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P HI T S

P HI T S. Multi-Purpose P article and H eavy I on T ransport code S ystem. Advanced Lecture (II): variance reduction techniques to improve efficiency of calculation. May. 2013 revised. title. 1. Contents of Lecture. 1. Introduction. 2. Neutron deep penetration calculation.

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P HI T S

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  1. PHITS Multi-Purpose Particle and Heavy Ion Transport code System Advanced Lecture (II): variance reduction techniques to improve efficiency of calculation May. 2013 revised title 1

  2. Contents of Lecture 1.Introduction 2.Neutron deep penetration calculation • [importance] Geometry splitting and Russian Roulette • [weight window] Weight windows 3.Calculation of particleproduction in thin target • [forced collision]

  3. Neutron deep penetration calculation Calculate neutron transport in thick shield and dose rate distribution to depth maxcas = 10000 maxbch = 2 Number of history = 20000 imp.inp 14 MeV neutron with 1 cm radius Concrete 50cm radius x 3 m thick cylinder Air

  4. Neutron deep penetration calculation Normal calculation using a single CPU 2.83GHz, Single Number of history= 2x104 total cpu time = 53.66 sec Normal calculation using 31 CPUs 2.83GHz, 31 CPUs Number of history= 1.3x109 total cpu time = about 6 hours Need to improve the efficiency of Monte Carlo simulation! Use variance reduction techniques

  5. Concept of weight in Monte Carlo calculation Example:track length tally Weight: Importance of the particle in Monte Carlo simulation always to be 1 for normal calculation Merit of controlling weight • Artificially increase the probability of rare event occurrences • Kill events that are not so important Demerit of controlling weight • Inadequate weight control induces wrong simulation results • Frequency distribution per a history cannot be calculated, e.g. [t-deposit] with output = deposit, NO MORE event generator!

  6. Contents of Lecture 1.Introduction 2.Neutron deep penetration calculation • [importance] Geometry splitting and Russian Roulette • [weight window] Weight windows 3.Calculation of particleproduction in thin target • [forced collision]

  7. Cell Importance Method Set important I to each cell. When a particle passes through the boarder of cell 1 and cell 2, multiple its weight by I1/I2 • For I1< I2, split the particle into I2/I1, and multiple its weight by I1/I2 e.g.1I2/I1 = 3 (integer) • Always split into 3 • Weights of all split particles are 1/3 I1=1 I2=3 W=1/3 W=1/3 e.g. 2I2/I1 = 2.75 (not an integer) • Split into 3 by 75% • Split into 2 by 25% • Weights of all split particles are 1/2.75 W=1/3 W=1 • For I1 > I2 , play Russian Roulette, and multiple its weight by I1/I2 I1=1 I2=1/3 e.g.3I2/I1 =0.33 • 33% of particles survives, rests are killed • Weights of all survived particle are 3 W=1 W=1 W=1 W=3

  8. Example of calculation using [importance] imp.inp Air Concrete 50cm radius x 3 m thick cylinder 14 MeV neutron with 1 cm radius Thickness of each cell: 15 cm [importance] part = neutron reg imp 1 2.5**0 2 2.5**1 3 2.5**2 4 2.5**3 5 2.5**4 6 2.5**5 7 2.5**6 8 2.5**7 9 2.5**8 • 10 2.5**9 • 11 2.5**10 • 12 2.5**11 • 13 2.5**12 • 14 2.5**13 • 15 2.5**14 • 16 2.5**15 • 17 2.5**16 • 18 2.5**17 • 19 2.5**18 • 2.5**19 Ii+1/Ii= 2.5

  9. Example of calculation using [importance] 2.83GHz, single Number of history 2x104 maxcas = 10000, maxbch = 2 Without [importance] total cpu time = 53.66 sec 1 0.1 0.01 Dose rate Relative error With [importance] total cpu time = 186.47 sec 1 0.1 0.01 It is important to check the relative error ! red :1.0, yellow: around 0.1, green: around 0.01 Estimate doses deep inside concrete !

  10. Example of calculation using [importance] Dose rate in each cell Neutron energy spectra in a cell 7 Good agreements between importance method and normal calculation → Indicate the adequacy of the importance setting!

