Contents
RAPTOR Exercise 1: Ramp-up current diffusion with varying heating
In this exercise you will test the effect of differently timed heating during a plasma current ramp.
First we set up the RAPTOR simulation.
clear addpath(fullfile(pwd,'..','RAPTOR_code'),'-end'); % add RAPTOR path % % load the default parameters, [~,params] = RAPTOR_config; % load default params params.grid.tgrid = [0:1e-3:0.2]; [model,params] = RAPTOR_config(params); % generate model structure for these params. params.dispopts.iterdisp = 10; % display every 10 % Plasma current ramp rampfun = @(t,tmin,ymin,tmax,ymax) max(ymin,min((ymax-ymin)/(tmax-tmin)*(t-tmin),ymax-ymin)+ymin); % anonymous function for ramps U(1,:) = rampfun(params.grid.tgrid,0,80e3,0.1,250e3); % input Ip trace U(2,:) = zeros(size(U(1,:))); % placeholder, will replace this with heating later. U(3,:) = zeros(size(U(1,:))); % placeholder, will replace this with heating later. % initial conditions [x0,g0,v0] = RAPTOR_initial_conditions(U(1),model,params); % Define the initial condition % Add one central heating actuator params.hcd = RAPTOR_hcd({@ECRH_ECCD}); % ECRH_ECCD module passed as function handle params.hcd.ECRH_ECCD.params.rdep = [0 0.4]; % One central heating actuator params.hcd.ECRH_ECCD.params.wdep = [0.35 0.35]; % wdep =0.35 params.hcd.ECRH_ECCD.params.cd_eff = [0 1]; % current drive efficiency factor: pure ECH for first, co-ECCD for second params.hcd.ECRH_ECCD.params.uindices = [2 3]; % index of power for each actuator in input vector % Nominal simulation (no heating) simres{1} = RAPTOR_predictive(x0,g0,v0,U,model,params); out{1} = RAPTOR_out(simres{1},model,params); qmin = out{1}.qmin;
Scaling Te initial condition to match edge value (50)
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.056 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.33 3 3.7e-11 10 1 0.097 0 0.0105 0.0866 13 2.3 2.3 4.4e+00 0.41 1.00 0.00 0.00 1.1e+01
21 0.53 2 4.8e-10 20 1 0.114 0 0.00945 0.105 11 1.5 1.5 3.9e+00 0.57 1.00 0.00 0.00 8.9e+00
31 0.7 2 7.5e-11 30 1 0.131 0 0.00882 0.122 9.7 1.2 1.2 3.5e+00 0.71 1.00 0.00 0.00 8.1e+00
41 0.88 2 1.2e-10 40 1 0.148 0 0.00839 0.14 8.6 1 1 3.3e+00 0.83 1.00 0.00 0.00 7.6e+00
51 1.1 2 2.5e-11 50 1 0.165 0 0.00807 0.157 7.7 0.92 0.92 3.1e+00 0.95 1.00 0.00 0.00 7.3e+00
