0 7.94 72 15.4 1.64 1.64 9.6e-01 0.78 0.78 1.00 1.9e-01
111 2.6 1 5.9e-10 110 1 80 0 7.95 72 15.4 1.62 1.62 9.6e-01 0.79 0.79 1.00 1.4e-01
121 2.8 1 3.1e-10 120 1 80 0 7.95 72 15.4 1.61 1.61 9.5e-01 0.79 0.79 1.00 1.0e-01
131 3 1 1.7e-10 130 1 80 0 7.96 72 15.4 1.6 1.6 9.5e-01 0.79 0.79 1.00 7.5e-02
141 3.2 1 8.9e-11 140 1 80 0 7.96 72 15.4 1.59 1.59 9.5e-01 0.79 0.79 1.00 5.5e-02
151 3.4 1 4.7e-11 150 1 80 0 7.97 72 15.4 1.59 1.59 9.4e-01 0.80 0.80 1.00 4.0e-02
161 3.5 1 2.5e-11 160 1 80 0 7.97 72 15.4 1.58 1.58 9.4e-01 0.80 0.80 1.00 2.9e-02
171 3.7 1 1.3e-11 170 1 80 0 7.97 72 15.4 1.58 1.58 9.4e-01 0.80 0.80 1.00 2.1e-02
181 3.9 1 7.2e-12 180 1 80 0 7.97 72 15.4 1.58 1.58 9.4e-01 0.80 0.80 1.00 1.6e-02
191 4.1 1 3.8e-12 190 1 80 0 7.97 72 15.4 1.58 1.58 9.4e-01 0.80 0.80 1.00 1.1e-02
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
201 4.2 1 2.0e-12 200 1 80 0 7.97 72 15.4 1.57 1.57 9.4e-01 0.80 0.80 1.00 8.3e-03
Error using matlab.graphics.axis.Axes/get
Invalid or deleted object.
Error in RAPTOR_plot_GUI>gui_init/wbmf (line 291)
haxposs = get(hax,'position');
Error using drawnow
Error while evaluating Figure WindowButtonMotionFcn
ans =
Figure (1: RAPTOR output) with properties:
Number: 1
Name: 'RAPTOR output'
Color: [0.9400 0.9400 0.9400]
Position: [0.0490 0.1983 0.9010 0.7058]
Units: 'normalized'
Use GET to show all properties
QualiKyz - Artificial Neural Network
Use ANN model first initialize new default parameters
config.chi_e = chi_e('qlkANN'); % % we now have a new set of parameters to change, but leave them fixed for now config.chi_e.params % make new model and parameters [model,params,init,g,v,U] = build_RAPTOR_model(config); % run simulation with new model params.debug.iterdisp = 10; % plot progress to see pedestal growing [simres_qlkANN] = RAPTOR_predictive(x0,g,v,U,model,params); out_qlkANN = RAPTOR_out(simres_qlkANN,model,params); RAPTOR_plot_GUI({out_noenhance,out_qlkANN},'overview')
ans =
constrains: 1
constrainq: 1
shearmin: 0.1000
shearmax: 3
qmin: 1
qmax: 5
IW_eef: [20x4 double]
L1W_eef: [20x20 double]
L2W_eef: [1x20 double]
b1_eef: [20x1 double]
b2_eef: [20x1 double]
b3_eef: -1.8186
max_qlk_eef: 4.9989
min_qlk_eef: 5.9621e-04
prepros_eef: -1
IW_ief: [20x4 double]
L1W_ief: [20x20 double]
L2W_ief: [1x20 double]
b1_ief: [20x1 double]
b2_ief: [20x1 double]
b3_ief: 1.4270
max_qlk_ief: 19.9961
min_qlk_ief: 0.0021
prepros_ief: -1
IW_dfe: [20x4 double]
L1W_dfe: [20x20 double]
L2W_dfe: [1x20 double]
b1_dfe: [20x1 double]
b2_dfe: [20x1 double]
b3_dfe: -0.1042
max_qlk_dfe: 49.8982
min_qlk_dfe: 0.0026
prepros_dfe: -1
IW_vce: [20x4 double]
L1W_vce: [20x20 double]
L2W_vce: [1x20 double]
b1_vce: [20x1 double]
b2_vce: [20x1 double]
