Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps
We recall some of the sensitive points and stages in random walk of neutron, frequent solutions and their consequences on quality and duration of MC neutronic and photonic simulations. We present some unconventional approaches we developed to precisely meet the double paramount MC goal: maximal prob...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps / B.V. Robouch, L. Ingrosso, J.S. Brzosko, K. Hübner // Вопросы атомной науки и техники. — 2002. — № 4. — С. 84-88. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860264927917244416 |
|---|---|
| author | Robouch, B.V. Ingrosso, L. Brzosko, J.S. Hübner, K. |
| author_facet | Robouch, B.V. Ingrosso, L. Brzosko, J.S. Hübner, K. |
| citation_txt | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps / B.V. Robouch, L. Ingrosso, J.S. Brzosko, K. Hübner // Вопросы атомной науки и техники. — 2002. — № 4. — С. 84-88. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | We recall some of the sensitive points and stages in random walk of neutron, frequent solutions and their consequences on quality and duration of MC neutronic and photonic simulations. We present some unconventional approaches we developed to precisely meet the double paramount MC goal: maximal probing at minimal variance, whence minimum CPU time. Instead of the traditional point observation, enhanced probing is used to limit collected random scatter dispersion. Vector probing by shower (through ”nuclear reaction‑channel” space) and drizzle (improved sampling throughout space involving even the deepest parts, with region fragmentation allowed) drastically reduces the collected variance. By treating analogically close‑collision flux-at-a-point tallies, the unphysical pole discontinuity at-the-detecting-point is avoided - this allows the study of even within-detector collisions. For deep shielding treatment the use of the two-step Cascade Monte Carlo is recommended as it reproduces from physical considerations the mathematical approach. Making sure to distinguish volumetric versus local destructive effects, the latter requiring the use of "statistics of extreme values".
|
| first_indexed | 2025-12-07T18:59:33Z |
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MONTE CARLO SIMULATION OF MIGRATION OF FUSION PLASMA
NEUTRONS - OPTIMIZATION AND TRAPS
B.V.Robouch1, L.Ingrosso2, J.S.Brzosko3, K.Hübner4
1 guest, Laboratori Nazionali di Frascati INFN, 00044 Frascati (RM), Italy
2 via Gregorio XIII 7, 00040-Monte Porzio Catone, Italy
3 Diana Hi-Tech LLC, 1109 Grand Ave, North Bergen, NJ-07047, USA
4 Kirchhoff-Institut für Physik, Universität Heidelberg, 69120 Germany.
We recall some of the sensitive points and stages in random walk of neutron, frequent solutions and their
consequences on quality and duration of MC neutronic and photonic simulations. We present some unconventional
approaches we developed to precisely meet the double paramount MC goal: maximal probing at minimal variance,
whence minimum CPU time. Instead of the traditional point observation, enhanced probing is used to limit collected
random scatter dispersion. Vector probing by shower (through ”nuclear reaction-channel” space) and drizzle
(improved sampling throughout space involving even the deepest parts, with region fragmentation allowed) drastically
reduces the collected variance. By treating analogically close-collision flux-at-a-point tallies, the unphysical pole
discontinuity at-the-detecting-point is avoided - this allows the study of even within-detector collisions. For deep
shielding treatment the use of the two-step Cascade Monte Carlo is recommended as it reproduces from physical
considerations the mathematical approach. Making sure to distinguish volumetric versus local destructive effects, the
latter requiring the use of "statistics of extreme values".
PACS: 52.65.Pp
1. INTRODUCTION
The quality of statistical simulation of neutron
migration through material space and the induced effects
under study, be they local (in situ) or far (as revealed by a
detector), can be judged by how fully the concerned
material space is probed, and how low is the variance
obtained for the values sought. This twin requirement
maximal probing with minimal variance is the essence of
any Monte Carlo calculation. Ever since the start, MC
probing and variance have been conditioned by memory
and speed constraints. Computer evolution drastically
improved the situation. Yet they still remain an issue, due
to ever-increased requirements of quality of simulations
of fusion device details. The gigantic codes built in the
past, as well as recent, object-specialized codes bargain
simplifications (shortcuts - that inevitably deform reality)
vs. quality of representation to keep simulations in
rational financial frame and timely delivery of results.