61 1.3 2 4.7e-11 60 1 0.182 0 0.00782 0.174 7 0.83 0.83 3.0e+00 1.07 1.00 0.00 0.00 7.1e+00
71 1.5 2 4.8e-11 70 1 0.199 0 0.00763 0.191 6.4 0.76 0.76 2.8e+00 1.18 1.00 0.00 0.00 6.9e+00
81 2 2 2.4e-11 80 1 0.216 0 0.00747 0.209 5.9 0.71 0.71 2.7e+00 1.28 1.00 0.00 0.00 6.7e+00
91 2.2 2 4.5e-11 90 1 0.233 0 0.00734 0.226 5.5 0.67 0.67 2.6e+00 1.39 1.00 0.00 0.00 6.6e+00
101 2.6 2 1.4e-10 1e+02 1 0.25 0 0.00724 0.243 5.1 0.63 0.63 2.5e+00 1.49 1.00 0.00 0.00 6.5e+00
111 2.8 2 3.9e-10 1.1e+02 1 0.25 0 0.00718 0.243 5.1 0.6 0.6 1.8e+00 1.58 1.00 0.00 0.00 4.4e+00
121 3.1 2 9.2e-11 1.2e+02 1 0.25 0 0.00712 0.243 5.1 0.57 0.57 1.7e+00 1.66 1.00 0.00 0.00 3.8e+00
131 3.3 2 3.4e-11 1.3e+02 1 0.25 0 0.00706 0.243 5.1 0.54 0.54 1.6e+00 1.72 1.00 0.00 0.00 3.4e+00
141 3.5 2 7.7e-11 1.4e+02 1 0.25 0 0.00701 0.243 5.1 0.51 0.51 1.5e+00 1.77 1.00 0.00 0.00 3.0e+00
151 3.6 2 3.9e-11 1.5e+02 1 0.25 0 0.00696 0.243 5.1 0.49 0.49 1.5e+00 1.82 1.00 0.00 0.00 2.7e+00
161 3.8 2 4.1e-11 1.6e+02 1 0.25 0 0.00693 0.243 5.1 0.46 0.46 1.4e+00 1.86 1.00 0.00 0.00 2.4e+00
171 4.1 2 5.6e-11 1.7e+02 1 0.25 0 0.00689 0.243 5.1 0.45 0.45 1.4e+00 1.90 1.00 0.00 0.00 2.1e+00
181 4.3 2 5.3e-11 1.8e+02 1 0.25 0 0.00686 0.243 5.1 0.43 0.43 1.3e+00 1.93 1.00 0.00 0.00 1.9e+00
191 4.5 2 5.3e-11 1.9e+02 1 0.25 0 0.00684 0.243 5.1 0.41 0.41 1.3e+00 1.96 1.00 0.00 0.00 1.6e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 4.6 2 8.5e-11 2e+02 1 0.25 0 0.00682 0.243 5.1 0.4 0.4 1.3e+00 1.98 1.00 0.00 0.00 1.5e+00
EXERCISES
- By varying U(1,:), investigate the effect of different plasma current ramp rates on the speed of penetration of inductive current, the evolution of the loop voltage profile U_{pl}, and the q profile.
- Returning to the original Ip time trace, now use U(2,:) to add 1MW of central heating at different times during the ramp-up. As starting times, choose. Examine the effect on the T_e q and jpar profiles and explain the results.
- Use U(3,:) to add 2MW of off-axis current drive at different times.
- Find a combination of timing for heating and current drive to keep qmin above 1 for all times of the simulation.
SOLUTION 1
tflattopgrid = [0.01:0.05:0.11];
cgrid = {'b','r','k','m'};
clf;
for ii=1:numel(tflattopgrid)
