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gyacomo/wk/analysis_2D.m
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analysis_2D.m
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%% Load results
compile_results
%% Retrieving max polynomial degree and sampling info
Npe = numel(Pe); Nje = numel(Je); [JE,PE] = meshgrid(Je,Pe);
Npi = numel(Pi); Nji = numel(Ji); [JI,PI] = meshgrid(Ji,Pi);
Ns5D = numel(Ts5D);
Ns2D = numel(Ts2D);
% renaming and reshaping quantity of interest
Ts5D = Ts5D';
Ts2D = Ts2D';
if strcmp(OUTPUTS.write_non_lin,'.true.')
Si00 = squeeze(Sipj(1,1,:,:,:));
Se00 = squeeze(Sepj(1,1,:,:,:));
end
%% Build grids
Nkr = numel(kr); Nkz = numel(kz);
[KZ,KR] = meshgrid(kz,kr);
Lkr = max(kr)-min(kr); Lkz = max(kz)-min(kz);
dkr = Lkr/(Nkr-1); dkz = Lkz/(Nkz-1);
Lk = max(Lkr,Lkz);
dr = 2*pi/Lk; dz = 2*pi/Lk;
Nr = max(Nkr,Nkz); Nz = Nr;
r = dr*(-Nr/2:(Nr/2-1)); Lr = max(r)-min(r);
z = dz*(-Nz/2:(Nz/2-1)); Lz = max(z)-min(z);
[ZZ,RR] = meshgrid(z,r);
%% Analysis %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Analysis :')
disp('- iFFT')
% IFFT (Lower case = real space, upper case = frequency space)
ne00 = zeros(Nr,Nz,Ns2D);
ni00 = zeros(Nr,Nz,Ns2D);
si00 = zeros(Nr,Nz,Ns5D);
phi = zeros(Nr,Nz,Ns2D);
drphi = zeros(Nr,Nz,Ns2D);
dzphi = zeros(Nr,Nz,Ns2D);
for it = 1:numel(Ts2D)
NE_ = Ne00(:,:,it); NI_ = Ni00(:,:,it); PH_ = PHI(:,:,it);
ne00(:,:,it) = real(fftshift(ifft2((NE_),Nr,Nz)));
ni00(:,:,it) = real(fftshift(ifft2((NI_),Nr,Nz)));
phi (:,:,it) = real(fftshift(ifft2((PH_),Nr,Nz)));
drphi(:,:,it) = real(fftshift(ifft2(1i*KR.*(PH_),Nr,Nz)));
dzphi(:,:,it) = real(fftshift(ifft2(1i*KZ.*(PH_),Nr,Nz)));
end
if strcmp(OUTPUTS.write_non_lin,'.true.')
for it = 1:numel(Ts5D)
si00(:,:,it) = real(fftshift(ifft2(squeeze(Si00(:,:,it)),Nr,Nz)));
end
end
% Post processing
disp('- post processing')
E_pot = zeros(1,Ns2D); % Potential energy n^2
E_kin = zeros(1,Ns2D); % Kinetic energy grad(phi)^2
ExB = zeros(1,Ns2D); % ExB drift intensity \propto |\grad \phi|
Flux_ri = zeros(1,Ns2D); % Particle flux Gamma = <ni drphi>
Flux_zi = zeros(1,Ns2D); % Particle flux Gamma = <ni dzphi>
Flux_re = zeros(1,Ns2D); % Particle flux Gamma = <ne drphi>
Flux_ze = zeros(1,Ns2D); % Particle flux Gamma = <ne dzphi>
Ne_norm = zeros(Npe,Nje,Ns5D);% Time evol. of the norm of Napj
Ni_norm = zeros(Npi,Nji,Ns5D);% .
if strcmp(OUTPUTS.write_non_lin,'.true.')
Se_norm = zeros(Npe,Nje,Ns5D);% Time evol. of the norm of Sapj
Si_norm = zeros(Npi,Nji,Ns5D);% .
