Contents

Synchrotron radiation demo

Reproduce the chart in the reference.

%--------------------------------------------------------------------------
% Reference: Bing-Ren, S. "Possibility of Establishing D-3He Fusion Reactor
% Using Spherical Tokamaks", Chinese Physics Letters, 2004
%--------------------------------------------------------------------------
% See also MaxwellianV, PowerDHe3, Synchrotron, Plot2D
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
%   Copyright (c) 2018 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------

T = linspace(0,140);
nI = [1e20 1e20]/3;
zI = [1 2];
b  = 2.7; % T
L  = 2.5; % m

rW = 0;
p0 = Synchrotron( nI, zI, b, T, L, rW);

rW = 0.9;
p9 = Synchrotron( nI, zI, b, T, L, rW);

d = PowerDHe3;
d.nD = nI(1);
d.nHe3 = nI(2);
d.fT = 0;
d.fD = 0;

Pf = [];
PB = [];
for k = 1:length(T)
  d.tHe3 = T(k);
  d.tD = T(k);
  d.tE = T(k);
  [Pf(k),~,PB(k)] = PowerDHe3(d);
end

% Reaction Rates
sV = MaxwellianV( 'D', 'He3', T );

% Note: cannot exactly reproduce the fusion power curve in the reference.
% The reaction rate equation below seems to be off
gamma = 0.36031698;
a1 = -27.7319978;
a2 = -31.058052;
a3 = 0.027991287;
a4 = -5.3895197e-4;
a5 = -2.6589549e-6;
sigV = exp(a1./(T.^gamma) + a2 + a3*T + a4*T.^2 + a5*T.^3);
Pf2 = 2.93e22*nI(1)*nI(2)*1e-40*sigV;

T10 = T/10;
Plot2D(T10,[Pf;p0;p9;PB],'Temperature (10keV)','Power (MW/m3)','5 m Reactor');
legend('Pfus','Psyn0','Psyn9','Pbr')

Now repeat for a smaller reactor

Assume Te is only a fraction of Ti

L  = 0.2; % m
b  = 5;   % T
T = linspace(0,100);

rW = 0;
p0 = Synchrotron( nI, zI, b, T, L, rW);

rW = 0.9;
p9 = Synchrotron( nI, zI, b, T, L, rW);

d = PowerDHe3;
d.nD = nI(1);
d.nHe3 = nI(2);
d.fT = 0;
d.fD = 0;

Pf = [];
PB = [];
for k = 1:length(T)
  d.tHe3 = T(k);
  d.tD = T(k);
  d.tE = T(k);
  [Pf(k),~,PB(k)] = PowerDHe3(d);
end

Plot2D(T10,[Pf;p0;p9;PB],'Temperature (10keV)','Power (MW/m3)','0.25 m Reactor');
legend('Pfus','Psyn0','Psyn9','Pbr')


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

Published with MATLAB® R2020a