tflattop = tflattopgrid(ii); U(1,:) = rampfun(params.grid.tgrid,0,80e3,tflattop,250e3); % input Ip trace simres{ii} = RAPTOR_predictive(x0,g0,v0,U,model,params); % run sim out{ii} = RAPTOR_out(simres{ii},model,params); % get outputs itplot = 1:2:40; % times to plot subplot(3,3,(ii-1)+1); plot(out{ii}.rho,out{ii}.jpar(:,itplot)/1e6,cgrid{ii}); hold on; ylabel('j_{||} [MA/m^2]') title(sprintf('t_{flattop}=%3.0f[ms]',tflattop*1e3)); subplot(3,3,(ii-1)+4); plot(out{ii}.rho,out{ii}.q(:,itplot),cgrid{ii}); hold on; ylabel('q [MA/m^2]') subplot(3,3,(ii-1)+7); plot(out{ii}.rho,out{ii}.Upl(:,itplot),cgrid{ii}); hold on; ylabel('U_{pl} [V]') drawnow
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.089 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.41 3 3.9e-11 10 1 0.25 0 0.0099 0.24 5.1 3 3.5 7.5e+00 0.65 1.00 0.00 0.00 3.5e+01
21 0.68 3 4.6e-11 20 1 0.25 0 0.0101 0.24 5.1 2 2.8 3.2e+00 1.04 1.00 0.00 0.00 1.4e+01
31 0.91 3 1.8e-11 30 1 0.25 0 0.00902 0.241 5.1 1.6 2.1 2.6e+00 1.18 1.00 0.00 0.00 1.1e+01
41 1.1 2 7.4e-10 40 1 0.25 0 0.00822 0.242 5.1 1.4 1.6 2.3e+00 1.27 1.00 0.00 0.00 8.8e+00
51 1.3 2 1.3e-10 50 1 0.25 0 0.00779 0.242 5.1 1.2 1.2 2.1e+00 1.35 1.00 0.00 0.00 7.3e+00
61 1.4 2 4.0e-11 60 1 0.25 0 0.00753 0.243 5.1 0.93 0.93 2.0e+00 1.44 1.00 0.00 0.00 6.2e+00
71 1.6 2 7.9e-11 70 1 0.25 0 0.00736 0.243 5.1 0.79 0.79 1.8e+00 1.52 1.00 0.00 0.00 5.3e+00
81 1.8 2 2.8e-11 80 1 0.25 0 0.00724 0.243 5.1 0.69 0.69 1.7e+00 1.59 1.00 0.00 0.00 4.6e+00
91 2 2 7.9e-11 90 1 0.25 0 0.00715 0.243 5.1 0.62 0.62 1.6e+00 1.66 1.00 0.00 0.00 4.0e+00
101 2.1 2 9.1e-11 1e+02 1 0.25 0 0.00708 0.243 5.1 0.57 0.57 1.6e+00 1.72 1.00 0.00 0.00 3.5e+00
111 2.3 2 1.0e-10 1.1e+02 1 0.25 0 0.00702 0.243 5.1 0.53 0.53 1.5e+00 1.77 1.00 0.00 0.00 3.1e+00
121 2.5 2 5.9e-11 1.2e+02 1 0.25 0 0.00697 0.243 5.1 0.5 0.5 1.5e+00 1.81 1.00 0.00 0.00 2.7e+00
131 2.6 2 6.0e-11 1.3e+02 1 0.25 0 0.00693 0.243 5.1 0.47 0.47 1.4e+00 1.86 1.00 0.00 0.00 2.4e+00
141 2.8 2 6.4e-11 1.4e+02 1 0.25 0 0.0069 0.243 5.1 0.45 0.45 1.4e+00 1.89 1.00 0.00 0.00 2.1e+00
151 2.9 2 3.4e-11 1.5e+02 1 0.25 0 0.00687 0.243 5.1 0.43 0.43 1.3e+00 1.93 1.00 0.00 0.00 1.9e+00
161 3.1 2 3.5e-11 1.6e+02 1 0.25 0 0.00684 0.243 5.1 0.42 0.42 1.3e+00 1.95 1.00 0.00 0.00 1.7e+00
171 3.3 2 4.0e-11 1.7e+02 1 0.25 0 0.00682 0.243 5.1 0.4 0.4 1.3e+00 1.98 1.00 0.00 0.00 1.5e+00
181 3.4 2 2.9e-11 1.8e+02 1 0.25 0 0.0068 0.243 5.1 0.39 0.39 1.3e+00 2.00 1.00 0.00 0.00 1.3e+00