Sne00_norm = zeros(1,Ns2D); % Time evol. of the amp of e nonlin term
Sni00_norm = zeros(1,Ns2D); %
end
Ddr = 1i*KR; Ddz = 1i*KZ; lapl = Ddr.^2 + Ddz.^2;
for it = 1:numel(Ts2D) % Loop over 2D arrays
NE_ = Ne00(:,:,it); NI_ = Ni00(:,:,it); PH_ = PHI(:,:,it);
E_pot(it) = pi/Lr/Lz*sum(sum(abs(NI_).^2))/Nkr/Nkr; % integrate through Parseval id
E_kin(it) = pi/Lr/Lz*sum(sum(abs(Ddr.*PH_).^2+abs(Ddz.*PH_).^2))/Nkr/Nkr;
ExB(it) = max(max(max(abs(phi(3:end,:,it)-phi(1:end-2,:,it))/(2*dr))),max(max(abs(phi(:,3:end,it)-phi(:,1:end-2,it))'/(2*dz))));
Flux_ri(it) = sum(sum(ni00(:,:,it).*dzphi(:,:,it)))*dr*dz/Lr/Lz;
Flux_zi(it) = sum(sum(-ni00(:,:,it).*drphi(:,:,it)))*dr*dz/Lr/Lz;
Flux_re(it) = sum(sum(ne00(:,:,it).*dzphi(:,:,it)))*dr*dz/Lr/Lz;
Flux_ze(it) = sum(sum(-ne00(:,:,it).*drphi(:,:,it)))*dr*dz/Lr/Lz;
end
E_kin_KZ = mean(mean(abs(Ddr.*PHI(:,:,it)).^2+abs(Ddz.*PHI(:,:,it)).^2,3),2);
E_kin_KR = mean(mean(abs(Ddr.*PHI(:,:,it)).^2+abs(Ddz.*PHI(:,:,it)).^2,3),2);
dEdt = diff(E_pot+E_kin)./dt2D;
for it = 1:numel(Ts5D) % Loop over 5D arrays
NE_ = Ne00(:,:,it); NI_ = Ni00(:,:,it); PH_ = PHI(:,:,it);
Ne_norm(:,:,it)= sum(sum(abs(Nepj(:,:,:,:,it)),3),4)/Nkr/Nkz;
Ni_norm(:,:,it)= sum(sum(abs(Nipj(:,:,:,:,it)),3),4)/Nkr/Nkz;
if strcmp(OUTPUTS.write_non_lin,'.true.')
Se_norm(:,:,it)= sum(sum(abs(Sepj(:,:,:,:,it)),3),4)/Nkr/Nkz;
Sne00_norm(it) = sum(sum(abs(Se00(:,:,it))))/Nkr/Nkz;
Si_norm(:,:,it)= sum(sum(abs(Sipj(:,:,:,:,it)),3),4)/Nkr/Nkz;
Sni00_norm(it) = sum(sum(abs(Si00(:,:,it))))/Nkr/Nkz;
end
end
%% Compute growth rate
disp('- growth rate')
tend = Ts2D(end); tstart = 0.6*tend;
g_ = zeros(Nkr,Nkz);
[~,ikr0KH] = min(abs(kr-KR0KH));
for ikr = 1:Nkr
for ikz = 1:Nkz
g_(ikr,ikz) = LinearFit_s(Ts2D,squeeze(abs(Ni00(ikr,ikz,:))),tstart,tend);
end
end
% gkr0kz_Ni00 = max(real(g_(:,:)),[],1);
gkr0kz_Ni00 = real(g_(ikr0KH,:));
%% PLOTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Plots')
FMT = '.fig';
%% Time evolutions
fig = figure; FIGNAME = ['t_evolutions',sprintf('_%.2d',JOBNUM)];
subplot(221);
for ip = 1:Npe
for ij = 1:Nje
plt = @(x) squeeze(x(ip,ij,:));
plotname = ['$N_e^{',num2str(ip-1),num2str(ij-1),'}$'];
semilogy(Ts5D,plt(Ne_norm),'DisplayName',plotname); hold on;
end
end
grid on; xlabel('$t$'); ylabel('$\sum_{k_r,k_z}|N_e^{pj}|$');
subplot(222)
for ip = 1:Npi
for ij = 1:Nji
plt = @(x) squeeze(x(ip,ij,:));
plotname = ['$N_i^{',num2str(ip-1),num2str(ij-1),'}$'];
semilogy(Ts5D,plt(Ni_norm),'DisplayName',plotname); hold on;
end
end
grid on; xlabel('$t$'); ylabel('$\sum_{k_r,k_z}|N_i^{pj}|$');
subplot(223)
plot(Ts2D,Flux_ri,'-','DisplayName','$\Gamma_{ri}$'); hold on;
plot(Ts2D,Flux_zi,'-','DisplayName','$\Gamma_{zi}$'); hold on;
plot(Ts2D,Flux_re,'-','DisplayName','$\Gamma_{re}$')
plot(Ts2D,Flux_ze,'-','DisplayName','$\Gamma_{ze}$')
grid on; xlabel('$t$'); ylabel('$\Gamma$'); %legend('show');
if strcmp(OUTPUTS.write_non_lin,'.true.')
