Generates a point design for a D-He3 engine.
Includes Bremsstrahlung and synchrotron but not transport.
See also: FusionPower, CentralPressure, VolumeAveragedPressure, BField, Synchrotron, Bremsstrahlung, PlasmaRadius, PlasmaVolume, FirstWallThermalPower, NumberOfElectrons, MagnetMass, PlasmaInternalEnergy
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Reference: Schaffer, M.J., "Considerations for Steady-State FRC-Based Fusion Space Propulsion", GA-A23579, December 2000. General Atomics, San Diego, CA
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%-------------------------------------------------------------------------- % Copyright (c) 2011 Princeton Satellite Systems, Inc. % All rights reserved. % 2021.2 fix order of inputs to Synchrotron %-------------------------------------------------------------------------- % Global parameters %------------------ pFusion = 6160; %(MW) beta = 1; rhoMag = 4300; % Titanium (kg/m^3) sigmaMag = 880e6; % Titanium rW = 0.998; % wall reflectivity % D-He3 %----- zDH = [1 2]; n1DH = 6.15e20; n2DH = 6.15e20; nIDH = [n1DH n2DH]; r1DH = 'd'; r2DH = 'he3'; tDH = 100; pFusDH = FusionPower( n1DH, n2DH, r1DH, r2DH, tDH ); pCDH = CentralPressure( tDH, [n1DH n2DH], zDH ); pVDH = VolumeAveragedPressure( tDH, [n1DH n2DH], zDH ); bDH = BField( pVDH, beta ); pSDH = Synchrotron( nIDH, zDH, bDH, tDH, 2, rW); pBDH = Bremsstrahlung( nIDH, zDH, tDH, 2 ); pNetDH = pFusDH - pSDH - pBDH; rPDH = PlasmaRadius( pNetDH, pFusion ); vPDH = PlasmaVolume( pNetDH, pFusion ); pWallDH = FirstWallThermalPower( (pSDH+pBDH)*vPDH, 1.1*rPDH ); nEDH = NumberOfElectrons( nIDH, zDH ); mMDH = MagnetMass( rhoMag, sigmaMag, bDH, rPDH); iEDH = PlasmaInternalEnergy( sum(nIDH), tDH, vPDH ); %Table s = {}; k = 1; s{k,1} = 'Fuel, Assumed'; s{k,2} = '50/50 D$^3$He'; s{k,3} = '50/50 D$^3$He'; k = k + 1; s{k,1} = 'First Wall Thermal Power (MW m$^{-2}$)'; s{k,2} = '10'; s{k,3} = sprintf('%4.1f',pWallDH); k = k + 1; s{k,1} = 'Plasma Radius (m)'; s{k,2} = '3.45'; s{k,3} = sprintf('%4.2f',rPDH); k = k + 1; s{k,1} = 'Plasma Volume (m$^3$)'; s{k,2} = '172'; s{k,3} = sprintf('%4.0f',vPDH); k = k + 1; s{k,1} = 'RMS Plasma Pressure (Pa)'; s{k,2} = '2.5e+07'; s{k,3} = sprintf('%5.1e',pVDH); k = k + 1; s{k,1} = 'Central Plasma Pressure (Pa)'; s{k,2} = '4.9e+07'; s{k,3} = sprintf('%5.1e',pCDH); k = k + 1; s{k,1} = 'Plasma Internal Energy (GJ)'; s{k,2} = '6.45'; s{k,3} = sprintf('%4.2f',iEDH); k = k + 1; s{k,1} = '$\beta$'; s{k,2} = '1'; s{k,3} = sprintf('%4.0f',beta); s{k,1} = 'Average Magnetic Field at Coil (T)'; s{k,2} = '7.9'; s{k,3} = sprintf('%4.1f',bDH); k = k + 1; s{k,1} = 'Magnet Specific Mass (kg/W)'; s{k,2} = '1.9e-05'; s{k,3} = sprintf('%6.1e',1e-6*mMDH/pFusion); k = k + 1; s{k,1} = 'Magnet Mass (kg)'; s{k,2} = '1.52e+05'; s{k,3} = sprintf('%5.2e',mMDH); k = k + 1; s{k,1} = 'Shield \& Magnet Mass (kg)'; s{k,2} = '500000'; s{k,3} = '473670'; k = k + 1; s{k,1} = 'Central Temperature (keV)'; s{k,2} = '100'; s{k,3} = sprintf('%4.0f',tDH); k = k + 1; s{k,1} = 'Ion Density 10$^{20}$ m$^{-3}$)'; s{k,2} = '12.3'; s{k,3} = sprintf('%4.1f',sum(nIDH)/1e20); k = k + 1; s{k,1} = 'Electron Density ( 10$^{20}$ m$^{-3}$)'; s{k,2} = '18.4'; s{k,3} = sprintf('%4.1f',nEDH/1e20); k = k + 1; s{k,1} = 'Synchrotron (MW m$^{-3}$)'; s{k,2} = '0.0'; s{k,3} = sprintf('%4.2f', pSDH); k = k + 1; s{k,1} = 'Bremsstrahlung (MW m$^{-3}$)'; s{k,2} = sprintf('%4.1f',0.23*8000/172); s{k,3} = sprintf('%4.2f',pBDH); k = k + 1; s{k,1} = 'Fusion Power (GW)'; s{k,2} = '8.0'; s{k,3} = sprintf('%4.1f',pFusDH*vPDH/1e3);k = k + 1; s{k,1} = 'Net Power (GW)'; s{k,2} = sprintf('%4.1f',8*0.77); s{k,3} = sprintf('%4.1f',pNetDH*vPDH/1e3); fprintf(1,'\n\n'); for k = 1:size(s,1) fprintf(1,'%60s %20s %20s \n',s{k,:}) end CreateLatexTable(s,'PointDesignTable' ); % PSS internal file version information %--------------------------------------
Fuel, Assumed 50/50 D$^3$He 50/50 D$^3$He
First Wall Thermal Power (MW m$^{-2}$) 10 31.5
Plasma Radius (m) 3.45 2.45
Plasma Volume (m$^3$) 172 61
RMS Plasma Pressure (Pa) 2.5e+07 2.5e+07
Central Plasma Pressure (Pa) 4.9e+07 4.9e+07
Plasma Internal Energy (GJ) 6.45 1812086813.44
Average Magnetic Field at Coil (T) 7.9 7.9
Magnet Specific Mass (kg/W) 1.9e-05 1.8e-06
Magnet Mass (kg) 1.52e+05 1.11e+04
Shield \& Magnet Mass (kg) 500000 473670
Central Temperature (keV) 100 100
Ion Density 10$^{20}$ m$^{-3}$) 12.3 12.3
Electron Density ( 10$^{20}$ m$^{-3}$) 18.4 18.4
Synchrotron (MW m$^{-3}$) 0.0 1.46
Bremsstrahlung (MW m$^{-3}$) 10.7 45.25
Fusion Power (GW) 8.0 9.0
Net Power (GW) 6.2 6.2