191 3.6 2 1.2e-10 1.9e+02 1 0.25 0 0.00679 0.243 5.1 0.38 0.38 1.2e+00 2.02 1.00 0.00 0.00 1.2e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 3.8 2 5.1e-11 2e+02 1 0.25 0 0.00677 0.243 5.1 0.38 0.38 1.2e+00 2.04 1.00 0.00 0.00 1.0e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.06 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.62 3 2.1e-11 10 1 0.108 0 0.0102 0.0982 12 2.4 2.4 4.9e+00 0.43 1.00 0.00 0.00 1.3e+01
21 0.77 2 9.6e-10 20 1 0.137 0 0.00906 0.128 9.3 1.6 1.6 4.3e+00 0.62 1.00 0.00 0.00 1.2e+01
31 0.92 2 2.3e-10 30 1 0.165 0 0.00842 0.157 7.7 1.3 1.3 3.9e+00 0.79 1.00 0.00 0.00 1.1e+01
41 1.1 2 8.5e-11 40 1 0.193 0 0.00801 0.185 6.6 1.1 1.1 3.6e+00 0.95 1.00 0.00 0.00 1.0e+01
51 1.2 2 3.8e-11 50 1 0.222 0 0.00774 0.214 5.7 0.95 0.95 3.4e+00 1.11 1.00 0.00 0.00 9.9e+00
61 1.7 2 6.1e-11 60 1 0.25 0 0.00755 0.242 5.1 0.86 0.86 3.2e+00 1.26 1.00 0.00 0.00 9.6e+00
71 1.9 2 2.7e-09 70 1 0.25 0 0.00746 0.243 5.1 0.79 0.79 2.2e+00 1.38 1.00 0.00 0.00 6.1e+00
81 2.1 2 2.0e-10 80 1 0.25 0 0.00735 0.243 5.1 0.73 0.73 1.9e+00 1.48 1.00 0.00 0.00 5.3e+00
91 2.3 2 4.9e-11 90 1 0.25 0 0.00725 0.243 5.1 0.67 0.67 1.8e+00 1.57 1.00 0.00 0.00 4.6e+00
101 2.4 2 2.0e-11 1e+02 1 0.25 0 0.00716 0.243 5.1 0.62 0.62 1.7e+00 1.64 1.00 0.00 0.00 4.1e+00
111 2.6 2 3.1e-11 1.1e+02 1 0.25 0 0.00709 0.243 5.1 0.57 0.57 1.6e+00 1.70 1.00 0.00 0.00 3.6e+00
121 2.7 2 3.0e-11 1.2e+02 1 0.25 0 0.00703 0.243 5.1 0.53 0.53 1.5e+00 1.75 1.00 0.00 0.00 3.2e+00
131 2.9 2 5.4e-11 1.3e+02 1 0.25 0 0.00698 0.243 5.1 0.5 0.5 1.5e+00 1.80 1.00 0.00 0.00 2.8e+00
141 3.1 2 7.0e-11 1.4e+02 1 0.25 0 0.00694 0.243 5.1 0.48 0.48 1.4e+00 1.84 1.00 0.00 0.00 2.5e+00
151 3.3 2 7.1e-11 1.5e+02 1 0.25 0 0.0069 0.243 5.1 0.45 0.45 1.4e+00 1.88 1.00 0.00 0.00 2.2e+00
161 3.4 2 9.0e-11 1.6e+02 1 0.25 0 0.00687 0.243 5.1 0.44 0.44 1.4e+00 1.92 1.00 0.00 0.00 1.9e+00
171 3.6 2 2.8e-11 1.7e+02 1 0.25 0 0.00685 0.243 5.1 0.42 0.42 1.3e+00 1.95 1.00 0.00 0.00 1.7e+00
181 3.8 2 3.4e-11 1.8e+02 1 0.25 0 0.00683 0.243 5.1 0.41 0.41 1.3e+00 1.97 1.00 0.00 0.00 1.5e+00
191 3.9 2 9.2e-11 1.9e+02 1 0.25 0 0.00681 0.243 5.1 0.4 0.4 1.3e+00 2.00 1.00 0.00 0.00 1.4e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 4.1 2 5.0e-11 2e+02 1 0.25 0 0.00679 0.243 5.1 0.39 0.39 1.3e+00 2.02 1.00 0.00 0.00 1.2e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.058 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.44 3 1.4e-11 10 1 0.0954 0 0.0106 0.085 13 2.3 2.3 4.4e+00 0.41 1.00 0.00 0.00 1.0e+01
