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gyacomo/wk/analysis_2D.m
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analysis_2D.m
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%% Load results
if 0
%%
outfile ='';
outfile ='';
outfile ='';
outfile ='';
outfile ='';
outfile ='';
outfile ='';
BASIC.RESDIR = load_marconi(outfile);
end
%%
% JOBNUM = 0; load_results;
% JOBNUM = 1; load_results;
compile_results
load_params
%% 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';
Si00 = squeeze(Sipj(1,1,:,:,:));
Se00 = squeeze(Sepj(1,1,:,:,:));
%% 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);
KPERP2 = KZ.^2+KR.^2;
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); % Gyrocenter density
ni00 = zeros(Nr,Nz,Ns2D);
np_i = zeros(Nr,Nz,Ns5D); % Ion particle density
si00 = zeros(Nr,Nz,Ns5D);
phi = zeros(Nr,Nz,Ns2D);
drphi = zeros(Nr,Nz,Ns2D);
dr2phi = 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)));
dr2phi(:,:,it)= real(fftshift(ifft2(-KR.^2.*(PH_),Nr,Nz)));
dzphi(:,:,it) = real(fftshift(ifft2(1i*KZ.*(PH_),Nr,Nz)));
end
for it = 1:numel(Ts5D)
[~, it2D] = min(abs(Ts2D-Ts5D(it)));
si00(:,:,it) = real(fftshift(ifft2(squeeze(Si00(:,:,it)),Nr,Nz)));
Np_i = zeros(Nkr,Nkz); % Ion particle density in Fourier space
for ij = 1:Nji
Kn = (KPERP2/2.).^(ij-1) .* exp(-KPERP2/2)/(factorial(ij-1));
Np_i = Np_i + Kn.*squeeze(Nipj(1,ij,:,:,it));
end
np_i(:,:,it) = real(fftshift(ifft2(squeeze(Np_i(:,:)),Nr,Nz)));
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|
GFlux_ri = zeros(1,Ns2D); % Gyrocenter flux Gamma = <ni drphi>
GFlux_zi = zeros(1,Ns2D); % Gyrocenter flux Gamma = <ni dzphi>
GFlux_re = zeros(1,Ns2D); % Gyrocenter flux Gamma = <ne drphi>
GFlux_ze = zeros(1,Ns2D); % Gyrocenter flux Gamma = <ne dzphi>
PFlux_ri = zeros(1,Ns5D); % Particle flux
Ne_norm = zeros(Npe,Nje,Ns5D);% Time evol. of the norm of Napj
Ni_norm = zeros(Npi,Nji,Ns5D);% .
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); %
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))));
GFlux_ri(it) = sum(sum(ni00(:,:,it).*dzphi(:,:,it)))*dr*dz/Lr/Lz;
GFlux_zi(it) = sum(sum(-ni00(:,:,it).*drphi(:,:,it)))*dr*dz/Lr/Lz;
GFlux_re(it) = sum(sum(ne00(:,:,it).*dzphi(:,:,it)))*dr*dz/Lr/Lz;
GFlux_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
[~, it2D] = min(abs(Ts2D-Ts5D(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;
Se_norm(:,:,it)= sum(sum(abs(Sepj(:,:,:,:,it)),3),4)/Nkr/Nkz;
Si_norm(:,:,it)= sum(sum(abs(Sipj(:,:,:,:,it)),3),4)/Nkr/Nkz;
Sne00_norm(it) = sum(sum(abs(Se00(:,:,it))))/Nkr/Nkz;
Sni00_norm(it) = sum(sum(abs(Si00(:,:,it))))/Nkr/Nkz;
% Particle flux
PFlux_ri(it) = sum(sum(np_i(:,:,it).*dzphi(:,:,it2D)))*dr*dz/Lr/Lz;
end
%% Compute growth rate
