tests for kperp scan

matlab/MOLI_kperp_scan.m

+%% Move to MOLI workspace
+cd ../../MoliSolver/MOLI/workspace/
+%% Add paths
+my_paths
+
+%% Directories
+ROOT = '/home/ahoffman/Documents/MoliSolver';
+options.dirs.COSOlverdir = fullfile(ROOT,'COSOlver');
+options.dirs.MOLIdir = fullfile(ROOT,'MOLI');
+
+%% MOLI Physical and Main Parameters
+
+% Solve DK AND/OR GK Linear Moment Hierarchy.
+options.DKI  = 0;   % First-order DK
+options.DKII = 0;   % Second-order DK
+options.GK   = 1;   % Gyrokinetic GK
+options.EM   = 0;   % Include Electromagnetic effects (only for GK=1)
+options.GD   = 0;   % Gyro-Drift
+options.GDI  = 0;   % First/second order
+
+% Solve MOLI
+options.MOLI = 1;    % 1 -> Solve MOLI, 0 -> off
+
+% MOLI Solver
+options.solver.solver = 2;
+
+% MOLI Linear Fit Solver
+options.LinFitSolver = 0;
+
+%% Main parameter scan
+
+% Closure by truncation
+params.Pmaxi = GRID.pmaxi;           % parallel ion Hermite moments
+params.Jmaxi = GRID.jmaxi;           % perpendicular ion Laguerre moments
+params.Pmaxe = GRID.pmaxe;           % parallel electron Hermite moments
+params.Jmaxe = GRID.jmaxe;           % perpendicular electron Laguerre moments
+
+% w/wo ions
+options.ions = 1;           % if ions are present -> 1, 0 otherwise
+
+% Adiabatic electrons
+options.electrons = 1;      % 0 ->  adiabatic electrons, 1 no adiabatic electrons
+
+% w/wo soundwaves
+options.sw = 1;             % 1 -> sound waves on, 0 -> put ion parallel velocity row/column to 0
+
+%% Collision Operator Models and COSOlver Input Parameters
+options.collI  = MODEL.CO;         % collI=-2 -> Dougherty, -1 -> COSOlver, 0 -> Lenard-Bernstein, other -> hyperviscosity exponent
+options.collGK = 0;         % collDKGK =1 -> GK collision operator, else DK collision operator
+options.COSOlver.GKE = 0;
+options.COSOlver.GKI = 0;
+
+% COSOlver Input Parameters (if collI = -1 only)
+options.COSOlver.eecolls = 1;	   % 1 -> electron-electron collisions, 0 -> off
+options.COSOlver.iicolls = 1;      % 1 -> ion-ion collisions, 0 -> off
+options.COSOlver.eicolls = 1;      % 1 -> electron-ion collisions (e-i) on, 0 -> off
+options.COSOlver.iecolls = 1;      % 1 -> ion-electron collisions (i-e) on, 0 -> off
+
+% Collisional Coulomb sum bounds (only if collI = -1, i.e. Coulomb)
+options.COSOlver.lmaxx = 10;                        % upper bound collision operator first sum first species
+options.COSOlver.kmaxx = 10;                        % upper bound collision operator second sum first species
+options.COSOlver.nmaxx = options.COSOlver.lmaxx;    % upper bound collision operator first sum second species
+options.COSOlver.qmaxx = options.COSOlver.kmaxx;    % upper bound collision operator second sum second species
+
+% Collsion FLR sum bounds
+options.COSOlver.nemaxxFLR = 0;         % upper bound FLR electron collision
+options.COSOlver.nimaxxFLR = 0;         % upper bound FLR ion collision
+
+% Collision Operator Model
+% Set electron/ion test and back-reaction model operator
+%
+%  0 => Coulomb Collisions
+options.COSOlver.ETEST = 1; % 0 --> Buffer Operator, 1 --> Coulomb, 2 --> Lorentz
+options.COSOlver.EBACK = 1;
+options.COSOlver.ITEST = 1;
+options.COSOlver.IBACK = 1;
+options.COSOlver.ESELF = 1;
+options.COSOlver.ISELF = 1;
+
+options.COSOlver.OVERWRITE = 0;    % overwrite collisional matrices even if exists
+
+options.COSOlver.cmd   = 'mpirun -np 6 ./bin/CO 2 2 2';
+%% Physical Parameters
+
+% Toroidal effects
+options.magnetic        = 1;           % 1-> Add toroidal magnetic gradient drift resonance effects
+
+% Physical Parameters
+params.tau              = MODEL.tau_i; % Ti/Te
+params.nu               = MODEL.nu;    % electron/ion collision frequency ... only for nu/ omega_pe < nuoveromegapemax (electron plasma frequency) [See Banks et al. (2017)]
+params.nuoveromegapemax = inf;         % Maximum ratio between electron/ion collision frequency and electron plasma frequency [See Banks et al. (2017)]. Set to inf if not desired !!!