Fusion devices have extended, non uniform (time and
space) neutron sources, numerous ports through the
structure and blanket and a variety of surrounding
materials and devices sensitive to fast or slow neutrons
and photon radiation that all need as close to reality a
simulation. It is no exaggeration to say that neutronics
and photonics of fusion devices is a most challenging MC
task among other nuclear related simulations.
The plague to the required variance precision resides
in the occurrence of collisions that result in rare-but-
strong-events (RSE) and explode the variance due to their
being out of proportion with the rest of event
probabilities. It is folly if one ignores them. A simple
solution to “smooth” them out is to increase the number
of iterations corresponding to the out-of-proportion ratio,
which often turns out to be prohibitive. The situation can
become dramatic when any of these RSE events
contributes to a narrow energy interval of interest.
Another solution, the one we advocate and have adopted
[1,2], is to ensure, while probing the required object,
collecting each contribution proportionately to its natural
importance. This is readily achieved using the approach
of which the essence is described below. The method has
proved powerful when applied to such different problems
as for example, in blanket tritium-breeding evaluations [3],
neutron detector calibration in the vicinity of a massive
structure, and fast-neutron diagnostics [4], fast-neutron
radiography [5,6], even gamma analysis [7], etc.
2. MC SIMULATION OF NEUTRON
MIGRATION - BASIC REQUIREMENTS
Modern thermonuclear plasma research is concerned,
both for project design or experimental diagnostic
interpretation, with ever more complex and sophisticated
systems accompanied by ever more stringent demands on
reliable estimation results. To be useful, the simulation of
radiation migration (neutron, gamma) has strict
requirements on variance [8] to be less than 40% for
feasibility projects, 20% for design, 10% for coding, 5%
for testing, 2% for installation, 1% for safety estimates.
Naturally, simulations must faithfully reproduce and
probe the provided shapes and compositions. The
revolutionary developments of computer speed and
memory help in conceiving such aims.
Neutron diagnostics at large plasma devices require
for the interpretation of the measurements often an
accompanying MC simulation. Here the importance of
obtaining small variances is far greater in diagnostics than
in detection. In fact, in detection a value is measured and
the standard deviation error is determined. In diagnostics,
as a parameter is varied, one aims to detect the variation
in the measured signal. To detect such a variation, the σ
errors of the simulated signal must be smaller than half the
variation in the signal!
The interpretation of neutron diagnostics for large
fusion facilities requires numerical simulation of the full
experiment: start from the neutron emission in a plasma
84 Problems of Atomic Science and Technology. 2002. № 4. Series: Plasma Physics (7). P. 84-88
with known parameters (either as per project parameters,
or experimentally measured on the facility); follow the
migration of the neutrons through the complicated
structures of the device and the detector; conclude with
the response of the detectors used. Naturally, uncertainties
and statistical errors at each step of the calculation sum up
nonlinearly and determine the overall quality of the
simulation.
Neutron flux decrease along
nuclear emulsion axis for
ASDEX discharge #16911
(collimator-1). Solid squares:
measured values, open circles:
MC estimation
Fig.1: A poloidal cross-section of ASDEX [1] through the vacuum chamber and the detecting pneumatic transport tube
(as seen by the computer). Numbers refer to a selection of parts of the device. Parts shown are
• Main section: 3-ASDEX vacuum chamber, 5-ohmic field coils, 18-divertor, 26-carbon shield, 65 & 67-thin
stainless steel shield protecting the divertor chamber.
• Blow-up: 81-nuclear emulsion or indium sample; 79 & 72-protective tubes; 59-transport tube; (e) transport
box.
• Nuclear emulsion plate track density of recoils MC-estimated vs. measured on ASDEX shot #16911 [9].
3. SPACE PROBING IN MC SIMULATION
OF NEUTRON MIGRATION
In essence, Monte Carlo (MC) neutron or gamma
simulation (of effects on structure, or detectors, or safety
hazard estimations) is a probabilistic probing of a given
space Sbody exposed to neutrons emanating from a
subspace Ssource, and registering select information about
effects produced either in Sbody itself at large, or in a
restricted subspace Sr (particular sensitive part as detector,
insulator, et al.). The aim is to estimate the values of
interest with as reduced statistical variance as possible.