if NON_LIN == 0
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,:));
end
%% PLOTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
default_plots_options
disp('Plots')
FMT = '.fig';
if 0
%% Time evolutions
fig = figure; FIGNAME = ['t_evolutions',sprintf('_%.2d',JOBNUM)];
set(gcf, 'Position', [100, 100, 900, 800])
subplot(221);
for ip = 1:Npe
for ij = 1:Nje
plt = @(x) squeeze(x(ip,ij,:));
plotname = ['$N_e^{',num2str(Pe(ip)),num2str(Je(ij)),'}$'];
semilogy(Ts5D,plt(Ne_norm),'DisplayName',plotname); hold on;
end
end
grid on; 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 = ['$N_i^{',num2str(Pi(ip)),num2str(Ji(ij)),'}$'];
semilogy(Ts5D,plt(Ni_norm),'DisplayName',plotname); hold on;
end
end
grid on; ylabel('$\sum_{k_r,k_z}|N_i^{pj}|$');
subplot(223)
plot(Ts2D,GFlux_ri,'-','DisplayName','$\Gamma_{ri}$'); hold on;
plot(Ts2D,GFlux_zi,'-','DisplayName','$\Gamma_{zi}$'); hold on;
plot(Ts2D,GFlux_re,'-','DisplayName','$\Gamma_{re}$')
plot(Ts2D,GFlux_ze,'-','DisplayName','$\Gamma_{ze}$')
grid on; xlabel('$t c_s/R$'); ylabel('$\Gamma$'); %legend('show');
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('$t c_s/R$'); ylabel('$\sum_{k_r,k_z}|S_i^{pj}|$'); %legend('show');
suptitle(['$\nu_{',CONAME,'}=$', num2str(NU), ', $\eta_B=$',num2str(ETAB)]);
save_figure
end
if 0
%% Photomaton : real space
% FIELD = ni00; FNAME = 'ni';
% FIELD = ne00; FNAME = 'ne';
FIELD = phi; FNAME = 'phi';
tf = 60; [~,it1] = min(abs(Ts2D-tf));
tf = 120; [~,it2] = min(abs(Ts2D-tf));
tf = 250; [~,it3] = min(abs(Ts2D-tf));
tf = 400; [~,it4] = min(abs(Ts2D-tf));
fig = figure; FIGNAME = [FNAME,'_snaps']; set(gcf, 'Position', [100, 100, 1500, 400])
plt = @(x) x;%./max(max(x));
subplot(141)
DATA = plt(FIELD(:,:,it1));
pclr = pcolor((RR),(ZZ),DATA); set(pclr, 'edgecolor','none');pbaspect([1 1 1])
xlabel('$r/\rho_s$'); ylabel('$z/\rho_s$');set(gca,'ytick',[]);
title(sprintf('$t c_s/R=%.0f$',Ts2D(it1)));
subplot(142)
DATA = plt(FIELD(:,:,it2));
pclr = pcolor((RR),(ZZ),DATA); set(pclr, 'edgecolor','none');pbaspect([1 1 1])
xlabel('$r/\rho_s$');ylabel('$z/\rho_s$'); set(gca,'ytick',[]);
title(sprintf('$t c_s/R=%.0f$',Ts2D(it2)));
subplot(143)
DATA = plt(FIELD(:,:,it3));
pclr = pcolor((RR),(ZZ),DATA); set(pclr, 'edgecolor','none');pbaspect([1 1 1])
xlabel('$r/\rho_s$');ylabel('$z/\rho_s$');set(gca,'ytick',[]);
title(sprintf('$t c_s/R=%.0f$',Ts2D(it3)));
subplot(144)
DATA = plt(FIELD(:,:,it4));
pclr = pcolor((RR),(ZZ),DATA); set(pclr, 'edgecolor','none');pbaspect([1 1 1])
xlabel('$r/\rho_s$');ylabel('$z/\rho_s$'); set(gca,'ytick',[]);
title(sprintf('$t c_s/R=%.0f$',Ts2D(it4)));
% suptitle(['$\',FNAME,'$, $\nu_{',CONAME,'}=$', num2str(NU), ', $\eta_B=$',num2str(ETAB),...