+params.mu               = MODEL.sigma_e;   % sqrt(m_e/m_i)
+params.kpar             = 0.0;         % normalized parallel wave number to the major radius
+params.kperp            = GRID.kzmin;  % normalized perpendicular wave number to the soundLarmor radius. Note: If ions ==0 (e.g. EPW), kperp --> b
+params.alphaD           = 0.0;         % (k*Debye length)^2
+params.Rn               = MODEL.eta_n; % Major Radius / Background density gradient length
+params.RTe              = MODEL.eta_T; % Major Radius * normalized kperp / Background electron temperature gradient length
+params.RTi              = MODEL.eta_T; % Major Radius * normalized kperp / Background ion temperature gradient length
+params.Rphi             = 0.0;         % Major Radius * normalized kperp / Background potentiel gradient length [presence of shear] - only for GK
+params.betae            = 1e-6;        % Electron Beta plasma.
+
+params.rhostar          = 1e-5;        % sound Larmor Radius/Major Radius ~ sqrt(Te)/(R_0*B).
+params.n0               = INITIAL.initback_moments;        % initial density perturbation
+
+params.gradB            = MODEL.eta_B;         % Magnetic field gradient
+params.curvB            = MODEL.eta_B;         % Curvature of B
+params.trappB           = 0.0;         % Trapping term
+
+%% MOLI Options
+
+% Save data in results dir
+options.save    = 0;
+options.verbose = 0;
+options.dbg     = 0;
+
+options.DR        = 0;      % 1 -> Solve kinetic dispersion relation,
+options.KineticDR = 0;      % Solve kinetic dispersion relation (Landau integral) for the given theory
+
+% Compute the kinetic susceptibility for EPW only
+options.SPTBLTY = 0;
+
+options.nharm   = 1;        % Number of harmonics in disp. rel. 1 and 4
+
+wlim = 5.0;
+options.DRsolver.wr_min = -wlim;     % Minimum of real part.
+options.DRsolver.wr_max =  wlim;     % Maximum of real part.
+options.DRsolver.wi_min = -wlim;     % Minimum of imag part.
+options.DRsolver.wi_max =  wlim;     % Maximum of imag part.
+options.DRsolver.nw     =  300;      % Grid resolution
+
+% Disp. Rel. Options
+options.FLRmodel    = 0;   % 1 -> Truncated Laguerre, 0 -> Exact representation
+options.FluidLandau = 0;   % 1 -> Add Landau Fluid Closure to Fluid Dispersion Relation, 0 -> off
+options.deltaLandau = 0;   % 1 -> Hammet-Perkins closure on, 0 -> off
+
+% Fluid dispersion relation
+options.FluidDR = 0;	     % Solve annamaria's fluid equations
+options.Fluid.sITGmm = 0;
+
+% Define scan parameters
+options.fscan = 1;         % 1 -> peform scan over scan.list, 0-> off
+
+options.scan.list = {'kperp'};% List of scan parameters. If empty, solve MOLI with params
+
+options.scan.kperp.array  = linspace(GRID.kzmin, GRID.kzmax, GRID.nkz);
+
+% Time-Evolution Problem [Solver==3] ...
+options.solver.TimeSolver.dt         = BASIC.dt;		% timestep of time evolution (R/c_s or 1/(k v/the) units)
+options.solver.TimeSolver.tmax       = BASIC.tmax;
+options.solver.TimeSolver.Trun       = BASIC.tmax;		  % total time to run time evolution
+options.solver.TimeSolver.t_fit_min  = 0.05;    % Phase-Mixing fit Lower time limit
+options.solver.TimeSolver.t_fit_max  = 8;       % Phase-Mixing fit Upper time limit
+options.solver.TimeSolver.en_fit_min = 0.15;    % Entropy Mode fit Lower time limit
+options.solver.TimeSolver.en_fit_max = 0.3;     % Entropy Mode fit Upper time limit
+options.solver.TimeSolver.movie      = 0;       % Display movie if 1, last frame otherwise
+options.solver.TimeSolver.save       = 0;       % 1 --> save during fscan, Warning: memory storage
+
+
+%% Run MOLI
+% Solve the MOLI
+[results,params,options] = MOLI_Control(params,options);
+
+%% Return to HeLaZ workspace
+cd ../../../HeLaZ/wk

wk/benchmark_kperp_scan.m

+SIMID = 'benchmark_kperp_scan'; % Name of the simulations
+addpath(genpath('../matlab')) % ... add 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% outputs options
