Synchrotron analysis

Compare Bingren's model with the NRL formulary for PFRC relevant parameters

%--------------------------------------------------------------------------
% See also: PowerDHe3, NumberOfElectrons, PlasmaConstant, BField,
% Synchrotron
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
%   Copyright (c) 2016 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
reflection = 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);

% Estimate magnetic field
c = PlasmaConstant('kev/m^3 to pa');
p = c*(nE*d.tE + d.nHe3*d.tHe3 + d.nD*d.tD);
b = BField( p, beta );
fprintf('Estimated field: %.1f T for beta of %.2f\n',b,beta);

% Bingren's model
pBingren = Synchrotron( [d.nD d.nHe3], Z, b, d.tE, rPlasma, reflection );
alpha = 1.15;
%1.262e-4*alpha*sqrt(nE*(1-reflection)*(0.1*tE*b).^5/rPlasma)

% Bingren's paper: should be in range 0.05to 0.25 MW/m3
Synchrotron( [1 1]/3*1e20, [1 2], 2.7, 20, 2.5, 0 )
Synchrotron( [1 1]/3*1e20, [1 2], 2.7, 50, 2.5, 0 )
Synchrotron( [1 1]/3*1e20, [1 2], 2.7, 90, 2.5, 0 )

% NRL Formulary - use CGS units
% "cyclotron" radiation
% assume only 10% of the volume is emitting for this relation
Pc = 6.21e-28*(b*1e4)^2*nE*1e-6*d.tE*1e3;
fracC = 0.1;

% isothermal plasma (beta = 1)
Pi = 5e-38*(nE*1e-6)^2*(d.tE*1e3)^2;
fracI = 0.1;

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

fprintf('\nFusion power: %f MW\n',pF*volume);
fprintf('    Plasma radius: %g m\n',rPlasma);
fprintf('    Plasma length: %g m\n',lPlasma);
fprintf('Synchrotron, Bingren: %f MW\n',pBingren*volume);
fprintf('Synchrotron, NRL: %f MW\n',Pc*volume*fracC);
fprintf('Synchrotron, Iso: %f MW\n',Pi*volume*fracI);

fprintf('Bingren:           %.1f%% \n',pBingren/pF*100);
fprintf('Isothermal @ 10%%: %.1f %%\n',Pi*fracI/pF*100);
fprintf('NRL @ 10%%:        %.1f %%\n',Pc*fracC/pF*100);


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

Density 3He: 3e+20 at 100 keV
Density D:   1e+20 at 70 keV
Density e-:  7e+20 at 30 keV
Estimated field: 5.8 T for beta of 0.70
Power (MW/m^3) =     0.005953 at Temperature (10 keV) =            2
Power (MW/m^3) =      0.06738 at Temperature (10 keV) =            5
Power (MW/m^3) =       0.3469 at Temperature (10 keV) =            9

Fusion power: 4.025413 MW
    Plasma radius: 0.25 m
    Plasma length: 2 m
Synchrotron, Bingren: 0.251858 MW
Synchrotron, NRL: 1.138935 MW
Synchrotron, Iso: 0.577268 MW
Bingren:           6.3% 
Isothermal @ 10%: 14.3 %
NRL @ 10%:        28.3 %

Published with MATLAB® R2020a