subplot(224)
for ip = 1:Npi
for ij = 1:Nji
plt = @(x) squeeze(x(ip,ij,:));
plotname = ['$S_i^{',num2str(ip-1),num2str(ij-1),'}$'];
semilogy(Ts5D,plt(Si_norm),'DisplayName',plotname); hold on;
end
end
grid on; xlabel('$t$'); ylabel('$S$'); %legend('show');
else
%% Growth rate
subplot(224)
[~,ikr0KH] = min(abs(kr-KR0KH));
plot(kz(1:ikr0KH)/kr(ikr0KH),gkr0kz_Ni00(1:ikr0KH)/(KR0KH*A0KH),...
'DisplayName',['J = ',num2str(JMAXI)]);
xlabel('$k_z/k_{r0}$'); ylabel('$\gamma_{Ni}/(A_0k_{r0})$');
xlim([0. 1.0]); %ylim([0. 0.04]);
end
save_figure
%%
if 1
%% Show frame in real space
tf = 100; [~,it] = min(abs(Ts2D-tf)); [~,it5D] = min(abs(Ts5D-tf));
fig = figure; FIGNAME = ['rz_frame',sprintf('_%.2d',JOBNUM)];
subplot(221); plt = @(x) (((x)));
pclr = pcolor((RR),(ZZ),plt(ne00(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$r$'); ylabel('$z$'); title(sprintf('t=%.3d',Ts2D(it))); legend('$|\hat n_e^{00}|$');
subplot(222); plt = @(x) ((x));
pclr = pcolor((RR),(ZZ),plt(ni00(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$r$'); ylabel('$z$'); title(sprintf('t=%.3d',Ts2D(it))); legend('$|\hat n_i^{00}|$');
subplot(223); plt = @(x) ((x));
pclr = pcolor((RR),(ZZ),plt(phi(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$r$'); ylabel('$z$'); title(sprintf('t=%.3d',Ts2D(it))); legend('$|\hat\phi|$');
if strcmp(OUTPUTS.write_non_lin,'.true.')
subplot(224); plt = @(x) fftshift((abs(x)),2);
pclr = pcolor((RR),(ZZ),plt(si00(:,:,it5D))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$r$'); ylabel('$z$'); title(sprintf('t=%.3d',Ts5D(it5D))); legend('$|S_i^{00}|$');
end
save_figure
end
%%
t0 = 0;
skip_ = 1;
DELAY = 0.01*skip_;
FRAMES = floor(t0/(Ts2D(2)-Ts2D(1)))+1:skip_:numel(Ts2D);
%% GIFS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if 0
%% Density ion
GIFNAME = ['ni00',sprintf('_%.2d',JOBNUM)]; INTERP = 0;
FIELD = real(ni00); X = RR; Y = ZZ; T = Ts2D;
FIELDNAME = '$n_i^{00}$'; XNAME = '$r$'; YNAME = '$z$';
create_gif
end
if 0
%% Density electron
GIFNAME = ['ne00',sprintf('_%.2d',JOBNUM)]; INTERP = 1;
FIELD = real(ne00); X = RR; Y = ZZ; T = Ts2D;
FIELDNAME = '$n_e^{00}$'; XNAME = '$r$'; YNAME = '$z$';
create_gif
end
if 0
%% Phi
GIFNAME = ['phi',sprintf('_%.2d',JOBNUM)];INTERP = 1;
FIELD = real(phi); X = RR; Y = ZZ; T = Ts2D;
FIELDNAME = '$\phi$'; XNAME = '$r$'; YNAME = '$z$';
create_gif
end
if 0
%% Density ion frequency
GIFNAME = ['Ni00',sprintf('_%.2d',JOBNUM)]; INTERP = 0;
FIELD =ifftshift((abs(Ni00)),2); X = fftshift(KR,2); Y = fftshift(KZ,2); T = Ts2D;
FIELDNAME = '$N_i^{00}$'; XNAME = '$k_r$'; YNAME = '$k_z$';
create_gif
end
if 0
%% Density ion frequency @ kr = 0
GIFNAME = ['Ni00_kr0',sprintf('_%.2d',JOBNUM)]; INTERP = 0;