21 0.78 2 4.7e-10 20 1 0.111 0 0.00953 0.101 11 1.5 1.5 3.8e+00 0.56 1.00 0.00 0.00 8.4e+00
31 0.95 2 6.9e-11 30 1 0.126 0 0.0089 0.118 10 1.2 1.2 3.5e+00 0.69 1.00 0.00 0.00 7.6e+00
41 1.1 2 9.5e-11 40 1 0.142 0 0.00847 0.133 9 1 1 3.2e+00 0.81 1.00 0.00 0.00 7.2e+00
51 1.3 2 6.9e-11 50 1 0.157 0 0.00815 0.149 8.1 0.92 0.92 3.1e+00 0.93 1.00 0.00 0.00 6.9e+00
61 1.4 2 7.2e-11 60 1 0.173 0 0.00789 0.165 7.4 0.83 0.83 2.9e+00 1.03 1.00 0.00 0.00 6.7e+00
71 1.6 2 2.4e-11 70 1 0.188 0 0.00769 0.181 6.8 0.76 0.76 2.8e+00 1.14 1.00 0.00 0.00 6.5e+00
81 1.8 2 2.3e-11 80 1 0.204 0 0.00753 0.196 6.2 0.71 0.71 2.7e+00 1.24 1.00 0.00 0.00 6.3e+00
91 2 2 4.1e-11 90 1 0.219 0 0.0074 0.212 5.8 0.67 0.67 2.6e+00 1.34 1.00 0.00 0.00 6.2e+00
101 2.1 2 8.3e-11 1e+02 1 0.235 0 0.00729 0.227 5.4 0.63 0.63 2.5e+00 1.44 1.00 0.00 0.00 6.1e+00
111 2.3 2 7.9e-11 1.1e+02 1 0.25 0 0.00719 0.243 5.1 0.6 0.6 2.4e+00 1.53 1.00 0.00 0.00 6.0e+00
121 2.4 2 2.7e-10 1.2e+02 1 0.25 0 0.00714 0.243 5.1 0.57 0.57 1.8e+00 1.62 1.00 0.00 0.00 4.1e+00
131 2.6 2 2.3e-11 1.3e+02 1 0.25 0 0.00708 0.243 5.1 0.55 0.55 1.7e+00 1.69 1.00 0.00 0.00 3.5e+00
141 2.8 2 2.2e-11 1.4e+02 1 0.25 0 0.00703 0.243 5.1 0.52 0.52 1.6e+00 1.74 1.00 0.00 0.00 3.1e+00
151 2.9 2 5.7e-11 1.5e+02 1 0.25 0 0.00698 0.243 5.1 0.5 0.5 1.5e+00 1.80 1.00 0.00 0.00 2.8e+00
161 3.1 2 1.2e-10 1.6e+02 1 0.25 0 0.00694 0.243 5.1 0.47 0.47 1.4e+00 1.84 1.00 0.00 0.00 2.5e+00
171 3.3 2 5.4e-11 1.7e+02 1 0.25 0 0.00691 0.243 5.1 0.45 0.45 1.4e+00 1.88 1.00 0.00 0.00 2.2e+00
181 3.4 2 1.4e-11 1.8e+02 1 0.25 0 0.00688 0.243 5.1 0.44 0.44 1.4e+00 1.91 1.00 0.00 0.00 2.0e+00
191 3.6 2 5.9e-11 1.9e+02 1 0.25 0 0.00685 0.243 5.1 0.42 0.42 1.3e+00 1.94 1.00 0.00 0.00 1.7e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 3.7 2 8.0e-11 2e+02 1 0.25 0 0.00683 0.243 5.1 0.41 0.41 1.3e+00 1.97 1.00 0.00 0.00 1.5e+00
end
The fastest ramp rate (t_{flattop}=10ms) leads to a non-monotinic current density profile and flatter, or more reversed, q profiles. This can lead to transport barriers. In reality, the ramp rate is limited by MHD modes which can appear, especially for very steep current density profiles.