  11. Important Notice of Setting [importance] source Good example 1 8 32 2 4 16 Bad example 1 8 32 1 8 8 It is better to set 2~3 for max importance ratio between neighboring cells. Reference: “A Sample Problem for Variance Reduction in MCNP” LA-10363-MS DE86 004380

  12. Bad Example for using [importance] Very large importance ratio imp.inp Number of history 2x104 maxcas = 10000, maxbch = 2 [importance] part = neutron reg imp 1 2.5**0 2 2.5**0 3 2.5**0 4 2.5**3 5 2.5**3 6 2.5**3 7 2.5**3 8 2.5**3 9 2.5**3 10 2.5**3 11 2.5**10 12 2.5**10 13 2.5**10 14 2.5**10 15 2.5**10 16 2.5**15 17 2.5**15 18 2.5**15 19 2.5**15 20 2.5**19 2.83GHz, single total cpu time = 92.0 sec Dose Relative error Relative errors are too large in comparison to previous setting!

  13. Contents of Lecture 1.Introduction 2.Neutron deep penetration calculation • [importance] Geometry splitting and Russian Roulette • [weight window] Weight windows 3.Calculation of particleproduction in thin target • [forced collision]

  14. Difference between cell importance and weight window methods • “Cell importance method” assign a single value of weight for each cell. • “Weight window method” assign allowed weight range (window) for each cell and each energy group. Efficient simulation with focusing on the important energy region, such as high-energy neutron. WU=2.5 WU=2.5 I1=1 I2=3 WU=1.25 W1=1 W=1 W1=1 Weight Weight Weight WU=0.83 WL=0.5 WL=0.5 W2=1/3 WL=0.25 W2=0.5 region1 region2 region1 energy group1 region2 energy group2 WL=0.17 Number of particle1  → 1→ W1/W2=2 Number of particle 1 → 1 I2/I1=3 Cell importance method Weight window method

  15. Example of calculation using [weight window] Number of history 2x104 maxcas = 10000, maxbch = 2 Normal calculation total cpu time = 53.66 sec 1 Relative error Dose 0.1 0.01 total cpu time = 186.47 sec [importance] • [weight window] • part = neutron • reg ww1 • 1 (1/3)/2.5**0 • (1/3)/2.5**1 • ・・・ [weight window] • Set the lowest weight allowed in the cell (WW1=WL) total cpu time = 120.16 sec

  16. Calculation using weight window with energy dependence • [weight window] • part = neutron • reg ww1 • 1 (1/3)/2.5**0 • (1/3)/2.5**1 • ・・・ Number of history 2x104 maxcas = 10000, maxbch = 2 1. One energy group: all energy total cpu time = 120.16 sec • [weight window] • part = neutron • eng = 2 • 1.0e-3 20.0 • reg ww1 ww2 • 1 (1/3)/2.5**0*10 (1/3)/2.5**0 • 2 (1/3)/2.5**1*10 (1/3)/2.5**1 • (1/3)/2.5**2*10(1/3)/2.5**2 • ・・・ 2. two energy group: 0-1keV and 1keV-20MeV Lower weight boundary for En<1 keV (ww1) is higher than lower weight boundary for En > 1 keV (ww2) to concentrate on high-energy neutron transport total cpu time = 68.77 sec

  17. Check the accuracy of simulations 300 cm 150 cm 225 cm Attenuation of dose behind the concrete shielding Good agreement ! → Calculation using weight window method with energy dependence is most efficient.

  18. Contents of Lecture 1.Introduction 2.Neutron deep penetration calculation • [importance] Geometry splitting and Russian Roulette • [weight window] Weight windows 3.Calculation of particleproduction in thin target • [forced collision]

  19. Forced collision The forced collision is useful for analyzing secondary particles generated from a thin target Split into two particles Weight of uncollided particle:Wi×exp(-σd) d: distance across cell Incoming weight Wi Uncollided particle Weight of collided particle: Wi×{1-exp(-σd)} Collided particle Forced collision cell σ: macroscopic cross section Collide position is decided by cross section and random number. Forced collision factor|fcl| 1 fcl = 0: no forced collision in cell, |fcl| = 1: 100% forced collision • fcl < 0 = applies only to particles entering the cell (weight cut-off is not applied) • fcl > 0 = applies to all particles surviving weight cutoff (weight cut-off is applied)

  20. Example of forced collision Energy distribution of neutron and alpha produced by reaction of 100MeV proton incidence on 1mm thick Si. maxcas = 10000 maxbch = 2 force.inp [forced collisions] part = proton reg fcl 1 1.0 Secondary particle flux calculated with forced collision: You can get good statistic data!! Secondary particle flux calculated without forced collision: No collision occurred in such thin target

  21. Summary • Cell importance and weight window methods are effective in deep penetration calculations. • Ratios of importance and weight window between neighboring cells are better to be be less than 3. • Weight window method with energy dependence is more efficient than other methods for deep penetration calculations. • Forced collision method is effective to calculate particle production in a thin target.

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