Values of interest may be local within the extended Sbody
with direct probabilistically high access by neutrons (such
as generation of tritium breading in blankets,
transmutation gas-products or induced radioactivity,
energy deposition, etc.) or within a remote space of low
probability of direct access to neutrons, due to either
small size (as detectors or sensitive parts as insulators et
al.) or deeply shielded parts. Naturally, the two
necessitate distinct approaches.
To ensure credibility of results the MC should densely
cover with stochastic points all of Ssource , Sbody and Sr.
1. Source Ssource is the emission seat of neutrons (or
neutron ¨package¨), to be defined each as realistically
as feasible: 1) starting point position, 2) energy ‘E’
spectrum (thermonuclear plasmas, plasmas with
additional heating, etc., 3) direction of emission ‘u’
anisotropy selected, 4) corresponding probabilistic
weight ‘W’. Sources vary from small sized Plasma
Focus emitters[5] , accelerator target source[10], or
neutron fission sources (as Californium), to vast
tokamaks with sophisticated space emission and
varying energy spectra as in case of ion injection, et
al. The starting neutron weight is to faithfully reflect
the project (as GDT [11]) or experimentally
determined probability profiles (tokamaks as ASDEX
[12], TEXTOR [13], etc.). When a part of Ssource has more
physical significance for the intended research as per
experimental setup (vicinity, collimation, etc.), the
split method [14] is to be applied to enhance the
influence of the effective part of Ssource, while
respecting the rest of the source, guarantying
invariance of the total source emission. In the case of
collimator shielded detectors to ensure optimal tally
collection and hence variance, one has to distinguish
points not in view of the collimator entrance (CE),
from those that view directly the entrance at a solid
angle ΩCE. Here again the split method is
recommended, selecting many more probing small
weight neutron-stories are "emitted" into ΩCE, while
proportionately fewer but "heavier" ones sent into the
85
complementary 4π-ΩCE. In case the emission-point is
in-view of the detecting point, to ensure in the correct
proportion for contributions of direct and back-
scattered fluxes, we use a further split with a neutron
story run for half the weight beamed forward into Ω
CE. This is followed by another story run with
identical all other start parameters, but beamed into
the vertex-opposite anti-beam-ΩCE; naturally here the
complementary stories are beamed into 4π − 2ΩCE.
Thus, the proportionality of scattered to direct
contributions is ensured.
2. The whole facility space Sbody has to be faithfully
reproduced. To simulate the Garching tokamak
ASDEX [12] or the Novosibirsk GDT neutron source
[11] required several hundred structural elemental
volumes, each with its proper chemical composition
involving several decades of nuclides with an average
of half a dozen reaction channels each. TEXTOR
used 1157 elemental volumes [13]. All these have to be
densely probed.
3. Eventual particularly sensitive parts Sr are to be
treated with stochastic tally point-collectors.
Detection is particularly sensitive to events close to,
and unshielded from the detector - whence the
importance of close collision. For detector
simulation, for each neutron story a stochastic
detecting point is selected within Sr , that is to be
densely probed.
4. Deeply shielded, as in GTD [11], vital parts require
both, special treatment to densely probe them, and
need the statistics of extreme-tallies interpretation.
The distinct MC software sets designed to solve each
one of the above problems are strongly correlated. The
output of the neutron source program serves as input to
the neutron migration software, whose output in turn
serves as input to the several software programs for
simulating the response of the different detectors.
Fig. 1 shows as an example our computer simulation
of the poloidal cross-section of the tokamak ASDEX [1]
and of the details of the head of our transport system
which was used to expose as well activation samples (e.g.
Indium) as nuclear emulsion plates [9] near the plasma
boundary. As an example of the results the simulated and
measured values and their variance of the neutron flux in
an emulsion is shown. This flux, as per figure, decreases
along the emulsion axis due to neutron absorption by
about 25%.
4. MC SIMULATION OF NEUTRON
MIGRATION – CLASSICAL NEUTRON
TALLY
Due to its zero charge, a neutron (or photon) flies
rectilinearly until the next event in space. The MC
simulation of neutron migration [14] follows each neutron
story that extends from emission down to disappearance
through an absorption event, or till energy or weight cut
off below which further simulation is estimated to be of
no interest (as in threshold-energy detector studies, or too
weak tallies). Event-wise a collided, neutron reacts
probabilistically with one of the nuclides at that position,
and follows one of the possible reaction channels.