FIELD =(squeeze(abs(Ni00(1,:,:)))); linestyle = 'o-.';
X = (kz); T = Ts2D; YMIN = -.1; YMAX = 1.1; XMIN = min(kz); XMAX = max(kz);
FIELDNAME = '$N_i^{00}(kr=0)$'; XNAME = '$k_r$';
create_gif_1D
% %% PJ ion moment frequency
% p_ = 0+1; j_ = 3+1;
% GIFNAME = ['Ni',num2str(p_),num2str(j_),sprintf('_%.2d',JOBNUM)]; INTERP = 0;
% FIELD =ifftshift(abs(squeeze(Nipj(p_,j_,:,:,:))),2); X = fftshift(KR,2); Y = fftshift(KZ,2); T = Ts;
% FIELDNAME = ['$N_i^{',num2str(p_-1),num2str(j_-1),'}$']; XNAME = '$k_r$'; YNAME = '$k_z$';
% create_gif
% %% non linear term frequ. space
% GIFNAME = ['Si00',sprintf('_%.2d',JOBNUM)]; INTERP = 0;
% FIELD = fftshift((abs(Si00)),2); X = fftshift(KR,2); Y = fftshift(KZ,2); T = Ts;
% FIELDNAME = '$S_i^{00}$'; XNAME = '$k_r$'; YNAME = '$k_z$';
% create_gif
% %% Electron mode growth
% GIFNAME = ['norm_Nepj',sprintf('_%.2d',JOBNUM)]; INTERP = 1;
% FIELD = Ne_norm; X = PE; Y = JE; T = Ts;
% FIELDNAME = '$\max_k{\gamma_e}$'; XNAME = '$p$'; YNAME = '$j$';
% create_gif
end
%%
if 0
%% Asymmetry error on kr = 0
up = 2:Nkz/2;
down = Nkz:-1:Nkz/2+2;
eps_asym_r = Ts5D;
eps_asym_i = Ts5D;
for it = 1:numel(Ts5D)
eps_asym_r(it) = max(squeeze(abs(real(Ni00(1,up,it))-real(Ni00(1,down,it)))));
eps_asym_i(it) = max(abs(imag(Ni00(1,up,it))+imag(Ni00(1,down,it))));
end
figure
it = 2;
subplot(311)
plot(kz(up),real(Ni00(1,up,it))); hold on
plot(kz(up),real(Ni00(1,down,it)),'--')
ylabel('Real'); title(['$N_i^{00}(t=',num2str(Ts5D(it)),')$'])
subplot(312)
plot(kz(up),imag(Ni00(1,up,it))); hold on
plot(kz(up),-imag(Ni00(1,down,it)),'--')
ylabel('Imag'); xlabel('$kz,kr=0$')
subplot(313)
plot(kz(2:Nkz/2),real(Ni00(1,up,it))-real(Ni00(1,down,it))); hold on
plot(kz(2:Nkz/2),imag(Ni00(1,up,it))+imag(Ni00(1,down,it)),'--')
legend('Re','Im');
ylabel('err'); xlabel('$kz,kr=0$')
%%
figure
semilogy(Ts5D,eps_asym_r); hold on
semilogy(Ts5D,eps_asym_i,'--');
title('$\max_{k_z}|N_i^{00}(0,k_z)-N_i^{00}(0,-k_z)|$');
legend('Re','Im'); grid on; xlabel('$t$')
end
if 0
%% Growth rate
fig = figure; FIGNAME = ['growth_rate',sprintf('_%.2d',JOBNUM)];
[~,ikr0KH] = min(abs(kr-KR0KH));
plot(kz/kr(ikr0KH),gkr0kz_Ni00/(kr(ikr0KH)*A0KH),'DisplayName',['J = ',num2str(JMAXI)])
xlabel('$k_z/k_{r0}$'); ylabel('$\gamma_{Ni}/(A_0k_{r0})$');
xlim([0. 1.0]); ylim([0. 0.6]);
save_figure
end
%%
if 0
%% Mode time evolution
[~,ik00] = min(abs(kz));
[~,idk] = min(abs(kz-dkz));
[~,ik50] = min(abs(kz-0.5*KR0KH));
[~,ik75] = min(abs(kz-0.7*KR0KH));
[~,ik10] = min(abs(kz-1.00*KR0KH));
plt = @(x) abs(squeeze(x));
fig = figure; FIGNAME = ['mode_time_evolution',sprintf('_%.2d',JOBNUM)];
semilogy(Ts2D,plt(Ni00(ikr0KH,ik00,:)),'DisplayName', ...
