Lecture 3

1. Lecture 3 • Source distributions using SDEF • Point flux tallies using F5 • Tally multipliers using FM

2. X axis of a distribution: SI Syntax: Description: The SIn and SPn cards work together to define a pdf to select a variable from. option= blank or Hhistogram =Ldiscrete =A(x,y) pairs interpolated =Sother distribution #’s

3. Y axis of a distribution: SP • Syntax: • Description: Specification of y axis of pdf for distribution n. • option=blankcompletes SI • =-ppredefined function • The P values are the y-axis values OR the parameters for the desired function p—and the SI numbers are the lower and upper limits • The predefined distribution we will use most often is 21: • SIxxrlowrhigh • SP -21 exponent

4. Examples SI2 H 0 5 20 SP2 0 1 2 … SI3 L 1 2 SP3 1 2 … SI4 A 0 5 20 SP4 0 1 2 … SI5 1 5 SP5 –21 2

5. Source description variables • Commands: • POS=Position of a point of interest • RAD=How to choose radial point • AXS=Direction vector of an axis • EXT=How to choose point along a vector • X,Y,Z=How to choose (x,y,z) dimensions • VEC=Vector of interest • DIR=Direction cosine vs. VEC vector • Combinations: • X,Y,Z: Cartesian (cuboid) shape • POS, RAD: Spherical shape • POS, RAD, AXS, EXT: Cylindrical shape • VEC,DIR: Direction of particle

6. Volumetric/beam sources • Cuboid sources: • X,Y,Z=How to choose (x,y,z) dimensions • Spherical sources • POS=Position of the sphere center • RAD=How to choose radial point (usually a distribution using -21 2) • Cylindrical sources • POS=Position of base of the cylinder • AXS=Direction vector of an axis • EXT=How to choose point along a vector • RAD=How to choose radial point • Beam source • POS=Position of the source center • VEC=Vector of direction of the beam • DIR=Direction cosine vs. VEC vector (distirbution or just 1.0)

7. Particle crossing tally: F1 • Syntax: • Description: Tally of current integrated over a surface. Prefixing with ‘*’ changes the units—particles to MeV. Like other tallies, the time dependence is inherited from the source—the code doesn’t care.

8. Surface flux tally: F2 • Syntax: • Description: Tally of flux averaged over a surface. Prefixing with ‘*’ changes the units—particles/cm2 to MeV/cm2.

9. Cell flux tally: F4 • Syntax: • Description: Tally of flux averaged over a cell. Prefixing with ‘*’ changes the units—particles/cm2 to MeV/cm2.

10. Point Flux Tally • A point flux tally is a special tally that collects the flux at a point • Now, of course, neither of the flux tallies that we have studied—collision estimates or track length estimates—could possibly be applied to a POINT • This is a very specially designed tally in EVERY source point created and EVERY scattered particle contributes its POTENTIAL for scattering to the point in question

11. Point Flux • The MCNP tally 5 is used to set this up, with syntax: Fx5:n x0 y0 z0 R0 x1 y1 z1 R1 … where: (x0,y0,z0) and (x1,y1,z1) are points where the flux is desired R0 and R1 are the radii around the points where flux contributions will NOT be made • An extra bonus that you get from a point flux tally is that the UNCOLLIDED flux (the contribution from particles that come straight from the source) are separately reported • Also, you can make it into a ring IF you have rotational symmetry

12. Point flux tally: F5 • Syntax: • Description: Tally of flux at a point or ring detector. Prefixing with ‘*’ changes the units—particles/cm2 to MeV/cm2. • The “a” is actually either “x” or “y” or “z” depending on the direction of the axis of the ring • MCNP5 Manual Page: 3-78

13. HW 3.1 • Find the Legendre coefficients for a 2nd order expansion of e-x, -1<x<1 • Create a curve of the approximation vs. the actual curve

14. HW 3.2 • If you have a parallelepiped volumetric isotropic source with a strength of 100 particles/cc/sec and W=20 cm, L=10 cm, H=50 cm: • Find the equivalent surface source if the analyst judges that L is insignificant. • Find the equivalent line source if the analyst judges that W is also insignificant; and • Find the equivalent point source if the analyst judges that H is insignificant as well. • For each of these be sure the source size, placement and strength (in appropriate units) is specified.

15. HW 3.3 For each of the four sources in the previous problem (the original cuboid + the three bulleted approximations) create the source in MCNP and compute the fluxes at the point (500,0,0) using an F5 tally.

16. HW 3.4 • Use the Appendix H data to give me the appropriate source description for an isotropic 1 microCurie Co-60 point source that is 10 years old.  • Use a hand calculation to find the total flux at a distance of 100 cm • Checkyour calculation with an MCNP calculation (within 1% error) using an F5 tally. Assume the source is distributed inside a cylinder of diameter and height of 5 cm (centered on the origin)

17. HW 3.5 • Use an MCNP calculation of a beam impinging on the small water sample to estimate the total cross section of water for 0.1 MeV, 1 MeV, and 10 MeV photons. Compare your answers to the values in Appendix C of the text.