Classically, this is recorded locally at the point of event,
or observed remotely at the detecting point, with tallying
and migration confound and related to points touched
upon by migration with the full contribution assigned
locally. The neutron then proceeds till the following event
with an altered direction (anisotropy selected), energy ‘E’
(either event defined or spectrum probabilistically
selected) and weight ‘W’ (material attenuated along the
flight path ‘x’ with dW/W(x) =Σnuclide nnuclide(x) Σchannel σ
nuclide,channel(x) dx) = dx/λ(x) with λ the radiation mean-free-
path. At the neutron-story end, the MC registers the
terminal contribution (usually accessible to an analytical
estimation), and a next neutron story is generated. To be
credible the simulation should probe, i.e., touch upon as
densely as possible all parts of Sbody. This requires many
stories. However, probing probability diminishes with
depth away from the source favoring parts directly
exposed to the source emission. To obviate to such
inconveniences, several solutions had been proposed in
the past [14] that force neutron propagation into directions
of interest at the expense of other directions.
This classical method yields a single tally per
migratory event. We shall refer to such tally collection as
"scalar probing”.
5. IMPROVEMENTS BY VECTOR PROBING
OF SPACE AND MATERIALS
Neutron probability of interaction or of probing is low
in the following situations.
1. The specimen is thin in size, and the mean-free-path
is far greater than the through size of the object. As in
Fig.1 the thin protective shields (for light, X-ray,
thermal neutron shields) as well as close thin shields
installed for other purposes, would lead to rare,
lumped, strong contributions totally offsetting the
variance of the collected distribution. Indeed, in the
Fig.1 illustrative case the thin shields attenuate the
neutron fluence passing to the detector by ~25%,
while contributing ~16% of the collided fluence
arriving at the detector. Here, forced-collision
approach [15] is recommended.
2. The object is small and remote (such as a detector),
the flux-at-a-point estimation method of uncollided
flux has been devised [16].
3. Regions are highly shielded hence poorly accessible
to neutrons as per project design [11].
4. The encountered nuclides are rare, and reaction
channels not predominant.
Whenever any such rare event occurs, the tally is out
of proportion with respect to other tallies, and the relative
variance explodes, requiring a high number of stories to
smooth the resulting discontinuity.
To offset the drawbacks of scalar probing we advocate
and use vector probing through space (drizzle [1]) and
nuclide reaction-channels (shower [1]), i.e. two additional
splitting methods [14]. Both methods have been described
earlier [1] and are here only briefly recalled. Indeed, in
defining migration, all nuclides and channels are
considered to determine the collision event that leads to
the next migration-step of the neutron story, and the tally
at the point of event, or of detection.
Vector probing through all nuclides and reaction
channels at each point, ensures the tallying of all the
shower of events proportionately to their probabilities, by
considering in a material all nuclide components,
accounting for different product of isotopic abundance
nnuclide and reaction-channel cross section σnuclide,channel. This
avoids out of scale contributions, ensuring a smoothly
converging variance collection. By guaranteeing a full
probing through all possible nuclear reactions, shower
totally eliminates perturbations introduced by rare nuclear
reactions due to trace elements or low cross-section
branches.
In selecting the migration event point one determines
the absorption attenuation of the neutron flux as it
proceeds along its line of flight till the very edge of Sbody.
This constitutes a beam probing through space even to
and across the most deep and remote parts. Along this
probing beam, and using the same algorithm as adopted
for the neutron migration, by vector probing a random
point of pseudo-event is selected for each traversed
absorbing material region (or in case of vast regions,
fractions of there of). The fraction of the flux absorbed in
each structural element (or sub-element) of the facility, is
considered to have its set of shower reactions leading to a
distributed drizzle of contributions through space, all in
perfect scale! Drizzle is useful in treating material regions
with a disproportionately large mean-free-path of
radiation – as thin detector protective foils, spaces that
stop neutrons only rarely, but when they do, the event
leads to intense tallies. The method ensures that the
absorbed flux is distributed to each solicited region
proportionally to the natural capacity to interact.).
