Contents

Bremmstrahlung analysis

%--------------------------------------------------------------------------
% See also: Bremsstrahlung, PowerDHe3, NumberOfElectrons,
% BremsstrahlungSantarius
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
%	  Copyright 2017 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------

% Reactor parameters
d = PowerDHe3;
d.tE = 30;      % keV
d.tD = 70;      % keV
d.tHe3 = 100;   % keV
d.nD = 1e20;    % per m3
d.nHe3 = 3e20;  % per m3
Z = [1 2];      % atomic number [D He3]
rPlasma = 0.25; % plasma "average" radius
lPlasma = 2;    % length of separatrix
relection = 0;  % wall reflection coefficient (0-1)
beta = 0.7;    % plasma beta

% Number of electrons
nE = NumberOfElectrons( [d.nD d.nHe3], Z );

fprintf('\nDensity 3He: %g at %g keV\n',d.nHe3,d.tHe3);
fprintf('Density D:   %g at %g keV\n',d.nD,d.tD);
fprintf('Density e-:  %g at %g keV\n',nE,d.tE);

% Estimated reactor power
volume = 2/3*pi*rPlasma^2*lPlasma;
[pF, pN, pB] = PowerDHe3( d );

% Point bremsstrahlung powers (per m3)
pNRL = Bremsstrahlung( [d.nD d.nHe3], Z, d.tE, 1 )
pTeller = Bremsstrahlung( [d.nD d.nHe3], Z, d.tE, 2 )
%pNRL = BremsstrahlungNRL( nE, d.nD, d.nHe3, d.tE ) % now in Bremsstrahlung
pSant = BremsstrahlungSantarius( nE, d.nD, d.nHe3, d.tE )

fprintf('\nFusion power: %f MW\n',pF*volume);
fprintf('    Plasma radius: %g m\n',rPlasma);
fprintf('    Plasma length: %g m\n',lPlasma);
%fprintf('Bremsstrahlung, Bingren: %f MW\n',pBingren*volume);
fprintf('Bremsstrahlung, NRL: %f MW\n',pNRL*volume);
fprintf('Bremsstrahlung, Teller: %f MW\n',pTeller*volume);

fprintf('Santarius:  %.1f%% \n',pSant/pF*100);
fprintf('Teller:   %.1f %%\n',pTeller/pF*100);
fprintf('NRL:      %.1f %%\n',pNRL/pF*100);

Density 3He: 3e+20 at 100 keV
Density D:   1e+20 at 70 keV
Density e-:  7e+20 at 30 keV
pNRL =
       2.6637
pTeller =
       3.0588
pSant =
       3.0801

Fusion power: 4.025413 MW
    Plasma radius: 0.25 m
    Plasma length: 2 m
Bremsstrahlung, NRL: 0.697361 MW
Bremsstrahlung, Teller: 0.800784 MW
Santarius:  20.0% 
Teller:   19.9 %
NRL:      17.3 %

Survey plot

rho = [1 3 5];
Te = linspace(20,100,20);
Pbingren = zeros(3,20);
Pteller = zeros(3,20);
Pnrl = zeros(3,20);
for k = 1:length(rho)
  nD = 1/3*rho(k)*1e20;
  nHe3 = rho(k)*1e20;
  nE2 = NumberOfElectrons( [nD nHe3], Z );
  for j = 1:length(Te)
    Pnrl(k,j) = Bremsstrahlung( [nD nHe3], Z, Te(j), 1 );
    Pteller(k,j) = Bremsstrahlung( [nD nHe3], Z, Te(j), 2 );
    %Pnrl(k,j) = BremsstrahlungNRL( nE2, nD, nHe3, Te(j) );
  end
end

[~,l1] = Plot2D(Te,Pnrl,'Electron Temperature (keV)','Bremsstrahlung (MW/m^3)',...
          'Model Comparison');
hold on;
l2 = plot(Te,Pteller,'--');
%plot(d.tE,[Pteller;pNRL],'k.')

text(50,1,'nHe3 = 1e20')
text(40,4,'nHe3 = 3e20')
text(30,9,'nHe3 = 5e20')

legend([l1.h(1);l2(1)],'NRL','Teller')

% Te is keV, n in /m3
function p = BremsstrahlungNRL( nE, nD, nHe3, Te )

p = 1.69e-32*nE*1e-6*sqrt(Te*1e3)*(nD+4*nHe3)*1e-6;

end

% Te is keV, n in /m3
function p = BremsstrahlungSantarius( nE, nD, nHe3, tE )

nI = [nD nHe3];
zI = [1 2];
zEff  = sum(nI.*zI.^2)/nE;
zEffC = sum(nI.*zI.^3)/nE;

h = 1 + 0.00155*tE + 7.15e-6*tE^2;
p = 5.4e-43*nE^2*sqrt(tE)*(0.00414*tE + 0.07*zEffC/sqrt(tE) + zEff*h);

end


%--------------------------------------

Published with MATLAB® R2020a