b3_vce: 0.3464
max_qlk_vce: 29.9993
min_qlk_vce: -8.7546
prepros_vce: -1
IW_vte: [20x4 double]
L1W_vte: [20x20 double]
L2W_vte: [1x20 double]
b1_vte: [20x1 double]
b2_vte: [20x1 double]
b3_vte: 0.4158
max_qlk_vte: 0.1151
min_qlk_vte: -29.9764
prepros_vte: -1
constrainrlti: 1
constraintite: 1
shift_chi_e: 0.7500
chiemin: 0.4000
chiimin: 0.4000
Dmin: 0
allowpospinch: 1
thresholdscan: 0
implicit: 1
check: 0
rhocore: 0.3000
rhoped: 0.8000
chieedge: 5
chiecore: 2
chiiedge: 5
chiicore: 2
rltimin: 2
rltimax: 12
titemin: 0.3000
titemax: 3
out_sm_kernel: 1
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 0.09 5 6.0e-09 0 1 80 0 1.41 78.6 15.4 5.79 5.79 2.0e+00 0.24 0.24 1.00 4.5e+00
Warning: Exceeded maximum newton iterations
Warning: exceeded maximum newton iterations
3 0.65 50 5.9e-03 2 1 80 0 5.11 74.9 15.4 5.43 5.43 1.3e+00 0.32 0.32 1.00 1.4e+00
Warning: NANs in X, RAPTOR simulation did not complete successfully
Warning: could not plot
Xdata:out.time
Ydata:out.tauE
ans =
Figure (1: RAPTOR output) with properties:
Number: 1
Name: 'RAPTOR output'
Color: [0.9400 0.9400 0.9400]
Position: [0.0490 0.1983 0.9010 0.7058]
Units: 'normalized'
Use GET to show all properties
Manual chie
We can also choose a fixed chi_e profile manually, by setting 'modeltype' to 'manual' and assigning the profile to 'cneo'.
config.chi_e = chi_e('manual'); [model,params,init,g,v,U] = build_RAPTOR_model(config); params.chi_e.chi_e = 10; % constant value params.debug.iterplot = 0; % no plots [simres_manual1] = RAPTOR_predictive(x0,g,v,U,model,params); out_manual1 = RAPTOR_out(simres_manual1,model,params); params.chi_e.chi_e = (5+10*model.rgrid.rhogauss.^2); % spatially varying profile params.debug.iterplot = 0; % no plots [simres_manual2] = RAPTOR_predictive(x0,g,v,U,model,params); out_manual2 = RAPTOR_out(simres_manual2,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 0.053 5 1.0e-14 0 1 80 0 1.41 78.6 15.4 5.78 5.78 2.1e+00 0.22 0.22 1.00 5.3e+00
21 0.55 2 5.8e-15 20 1 80 0 5.22 74.8 15.4 4.13 4.13 1.4e+00 0.33 0.33 1.00 7.0e-01
41 0.97 1 2.9e-09 40 1 80 0 5.24 74.7 15.4 3.84 3.84 1.4e+00 0.33 0.33 1.00 1.6e-01
61 1.3 1 1.5e-10 60 1 80 0 5.24 74.7 15.4 3.78 3.78 1.4e+00 0.33 0.33 1.00 3.7e-02
81 1.6 1 8.0e-12 80 1 80 0 5.24 74.7 15.4 3.77 3.77 1.4e+00 0.33 0.33 1.00 8.5e-03
101 1.9 1 4.3e-13 100 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.33 0.33 1.00 2.0e-03
121 2.2 1 3.3e-14 120 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.34 0.34 1.00 4.5e-04
141 2.5 1 4.8e-14 140 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.34 0.34 1.00 1.0e-04
161 2.8 1 3.8e-14 160 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.34 0.34 1.00 2.4e-05