+OUTPUTS.nsave_0d = 0;
+OUTPUTS.nsave_1d = 0;
+OUTPUTS.nsave_2d = 1;
+OUTPUTS.nsave_5d = 0;
+OUTPUTS.write_Ni00    = '.true.';
+OUTPUTS.write_moments = '.true.';
+OUTPUTS.write_phi     = '.true.';
+OUTPUTS.write_doubleprecision = '.true.';
+OUTPUTS.resfile0      = '''results''';
+%% Grid parameters
+GRID.pmaxe = 15;
+GRID.jmaxe = 6;
+GRID.pmaxi = 15;
+GRID.jmaxi = 6;
+GRID.nkr   = 1;
+GRID.krmin = 0.;
+GRID.krmax = 0.;
+GRID.nkz   = 20;
+GRID.kzmin = 0.1;
+GRID.kzmax = 1.5;
+%% Model parameters
+MODEL.CO      = -2;  % Collision operator (0 : L.Bernstein, -1 : Full Coulomb, -2 : Dougherty)
+MODEL.nu      = 0.1; % collisionality nu*L_perp/Cs0
+% temperature ratio T_a/T_e
+MODEL.tau_e   = 1.0;
+MODEL.tau_i   = 1.0;
+% mass ratio sqrt(m_a/m_i)
+MODEL.sigma_e = 0.0233380;
+MODEL.sigma_i = 1.0;
+% charge q_a/e
+MODEL.q_e     =-1.0;
+MODEL.q_i     = 1.0;
+% gradients L_perp/L_x
+MODEL.eta_n   = 1.0;        % Density
+MODEL.eta_T   = 0.0;        % Temperature
+MODEL.eta_B   = 0.5;        % Magnetic
+% Debye length
+MODEL.lambdaD = 0.0;
+%% Time integration and intialization parameters
+TIME_INTEGRATION.numerical_scheme  = '''RK4''';
+BASIC.nrun                = 100000;
+BASIC.dt                  = 0.05;
+BASIC.tmax                = 100.0;
+INITIAL.initback_moments  = 0.01;
+INITIAL.initnoise_moments = 0.;
+INITIAL.iseed             = 42;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Write input file
+INPUT = write_fort90(OUTPUTS,GRID,MODEL,INITIAL,TIME_INTEGRATION,BASIC);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Run HeLaZ
+nproc = 1;
+EXEC  = ' ../bin/helaz ';
+RUN   = ['mpirun -np ' num2str(nproc)];
+CMD   = [RUN, EXEC, INPUT];
+system(CMD);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Run MOLI with same input parameters
+params.RK4 = 1;
+run ../matlab/MOLI_kperp_scan
+if params.RK4; MOLIsolvername = 'RK4';
+else;          MOLIsolvername = 'ode15i';
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Analysis and basic figures
+SAVEFIG = 1;
+filename = 'results_00.h5';
+
+if     MODEL.CO == -1; CONAME = 'FC';
+elseif MODEL.CO == -2; CONAME = 'DC';
+elseif MODEL.CO ==  0; CONAME = 'LB'; end;
+
+TITLE  = [];
+TITLE = [TITLE,'$\eta_n=',num2str(MODEL.eta_n),'$, '];
+TITLE = [TITLE,'$\eta_B=',num2str(MODEL.eta_B),'$, '];
+TITLE = [TITLE,'$\eta_T=',num2str(MODEL.eta_T),'$, '];
+TITLE = [TITLE,   '$\nu=',num2str(MODEL.nu),'$, '];
+TITLE = [TITLE, '$(P,J)=(',num2str(GRID.pmaxe),',',num2str(GRID.jmaxe),')$'];
+
+%% Growth rate analysis
+gammas = zeros(numel(kr),numel(kz));
+shifts = zeros(numel(kr),numel(kz));
+
+moment = 'Ni00';
+
+kr       = h5read(filename,['/data/var2d/' moment '/coordkr']);
+kz       = h5read(filename,['/data/var2d/' moment '/coordkz']);
+timeNi   = h5read(filename,'/data/var2d/time');
+Nipj     = zeros(numel(timeNi),numel(kr),numel(kz));
+
+for it = 1:numel(timeNi)
+    tmp          = h5read(filename,['/data/var2d/', moment,'/', num2str(it,'%06d')]);
+    Nipj(it,:,:) = tmp.real + 1i * tmp.imaginary; 
+end
+
+% Linear fit of log(Napj)
+x1    = timeNi;
+itmin = ceil(0.5 * numel(timeNi)); %Take the second half of the time evolution
+ikr   = 1;
+
+for ikz = 1:numel(kz)
+    fit = polyfit(x1(itmin:end),log(abs(Nipj(itmin:end,ikr,ikz))),1);
+    gammas(ikr,ikz) = fit(1);
+    shifts(ikr,ikz) = fit(2);
+end
+
+%% Plot
+fig = figure;
+
+%HeLaZ results
+X = kz*sqrt(1+MODEL.tau_i);
+Y = gammas(1,:);
+plot(X,Y,'-','DisplayName','HeLaZ')
+hold on
+
+%MOLI results
+X = kz*sqrt(1+MODEL.tau_i);
+Y = results.kperp.Maxgammas;
+plot(X,Y,'--','DisplayName','MOLI');
+title(TITLE);
+grid on
+legend('show')
+xlabel('$k_\perp * (1+\tau)^{1/2}$')
+ylabel('$\gamma L_\perp/c_{s} $')
+if SAVEFIG; FIGNAME = 'g_vs_kz'; save_figure; end;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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