% ', $P=',num2str(PMAXI),'$, $J=',num2str(JMAXI),'$']);
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 = ['ni',sprintf('_%.2d',JOBNUM)]; INTERP = 1;
FIELD = real(ni00); X = RR; Y = ZZ; T = Ts2D;
FIELDNAME = '$n_i$'; XNAME = '$r/\rho_s$'; YNAME = '$z/\rho_s$';
create_gif
end
if 0
%% Density electron
GIFNAME = ['ne',sprintf('_%.2d',JOBNUM)]; INTERP = 1;
FIELD = real(ne00); X = RR; Y = ZZ; T = Ts2D;
FIELDNAME = '$n_e$'; XNAME = '$r/\rho_s$'; YNAME = '$z/\rho_s$';
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 = '$r/\rho_s$'; YNAME = '$z/\rho_s$';
create_gif
end
if 0
%% phi @ z = 0
GIFNAME = ['phi_r0',sprintf('_%.2d',JOBNUM)]; INTERP = 0;
FIELD =(squeeze(real(phi(:,1,:)))); linestyle = '-.';
X = (r); T = Ts2D; YMIN = -1.1; YMAX = 1.1; XMIN = min(r); XMAX = max(r);
FIELDNAME = '$\phi(r=0)$'; XNAME = '$r/\rho_s$';
create_gif_1D
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 = '$k_r\rho_s$'; YNAME = '$k_z\rho_s$';
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 = '$k_r\rho_s$';
create_gif_1D
end
%%
if 1
%% Space time diagramm (fig 11 Ivanov 2020)
fig = figure; FIGNAME = 'space_time_drphi';set(gcf, 'Position', [100, 100, 1200, 400])
subplot(211)
yyaxis left
plot(Ts2D,GFlux_ri); hold on
plot(Ts5D,PFlux_ri,'o');
ylabel('$\Gamma_r$'); grid on
ylim([0,1.1*max(GFlux_ri)]);
yyaxis right
plot(Ts2D,squeeze(mean(max(dr2phi))))
ylabel('$s\sim\langle\partial_r^2\phi\rangle_z$'); grid on
title(['$\eta=',num2str(ETAB),'\quad',...
'\nu_{',CONAME,'}=',num2str(NU),'$'])
legend(['$P=',num2str(PMAXI),'$, $J=',num2str(JMAXI),'$'])
subplot(212)
[TY,TX] = meshgrid(r,Ts2D);
pclr = pcolor(TX,TY,squeeze(mean(drphi(:,:,:),2))'); set(pclr, 'edgecolor','none'); %colorbar;
xlabel('$t c_s/R$'), ylabel('$r/\rho_s$')
legend('$\langle\partial_r \phi\rangle_z$')
save_figure
end
%%
if 0
%% Mode time evolution
[~,ikr ] = min(abs(kr-dkr));
[~,ik00] = min(abs(kz));
[~,idk] = min(abs(kz-dkz));
[~,ik50] = min(abs(kz-0.1*max(kz)));
[~,ik75] = min(abs(kz-0.2*max(kz)));
[~,ik10] = min(abs(kz-0.3*max(kz)));
plt = @(x) abs(squeeze(x));
fig = figure; FIGNAME = ['mode_time_evolution',sprintf('_%.2d',JOBNUM)];
semilogy(Ts2D,plt(Ni00(ikr,ik00,:)),'DisplayName', ...
['$k_z = $',num2str(kz(ik00))]); hold on
semilogy(Ts2D,plt(Ni00(ikr,idk,:)),'DisplayName', ...
['$k_z = $',num2str(kz(idk))]); hold on
semilogy(Ts2D,plt(Ni00(ikr,ik50,:)),'DisplayName', ...
['$k_z = $',num2str(kz(ik50))]); hold on
semilogy(Ts2D,plt(Ni00(ikr,ik75,:)),'DisplayName', ...
['$k_z = $',num2str(kz(ik75))]); hold on
semilogy(Ts2D,plt(Ni00(ikr,ik10,:)),'DisplayName', ...
['$k_z = $',num2str(kz(ik10))]); hold on
xlabel('$t$'); ylabel('$\hat n_i^{00}$'); legend('show');
title(sprintf('$k_r=$ %1.1f',kr(ikr)))
save_figure
end
%%
if 0
%% Show frame in kspace
tf = 300; [~,it2] = min(abs(Ts2D-tf)); [~,it5] = min(abs(Ts5D-tf));
fig = figure; FIGNAME = ['krkz_frame',sprintf('t=%.0f',Ts2D(it2))];set(gcf, 'Position', [100, 100, 700, 600])
subplot(221); plt = @(x) fftshift((abs(x)),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(PHI(:,:,it2))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); title(sprintf('$t c_s/R=%.0f$',Ts2D(it2))); legend('$|\hat\phi|$');
subplot(222); plt = @(x) fftshift(abs(x),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Ni00(:,:,it2))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); legend('$|\hat n_i^{00}|$');
subplot(223); plt = @(x) fftshift(abs(x),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Ne00(:,:,it2))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$'); legend('$|\hat n_e^{00}|$');
subplot(224); plt = @(x) fftshift((abs(x)),2);
pclr = pcolor(fftshift(KR,2),fftshift(KZ,2),plt(Si00(:,:,it5))); set(pclr, 'edgecolor','none'); colorbar;
xlabel('$k_r$'); ylabel('$k_z$');legend('$\hat S_i^{00}$');
save_figure
end
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