Patent ID: 8117013

Claim:
A computer-implemented method for calculating a transport of a high-energy neutron/ion transport flux to a target of interest within a shielded region, comprising: defining boundaries for the transport of the high-energy neutron/ion transport flux to the target of interest within the shielded region; receiving, as input, at least one of shielding dimensions, identification of shielding materials, high-energy neutron/ion flux at the boundaries, and a spatial location for the target of interest; calculating the transport of the high-energy neutron/ion transport flux to the target of interest via the equation ψ j ( x+h,r )=exp[−ζ j ( r,h )]ψ j ( x,r+v j h )+Σ k ( v j /v k )σ jk ( r+v j h/ 2)ψ k [x,r +( v j +v k ) h/ 2]×∫ 0 h exp{−σ j ( r+v j h/ 2) x′−σ k [r+ ( v j +v k ) h/ 2)( h−x ′)]}) dx ′=exp[−ζ j ( r,h )]ψ j ( x,r+v j h )+Σ k ( v j /v k )σ jk ( r+v j h/2)ψ k [x,r+ (v j +v k ) h/ 2]×[exp{−σ j ( r+v j h/ 2) h }−exp{−σ k [r+ ( v j +v k ) h/ 2 ]h}]/{σ k [r +( v j +v k ) h/ 2)]−σ j ( r+v j h/ 2)}+ O ( h 2 ) wherein ψ j (x+h,r) and ψ k (x+h,r) are scaled fluxes for j-particles and k-particles at an end of a subinterval computational point, ζ j and ζ k are high-energy neutron/ion fluxes at the boundaries, x and h are spatial coordinates, r is a single residual range coordinate, v j and v k are scaling factors associated with j-particles and k-particles, respectively, and σ j and σ k are cross-sections for the j-particles and k-particles, respectively; wherein, when calculating the high-energy neutron/ion transport flux to the target of interest, propagated error for values calculated by the computer implemented numerical method is controlled by controlling truncation error as a third order in step size; wherein, when calculating the high-energy neutron/ion transport flux to the target of interest, the scaling factors are added to adjust for behavior associated with production of j-particles from collisions of k-particles; and wherein, when calculating the high-energy neutron/ion transport flux to the target of interest, the single residual range coordinate is introduced for all neutrons/ions in the computer implemented numerical method.