181 3.1 0 6.1e-09 180 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.34 0.34 1.00 5.9e-06
201 3.3 0 2.6e-09 200 1 80 0 5.24 74.7 15.4 3.76 3.76 1.4e+00 0.34 0.34 1.00 1.2e-06
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 0.053 5 5.9e-15 0 1 80 0 1.41 78.6 15.4 5.74 5.74 2.3e+00 0.23 0.23 1.00 6.4e+00
21 0.51 2 3.0e-14 20 1 80 0 5.05 74.9 15.4 3.53 3.53 1.5e+00 0.37 0.37 1.00 1.3e+00
41 0.93 2 1.4e-14 40 1 80 0 5.1 74.9 15.4 3.08 3.08 1.5e+00 0.38 0.38 1.00 3.6e-01
61 1.2 1 9.0e-10 60 1 80 0 5.11 74.9 15.4 2.97 2.97 1.4e+00 0.39 0.39 1.00 1.0e-01
81 1.5 1 7.3e-11 80 1 80 0 5.11 74.9 15.4 2.94 2.94 1.4e+00 0.39 0.39 1.00 2.9e-02
101 1.8 1 5.9e-12 100 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 8.2e-03
121 2.1 1 4.8e-13 120 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 2.3e-03
141 2.4 1 5.5e-14 140 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 6.7e-04
161 2.7 1 4.8e-14 160 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 1.9e-04
181 3 1 4.4e-14 180 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 5.4e-05
201 3.3 1 3.4e-14 200 1 80 0 5.11 74.9 15.4 2.93 2.93 1.4e+00 0.39 0.39 1.00 1.5e-05
plot some comparisons
figure; clf; subplot(211) plot(out_manual1.rho,out_manual1.te(:,end)/1e3,'r',... out_manual2.rho,out_manual2.te(:,end)/1e3,'k'... ); ylabel('T_e [keV]'), xlabel('\rho') subplot(212) plot(out_manual1.rho,out_manual1.chie(:,end),'r',... out_manual2.rho,out_manual2.chie(:,end),'k'... ); ylabel('\chi_e'), xlabel('\rho')
Time-varying Manual Chie
It is also possible to assign to 'cneo' a time-varying cie_e profile. This profile should be provided as a matrix of dimension:$\rho_{gauss}$ by t. Here is an example of a profile which is based on a parabolic function with time dependent gradient. A default value for tgrid is used of dimension 2 by 1 so that the previous examples hold because these have dimension # of rhogauss by 1.
% Create a matrix of the right size with a parabol which gradient increases % in time: [X,Y] = meshgrid(25*params.tgrid,model.rgrid.rhogauss); params.chi_e.chi_e = 5 + 2.^(X).*Y.^2; [simres_manual_time] = RAPTOR_predictive(x0,g,v,U,model,params); out_manual_time = RAPTOR_out(simres_manual_time,model,params); % Plot the result subplot(211) plot(out_manual_time.rho,out_manual_time.te(:,end)/1e3,'r'); ylabel('T_e [keV]'), xlabel('\rho') subplot(212) % Chi at the beginning and the end plot(out_manual_time.rho,out_manual_time.chie(:,end),'r',... out_manual_time.rho,out_manual_time.chie(:,1),'b'... ); ylabel('\chi_e'), xlabel('\rho') 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 0.069 5 3.2e-14 0 1 80 0 1.41 78.6 15.4 5.78 5.78 2.0e+00 0.23 0.23 1.00 5.2e+00