['$k_z/k_{r0} = $',num2str(kz(ik00)/KR0KH)]); hold on
semilogy(Ts2D,plt(Ni00(ikr0KH,idk,:)),'DisplayName', ...
['$k_z/k_{r0} = $',num2str(kz(idk)/KR0KH)]); hold on
semilogy(Ts2D,plt(Ni00(ikr0KH,ik50,:)),'DisplayName', ...
['$k_z/k_{r0} = $',num2str(kz(ik50)/KR0KH)]); hold on
semilogy(Ts2D,plt(Ni00(ikr0KH,ik75,:)),'DisplayName', ...
['$k_z/k_{r0} = $',num2str(kz(ik75)/KR0KH)]); hold on
semilogy(Ts2D,plt(Ni00(ikr0KH,ik10,:)),'DisplayName', ...
['$k_z/k_{r0} = $',num2str(kz(ik10)/KR0KH)]); hold on
xlabel('$t$'); ylabel('$\hat n_i^{00}$'); legend('show');
semilogy(Ts2D,plt(Ni00(ikr0KH,ik00,end))*exp(gkr0kz_Ni00(ik00)*(Ts2D-Ts2D(end))),'k--')
semilogy(Ts2D,plt(Ni00(ikr0KH,idk,end))*exp(gkr0kz_Ni00(idk)*(Ts2D-Ts2D(end))),'k--')
semilogy(Ts2D,plt(Ni00(ikr0KH,ik50,end))*exp(gkr0kz_Ni00(ik50)*(Ts2D-Ts2D(end))),'k--')
semilogy(Ts2D,plt(Ni00(ikr0KH,ik75,end))*exp(gkr0kz_Ni00(ik75)*(Ts2D-Ts2D(end))),'k--')
semilogy(Ts2D,plt(Ni00(ikr0KH,ik10,end))*exp(gkr0kz_Ni00(ik10)*(Ts2D-Ts2D(end))),'k--')
plot(tstart*[1 1],ylim,'k-','LineWidth',0.5);
plot(tend*[1 1],ylim,'k-','LineWidth',0.5);
save_figure
end
%%
if 0
%% Show frame in kspace
tf = 20; [~,it] = min(abs(Ts5D-tf));
fig = figure; FIGNAME = ['krkz_frame',sprintf('_%.2d',JOBNUM)];
subplot(221); plt = @(x) fftshift((abs(x)),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(PHI(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); title(sprintf('t=%.3d',Ts5D(it))); legend('$|\hat\phi|$');
subplot(222); plt = @(x) fftshift(abs(x),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Ni00(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); title(sprintf('t=%.3d',Ts5D(it))); legend('$|\hat n_i^{00}|$');
subplot(223); plt = @(x) fftshift(abs(x),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Ne00(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); title(sprintf('t=%.3d',Ts5D(it))); legend('$|\hat n_e^{00}|$');
if strcmp(OUTPUTS.write_non_lin,'.true.')
subplot(224); plt = @(x) fftshift((abs(x)),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Si00(:,:,it))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$');legend('$\hat S_i^{00}$');
end
save_figure
end
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