SOLUTION 2
clf; % Back to default Ip trace U(1,:) = rampfun(params.grid.tgrid,0,80e3,0.1,250e3); % input Ip trace tstartgrid = [0.01:0.03:0.09]; for ii=1:numel(tstartgrid); tstart = tstartgrid(ii); U(2,:) = rampfun(params.grid.tgrid,tstart,0,tstart+1e-3,1e6); simres{ii} = RAPTOR_predictive(x0,g0,v0,U,model,params); out{ii} = RAPTOR_out(simres{ii},model,params); itplot = 1:2:40; % times to plot subplot(3,3,(ii-1)+1); plot(out{ii}.rho,out{ii}.jpar(:,itplot)/1e6,cgrid{ii}); hold on; ylabel('j_{||} [MA/m^2]') title(sprintf('t_{flattop}=%3.0f[ms]',tflattop*1e3)); subplot(3,3,(ii-1)+4); plot(out{ii}.rho,out{ii}.q(:,itplot),cgrid{ii}); hold on; ylabel('q [MA/m^2]') subplot(3,3,(ii-1)+7); plot(out{ii}.rho,out{ii}.te(:,itplot),cgrid{ii}); hold on; ylabel('T_e [eV]') end
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.073 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.69 3 3.7e-11 10 1 0.097 0 0.0105 0.0866 13 2.3 2.3 4.4e+00 0.41 1.00 0.00 0.00 1.1e+01
21 0.96 2 4.9e-09 20 1 0.114 0 0.0481 0.0671 11 2.6 2.8 1.2e+00 6.33 1.00 0.00 0.00 5.3e+00
31 1.1 2 2.0e-11 30 1 0.131 0 0.0512 0.0812 9.7 2.4 3.3 1.2e+00 7.46 1.00 0.00 0.00 5.4e+00
41 1.3 2 1.0e-10 40 1 0.148 0 0.0535 0.0959 8.6 2.2 3.7 1.2e+00 8.51 1.00 0.00 0.00 5.4e+00
51 1.4 2 3.3e-11 50 1 0.165 0 0.0549 0.112 7.7 2 4 1.2e+00 9.38 1.00 0.00 0.00 5.3e+00
61 1.6 2 1.5e-11 60 1 0.182 0 0.0556 0.128 7 1.8 4.1 1.2e+00 10.13 1.00 0.00 0.01 5.3e+00
71 1.8 2 1.8e-11 70 1 0.199 0 0.0559 0.145 6.4 1.7 4.1 1.1e+00 10.82 1.00 0.00 0.01 5.2e+00
81 1.9 2 1.5e-11 80 1 0.216 0 0.0562 0.161 5.9 1.6 4.1 1.1e+00 11.48 1.00 0.00 0.01 5.2e+00
91 2.1 2 5.4e-11 90 1 0.233 0 0.0565 0.178 5.5 1.5 4.2 1.1e+00 12.14 1.00 0.00 0.01 5.2e+00
101 2.3 2 3.5e-11 1e+02 1 0.25 0 0.0567 0.195 5.1 1.5 4.4 1.1e+00 12.79 1.00 0.00 0.01 5.1e+00
111 2.4 2 1.4e-10 1.1e+02 1 0.25 0 0.0569 0.195 5.1 1.4 4.6 6.5e-01 13.40 1.00 0.00 0.01 3.4e+00
121 2.6 2 4.3e-11 1.2e+02 1 0.25 0 0.0569 0.195 5.1 1.3 4.8 5.4e-01 13.96 1.00 0.00 0.01 2.9e+00
131 2.8 2 1.3e-10 1.3e+02 1 0.25 0 0.0569 0.195 5.1 1.3 5.1 4.8e-01 14.48 1.00 0.00 0.01 2.6e+00
141 3 2 7.0e-11 1.4e+02 1 0.25 0 0.0566 0.195 5.1 1.2 5.3 4.4e-01 14.93 1.00 0.00 0.01 2.4e+00
151 3.1 2 5.1e-11 1.5e+02 1 0.25 0 0.056 0.196 5.1 1.1 5.4 4.0e-01 15.29 1.00 0.00 0.01 2.3e+00
161 3.3 2 4.3e-11 1.6e+02 1 0.25 0 0.0551 0.196 5.1 1.1 5.6 3.7e-01 15.51 1.00 0.00 0.01 2.1e+00