21 0.56 2 6.3e-15 20 1 80 0 7.26 72.7 15.4 4.1 4.1 1.1e+00 0.42 0.42 1.00 1.0e+00
41 1 2 6.4e-15 40 1 80 0 7.06 72.9 15.4 3.6 3.6 1.1e+00 0.42 0.42 1.00 4.2e-01
61 1.5 2 1.6e-14 60 1 80 0 6.78 73.2 15.4 3.41 3.41 1.1e+00 0.42 0.42 1.00 2.3e-01
81 1.9 2 1.1e-14 80 1 80 0 6.42 73.6 15.4 3.3 3.3 1.2e+00 0.42 0.42 1.00 1.9e-01
101 2.4 2 3.6e-14 100 1 80 0 5.99 74 15.4 3.21 3.21 1.3e+00 0.41 0.41 1.00 2.0e-01
121 2.8 2 4.0e-14 120 1 80 0 5.51 74.5 15.4 3.1 3.1 1.4e+00 0.40 0.40 1.00 2.3e-01
141 3.3 2 1.5e-14 140 1 80 0 4.98 75 15.4 2.98 2.98 1.5e+00 0.38 0.38 1.00 2.5e-01
161 3.8 2 2.4e-14 160 1 80 0 4.43 75.6 15.4 2.85 2.85 1.6e+00 0.37 0.37 1.00 2.6e-01
181 4.2 2 2.9e-14 180 1 80 0 3.88 76.1 15.4 2.72 2.72 1.8e+00 0.35 0.35 1.00 2.5e-01
201 4.7 2 4.3e-14 200 1 80 0 3.35 76.6 15.4 2.59 2.59 2.0e+00 0.34 0.34 1.00 2.3e-01
Analytical formula for chi_e with caracteristic scalelength
L-mode simulation
config.chi_e = chi_e('MS'); % A new set of parameters for chi_e module config.chi_e.params % Time grid config.grid.tgrid = [0:0.001:0.15]; % Define reference He factor(==tauEe/tauE_H98) on RAPTOR time grid config.chi_e.params.hefactor = 0.2*ones(size(config.grid.tgrid)); % Make new model and parameters [model,params,init,g,v,U] = build_RAPTOR_model(config); % Run simulation with new model simres_MS = RAPTOR_predictive(x0,g,v,U,model,params); out_MS = RAPTOR_out(simres_MS,model,params); % Profile of electron temperature plot(out_MS.rho,out_MS.te(:,end),'m','LineWidth',2); hold on % Define inded for rho_inv on gauss grid [~,ind_rinv] = min((out_MS.rhogauss - params.chi_e.rhoinv).^2); % rho_ped index [~,ind_rped] = min((out_MS.rhogauss - params.chi_e.rhoped(1)).^2); % Te on gauss grid tegauss = eval_te(simres_MS.X(:,end),simres_MS.G(:,1),simres_MS.V(:,1),model,'gauss'); % dlnTe/drho dlnTe_drhogauss = bsxfun(@rdivide,diff(log(tegauss(:,end))),diff(out_MS.rhogauss(:,end))); dlnTe_drhogauss = [dlnTe_drhogauss' dlnTe_drhogauss(end)]'; % Get lambdaTe value from simulation slambdaTe = -dlnTe_drhogauss(ind_rinv:ind_rped,end); % Get muTe value from simulation smuTe = -tegauss(ind_rped:end,end).*dlnTe_drhogauss(ind_rped:end,end); muTe = mean(smuTe); % Add core part coeffl = tegauss(ind_rped)/exp(-params.chi_e.lambdaTe(1)*out_MS.rhogauss(ind_rped)); te_core = coeffl*exp(-params.chi_e.lambdaTe(1)*out_MS.rhogauss(ind_rinv:ind_rped)); plot(out_MS.rhogauss(ind_rinv:ind_rped),te_core,'b--','LineWidth',2); % Add pedestal part coeffm = tegauss(end) + muTe*out_MS.rhogauss(end); te_edge = coeffm - muTe*out_MS.rhogauss(ind_rped:end); plot(out_MS.rhogauss(ind_rped:end),te_edge,'r--','LineWidth',2); xlabel('rho');legend('Te\_prof','labmdaTe','muTe','Location','SouthWest'); title('Te profile');