Naturally, such a drizzle approach uses the forced-
collision, which accounts for the fraction of the flux lost
at the beam-end, while the remaining flux is distributed
proportionately to absorption in each traversed region, be
it for local or remote tallying. The drizzle-shower
approach is particularly useful to account for thin
protective foils around small detectors exposed to the
plasma direct radiation. Drizzle’s beam-probing greatly
enhances probing of space.
For each collected shower-drizzle tallies the following
data are stored:
a) coordinates of the points of emission, events and
detection for each story,
b) time of emission or event, necessary for time-of-flight
detection or other time-resolved studies,
c) weight probability, or flux, and energy of the neutron
contribution arriving at the detection point,
d) identifiers for the origin of neutron re-emission as
collided nuclide and reaction branch, tokamak
structural element (region), and the partition of space
as observed by the detector (zone), etc.
This tally database allows identifying quantitatively
the contribution of different parts of Sbody or nuclear
contributors, such as the different fluence components
(direct or scattered; structural part in which scatter
occurred, etc.), spectra and fluence of neutrons arriving at
the detector. The tally database also serves to determine
the collimator response function, as well as that of the
detector using post processing software. Example of such
software are ACTIN for indium-activation diagnostics
[4,13,17], NEPMC for nuclear emulsion plate (NEP)
measurements of proton recoil parameters (track length,
angle, proton energy, accounting for track strangling,
emulsion thickness variation) as was applied in [4,9, 13,17].
6. CLOSE COLLISION SIMULATION
Detection simulation has long been plagued with RSE
occurring close or within the detector collecting the tally.
Close collisions are unavoidably part of a true detector
simulation. Indeed, the reduction of the detected intensity
by surrounding material structures and attenuation due to
distance, limits the space of origin of the intense tally
contributors to but a few mean-free-paths around the
detector. Thus paramount is the attention to events within
their close vicinity. The flux-at-a-point as per Kalos-
expression [15] intrinsically contains the 1/4πd2 singularity.
To tackle close-collisions several treatments have been
proposed [16], as the once collided estimator and other
similar treatments.
We chose an analogic approach. To record flux
information in a small subspace Sr we estimate the
fraction of the scatter of each event into 4π space that
reaches per cm2 at Sr [δΩ/4π =½ [1-d/(d2+1/π)½]. Such
estimation is perfectly regular (with no singularity) and
hence fit to tackle even the very close events (see for
instance [9]). But most important it reproduces the physical
reality that no more than ½ of the emanating flux may be
gathered at any surface, the other half traveling the
opposite direction and hence is lost. The unphysical pole
discontinuity at-the-detecting-point is thus avoided, and
the study of even within-the detector (as in nuclear
emulsion detection simulations) becomes possible [9]. The
treatment of very close events is fundamental to correctly
simulate neutron diagnostics.
7. HEAVILY SHIELDED PARTS AND THE
TWO-STEP CASCADE MC
Damage effects in heavily shielded parts SHeavySh,
require close attention. Indeed, heavy shielding implies,
as per project intent, that only a negligible part of
neutrons reach those sensitive parts. Such parts receive
mostly events attenuated in energy and flux intensity,
with very few but very damaging exceptional high-energy
arrivals. To correctly simulate such a situation a two-step
Cascade Monte Carlo [2] is recommended. The method
reproduces from physical considerations the mathematical
approach [18]. It consists of an initial MC simulation in
which the deeply-shielded part surface serves as a
collector of all arriving beamed (onto the probing point
selected within Sr for that story) neutrons (defined each in
weight, energy, direction) while the SHeavySh volume is
assumed normally absorbing but non-collisional.
In the second step of the cascade SHeavySh becomes
normally colliding to all effects, while the space around it,
Sbody-SHeavySh is either dropped if Sbody is singly connected,
87
otherwise considered collisionless for economy of
computation time. Only a skin is retained to be able to
account for reentering neutrons that scatter out of SHeavySh
[2]. Each of the registered neutron contributions now acts
as the neutron-story start, and the MC is run normally.
Yet, in recording destructive effects, a strong distinction
is to be made between volumetric versus local effects, the
latter requiring the use of "statistics of extreme values"
[11]. Indeed, while energy deposition is an integrated value
that is mediated with a majority of low values adding to
very few strong contributions, damage to an insulator or
superconductor is a local effect and destruction occurs
with single local damage. This implies that in estimating
the survival life of a critical part, statistics ought to be
carried out on collected "extreme values". Thus the
second cascade is repeated several times, collecting a
sufficient number of extreme values, whence the statistics
of these extreme values serves to determine the effective
survival time.