171 3.5 2 3.5e-11 1.7e+02 1 0.25 0 0.0539 0.198 5.1 1.1 5.9 3.5e-01 15.60 1.00 0.00 0.01 2.0e+00
181 3.7 2 4.4e-11 1.8e+02 1 0.25 0 0.0524 0.199 5.1 1 6.3 3.3e-01 15.60 1.00 0.00 0.01 1.9e+00
191 3.8 2 2.3e-11 1.9e+02 1 0.25 0 0.0509 0.201 5.1 0.98 6.8 3.1e-01 15.54 1.00 0.00 0.01 1.8e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 4 2 5.5e-11 2e+02 1 0.25 0 0.0494 0.202 5.1 0.94 7.4 3.0e-01 15.43 1.00 0.00 0.01 1.7e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.05 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.35 3 3.7e-11 10 1 0.097 0 0.0105 0.0866 13 2.3 2.3 4.4e+00 0.41 1.00 0.00 0.00 1.1e+01
21 0.59 2 4.8e-10 20 1 0.114 0 0.00945 0.105 11 1.5 1.5 3.9e+00 0.57 1.00 0.00 0.00 8.9e+00
31 0.76 2 7.5e-11 30 1 0.131 0 0.00882 0.122 9.7 1.2 1.2 3.5e+00 0.71 1.00 0.00 0.00 8.1e+00
41 0.96 2 6.4e-11 40 1 0.148 0 0.00839 0.14 8.6 1 1 3.3e+00 0.83 1.00 0.00 0.00 7.6e+00
51 1.3 3 1.1e-10 50 1 0.165 0 0.0338 0.132 7.7 1 1 1.0e+00 7.96 1.00 0.00 0.00 4.5e+00
61 1.5 2 1.2e-10 60 1 0.182 0 0.0346 0.148 7 1.1 1.1 1.0e+00 8.50 1.00 0.00 0.00 4.6e+00
71 1.7 2 4.3e-11 70 1 0.199 0 0.0346 0.165 6.4 1.1 1.1 1.1e+00 8.88 1.00 0.00 0.01 4.8e+00
81 2 2 6.0e-11 80 1 0.216 0 0.0348 0.182 5.9 1.1 1.1 1.1e+00 9.28 1.00 0.00 0.01 4.8e+00
91 2.2 2 1.0e-10 90 1 0.233 0 0.0349 0.199 5.5 1.1 1.1 1.1e+00 9.69 1.00 0.00 0.01 4.8e+00
101 2.3 2 1.2e-10 1e+02 1 0.25 0 0.0352 0.216 5.1 1.1 1.1 1.1e+00 10.13 1.00 0.00 0.01 4.9e+00
111 2.5 2 1.7e-10 1.1e+02 1 0.25 0 0.0354 0.215 5.1 1.1 1.1 6.1e-01 10.55 1.00 0.00 0.01 3.0e+00
121 2.9 2 3.8e-11 1.2e+02 1 0.25 0 0.0356 0.215 5.1 1.1 1.1 5.1e-01 10.93 1.00 0.00 0.01 2.6e+00
131 3.1 2 5.1e-11 1.3e+02 1 0.25 0 0.0358 0.215 5.1 1.1 1.1 4.6e-01 11.30 1.00 0.00 0.01 2.3e+00
141 3.3 2 3.1e-11 1.4e+02 1 0.25 0 0.0359 0.215 5.1 1.1 1.1 4.1e-01 11.65 1.00 0.00 0.01 2.1e+00
151 3.6 2 1.4e-10 1.5e+02 1 0.25 0 0.0359 0.215 5.1 1 1 3.8e-01 11.98 1.00 0.00 0.01 2.0e+00
161 3.7 2 6.8e-11 1.6e+02 1 0.25 0 0.0359 0.215 5.1 1 1 3.6e-01 12.28 1.00 0.00 0.01 1.9e+00
171 3.9 2 4.8e-11 1.7e+02 1 0.25 0 0.0358 0.215 5.1 0.98 1 3.4e-01 12.54 1.00 0.00 0.01 1.7e+00
181 4.1 2 1.0e-10 1.8e+02 1 0.25 0 0.0357 0.215 5.1 0.95 1 3.2e-01 12.76 1.00 0.00 0.01 1.6e+00
191 4.2 2 1.2e-10 1.9e+02 1 0.25 0 0.0354 0.215 5.1 0.92 1 3.0e-01 12.93 1.00 0.00 0.01 1.6e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 4.4 2 6.8e-11 2e+02 1 0.25 0 0.0351 0.216 5.1 0.9 1 2.9e-01 13.07 1.00 0.00 0.01 1.5e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