8. CONCLUSION REMARKS
A classical analogical simulation run requires usually
great many thousands of MC stories. The introduction of
some evaluation methods as flux-at-a-point, forced-
collisions, greatly reduces the required number of story
runs. The analogical flux-at-a-point consents the
treatment of very close events. Drizzle and shower
splitting, rend conceivable numerical experiments of high
complexity and sophistication, that otherwise would be
inaccessible due to the time they would require (in spite
of the ever faster computers). This is due to their capacity
of collecting tallies with rapidly converging random
statistical dispersion to the experimental values due to
their greatly enhanced probing of space, of material
nuclides, of reaction-channels, all gathered
proportionately to their relative natural contributions.
Drizzle beam probing is more powerful than regional
biasing when applied to tritium-breeding blankets of
thermonuclear facilities or in estimating safety hazards
from radioactivity hands-on after shut down of the
tokamak. For the latter we recommend full drizzle and
shower biased to the reactions of interest. The two-step
cascade MC is a technique that consents tackling extreme
experiments.
Both our VINIA-3DAMC (see for instance [4]) and
3DMCSC-RWR (see [7]) software complexes have drizzle,
shower, and the analogical close-collision estimator as
functional and integral parts. They yield results in
absolute units referred to the total measured or project
yield of the facility, and do not use any parameters or
normalization factors.
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Monte Carlo Simulation of Migration of Fusion Plasma Neutrons - OPTIMIZATION and traps
1.INTRODUCTION
2.MC SIMULATION OF NEUTRON MIGRATION - BASIC REQUIREMENTS
3.SPACE PROBING IN MC SIMULATION OF NEUTRON MIGRATION
4.MC SIMULATION OF NEUTRON MIGRATION – CLASSICAL NEUTRON TALLY
5.IMPROVEMENTS BY VECTOR PROBING OF SPACE AND MATERIALS
6.CLOSE COLLISION SIMULATION
7.HEAVILY SHIELDED PARTS AND THE TWO-STEP CASCADE MC
8. CONCLUSION REMARKS
BIBLIOGRAPHY
|
| id | nasplib_isofts_kiev_ua-123456789-80259 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:59:33Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Robouch, B.V. Ingrosso, L. Brzosko, J.S. Hübner, K. 2015-04-14T05:24:15Z 2015-04-14T05:24:15Z 2002 Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps / B.V. Robouch, L. Ingrosso, J.S. Brzosko, K. Hübner // Вопросы атомной науки и техники. — 2002. — № 4. — С. 84-88. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 52.65.Pp https://nasplib.isofts.kiev.ua/handle/123456789/80259 We recall some of the sensitive points and stages in random walk of neutron, frequent solutions and their consequences on quality and duration of MC neutronic and photonic simulations. We present some unconventional approaches we developed to precisely meet the double paramount MC goal: maximal probing at minimal variance, whence minimum CPU time. Instead of the traditional point observation, enhanced probing is used to limit collected random scatter dispersion. Vector probing by shower (through ”nuclear reaction‑channel” space) and drizzle (improved sampling throughout space involving even the deepest parts, with region fragmentation allowed) drastically reduces the collected variance. By treating analogically close‑collision flux-at-a-point tallies, the unphysical pole discontinuity at-the-detecting-point is avoided - this allows the study of even within-detector collisions. For deep shielding treatment the use of the two-step Cascade Monte Carlo is recommended as it reproduces from physical considerations the mathematical approach. Making sure to distinguish volumetric versus local destructive effects, the latter requiring the use of "statistics of extreme values". en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники ITER and fusion reactor aspects Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps Article published earlier |
| spellingShingle | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps Robouch, B.V. Ingrosso, L. Brzosko, J.S. Hübner, K. ITER and fusion reactor aspects |
| title | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| title_full | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| title_fullStr | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| title_full_unstemmed | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| title_short | Monte Carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| title_sort | monte carlo simulation of migration of fusion plasma neutrons - optimization and traps |
| topic | ITER and fusion reactor aspects |
| topic_facet | ITER and fusion reactor aspects |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80259 |
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