1 0.05 6 1.6e-11 0 1 0.08 0 0.025 0.0554 16 7.5 9.3 6.3e+00 0.59 1.00 0.00 0.00 3.1e+01
11 0.34 3 3.7e-11 10 1 0.097 0 0.0105 0.0866 13 2.3 2.3 4.4e+00 0.41 1.00 0.00 0.00 1.1e+01
21 0.53 2 4.8e-10 20 1 0.114 0 0.00945 0.105 11 1.5 1.5 3.9e+00 0.57 1.00 0.00 0.00 8.9e+00
31 0.73 2 7.5e-11 30 1 0.131 0 0.00882 0.122 9.7 1.2 1.2 3.5e+00 0.71 1.00 0.00 0.00 8.1e+00
41 0.91 2 1.2e-10 40 1 0.148 0 0.00839 0.14 8.6 1 1 3.3e+00 0.83 1.00 0.00 0.00 7.6e+00
51 1.1 2 2.5e-11 50 1 0.165 0 0.00807 0.157 7.7 0.92 0.92 3.1e+00 0.95 1.00 0.00 0.00 7.3e+00
61 1.3 2 4.7e-11 60 1 0.182 0 0.00782 0.174 7 0.83 0.83 3.0e+00 1.07 1.00 0.00 0.00 7.1e+00
71 1.5 2 3.8e-11 70 1 0.199 0 0.00763 0.191 6.4 0.76 0.76 2.8e+00 1.18 1.00 0.00 0.00 6.9e+00
81 1.8 3 4.3e-11 80 1 0.216 0 0.0299 0.187 5.9 0.76 0.76 9.7e-01 9.43 1.00 0.00 0.01 4.2e+00
91 2.1 2 5.0e-11 90 1 0.233 0 0.0312 0.202 5.5 0.76 0.76 9.7e-01 10.11 1.00 0.00 0.01 4.3e+00
101 2.3 2 5.9e-11 1e+02 1 0.25 0 0.0313 0.219 5.1 0.76 0.76 1.0e+00 10.43 1.00 0.00 0.01 4.5e+00
111 2.5 2 1.4e-10 1.1e+02 1 0.25 0 0.0313 0.219 5.1 0.76 0.76 5.4e-01 10.71 1.00 0.00 0.01 2.6e+00
121 2.6 2 3.5e-11 1.2e+02 1 0.25 0 0.0313 0.219 5.1 0.76 0.76 4.5e-01 10.96 1.00 0.00 0.01 2.2e+00
131 2.8 2 1.4e-10 1.3e+02 1 0.25 0 0.0313 0.219 5.1 0.76 0.76 4.0e-01 11.18 1.00 0.00 0.01 1.9e+00
141 3 2 5.9e-11 1.4e+02 1 0.25 0 0.0313 0.219 5.1 0.76 0.76 3.7e-01 11.39 1.00 0.00 0.01 1.8e+00
151 3.1 2 9.9e-11 1.5e+02 1 0.25 0 0.0312 0.219 5.1 0.75 0.75 3.4e-01 11.59 1.00 0.00 0.01 1.6e+00
161 3.3 2 1.0e-10 1.6e+02 1 0.25 0 0.0312 0.219 5.1 0.75 0.75 3.2e-01 11.78 1.00 0.00 0.01 1.5e+00
171 3.5 2 1.5e-10 1.7e+02 1 0.25 0 0.0311 0.22 5.1 0.75 0.75 3.0e-01 11.95 1.00 0.00 0.01 1.5e+00
181 3.6 2 6.2e-11 1.8e+02 1 0.25 0 0.0309 0.22 5.1 0.75 0.75 2.9e-01 12.10 1.00 0.00 0.01 1.4e+00
191 3.8 2 1.6e-10 1.9e+02 1 0.25 0 0.0308 0.22 5.1 0.75 0.75 2.7e-01 12.23 1.00 0.00 0.01 1.3e+00
istep telaps newt res t[ms] dt[ms] Ip[MA] Icd[MA] Ibs[MA] Ioh[MA] qe qmin q0 Vl[V] Te0[keV] ne0[e19] Wi[MJ] We[MJ] f_ss
201 4 2 8.1e-11 2e+02 1 0.25 0 0.0306 0.22 5.1 0.74 0.74 2.6e-01 12.35 1.00 0.00 0.01 1.3e+00
Turning on the heating very early creates a transport barrier which much higher temperature than the other cases, with an off-axis peak in the current density due to the bootstrap current.