MASSACHUSETTS INSTITUTE
OF TECHNOLOLG'°
,
JUN 02 2015
LIBRARIES
Investigation of Sub-meter Shields for a Low
Aspect Ratio D-T Tokamak Fusion Reactor
by
Cameron T. French
Submitted to the Department of Nuclear Science and Engineering
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Nuclear Science and Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2014
@Cameron T. French. All rights reserved.
2 Ofi..f
The author hereby grants to MIT permission to reproduce and to distribute publicly
paper and electronic copies of this thesis document in whole or in part.
Author ............................ .
Signature redacted
Cameron T. French
Department of Nuclear Science and Engineering
9 2014
Certified by......
Signature redactedM•y
,
................ .
Dennis G.
Prof1Tf Nuclea/clnc
/
1
Acceptedby...... :..
(.
,hyte
/J /J
i:eer~:~
Signature redacted
(,}
~apan St:ndustcy P:::: :.:dr::
Department of Nuclear Science and Engineering
1
Investigation of Sub-meter Shields for a Low
Aspect Ratio D-T Tokamak Fusion Reactor
by
Cameron T. French
Submitted to the Department of Nuclear Science and Engineering
on May 9, 2014, in partial fulfillment of the requirements for the degree of
Bachelor of Science in Nuclear Science and Engineering
Abstract
A significant effort is being made by fusion researchers to minimize the
total size of magnetic fusion devices on the path toward developing fusion
energy. The spherical tokamak, which has a very low aspect ratio, is the
most promising of the compact magnetic fusion reactor designs. This compactness imposes a severe material constraint on the design, as a highly
compact device will have very thin inner shielding. This inner shielding,
which in traditional designs is required to be around 1 meter thick, acts to
protect the central solenoid and return toroidal field coil legs from material
damage and nuclear heating resulting from high neutron fluxes. The use of
a sub-meter inner shield creates potential for the design of a proof of principle magnetic fusion device, sacrificing the central component materials
for a demonstration of temporary fusion power production. The nuclear
heating of thin shields (~ 0.1 - 0.2m) of various compositions was explored
using the Monte Carlo N-Particle (MCNP) transport code. The principal
finding was that nuclear heating is the largest concern to the central inboard components. Nuclear heating of these sensitive materials was found
to be minimized by the use of a magnesium borohydride blanket with a
tungsten first wall. The resulting nuclear heating density for a 100MW,
R=1m D-T tokamak employing 0.1 - 0.2m shields is shown to have the
potential to threaten the ability of such a device to sustain net electricity.
Thesis Supervisor: Dennis G. Whyte
Title: Professor of Nuclear Science and Engineering
2
Acknowledgements
First and foremost, I would like to thank the faculty members of the Department of Nuclear Science and Engineering for their support and encouragement.
In particular, I would like to thank two of the most inspiring instructors at
MIT; Dennis Whyte and Anne White, whose dedication to fusion research and
education has inspired me beyond measure.
I would also like to thank my parents, who have selflessly supported my
education for the past 22 years.
3
Contents
1 Introduction
5
2
Background
2.1 Low Aspect Ratio Tokamaks . . . . . . . . . . . . . . . . . . . .
2.2 Plasma-facing Materials & Nuclear Heating . . . . . . . . . . . .
6
6
8
3
Methods
11
3.1 M CNP M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 M aterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Neutronics Simulations . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Results & Discussion
14
5
21
Conclusions
References
6
22
Appendix
23
6.1 M CNP Input File. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4
1
Introduction
While the current state of fusion power development is primarily focused on
the creation of long-term energy solutions as pioneered by ITER[1] and other
magnetic fusion projects, it has recently become of interest to some researchers
to explore an alternative route of developing a more compact toroidal device to
generate short-term fusion power as a proof of principle demonstration.
This
"throw away" device concept would be purposed to reach energy breakeven,
yielding more energy than is put in, but only for a relatively short period of time
in comparison to commercial fusion reactors. This demonstration would serve
as a first step toward developing a very compact D-T tokamak that produces
high energy gain. Due to basic constraints on plasma stability and confinement,
the best choice for a very compact device is a low aspect ratio (R/a) tokamak.
This desired compactness, however, introduces a severe material constraint
on the design of the device's inboard shielding. Inboard shielding acts to protect
the central components, namely the central solenoid and toroidal field coils, from
nuclear heating and neutron damage. As dictated by the mean free path of 14
MeV fusion neutrons, traditional fusion tori require inboard shielding that is
~1m thick. In order to minimize the aspect ratio and achieve a suitable level of
compactness, this shield thickness will also have to be minimized. This reality
presents a difficult design challenge, as the use of minimally thin shields (~.1.2m) is certain to result in the central components receiving higher neutron
fluxes.
For the purpose of demonstrating fusion power generation at the expense
of material integrity, the use of very thin shielding on a low aspect ratio D-T
tokamak may be valid. What remains to be seen is exactly which materials
will minimize nuclear heating and thereby maximize the expected lifetime of
the central components. The objective of this thesis is to determine the optimal
5
composition and dimensions of sub-meter (.1-. 2m) shields for use in a low aspect
ratio D-T tokamak.
2
Background
2.1
Low Aspect Ratio Tokamaks
In order to make a traditional tokamak more compact, its aspect ratio must
be lowered. The aspect ratio of a tokamak is the ratio of its major radius (R)
to its minor radius (a). As such, the limit of compactness is a sphere with
aspect ratio (R/a)=1. The magnetic fusion device that most closely achieves
this compactness limit is the spherical tokamak, whose major and minor radii
are near equal. Figure 1 shows the geometric differences between a conventional
tokamak (large aspect ratio) and a spherical tokamak (low aspect ratio).
Figure 1: Differences in tokamak gemoetry are shown across a range of aspect
ratios. Conventional tokamaks have large aspect ratios, while spherical tokamaks have low aspect ratios approaching (R/a)=1.[2]
The spherical tokamak is also an attractive design because its compactness
allows for the maximization of , a very important plasma parameter relevant to
magnetic fusion concepts. The
of a plasma is defined as the ratio of the plasma
pressure to the magnetic pressure in the reactor. Also called the magnetic field
utlization factor,
P is
a measure of how efficiently the magnetic field energy
is used to confine the plasma energy.
The low aspect ratio of the spherical
6
tokamak allows for the fusion plasma within to achieve greater elongation than
in conventional tokamaks. As a plasma becomes elongated, its n-limit increases
[3]. Thus, spherical tokamak plasmas are capabale of reaching much higher
P
than conventional tokamaks. This parameter is of particular importance because
fusion power output (per unit volume of plasma) is proportional to
P according
to the relation
2
Pf ~
B4 ,
(1)
where B is the magnetic field strength [3]. This relation further illustrates
the difference in approach between large scale fusion experiments like ITER
and smaller endeavors such as spherical tokamaks. While those behind ITER
have chosen to spend billions of dollars maximizing magnetic field strength
to achieve high fusion power, spherical tokamaks maximize fusion power in a
smaller package by reaching higher
P as
allowed by geometric differences.
It
should be noted that while a lower aspect ratio allows tokamaks to achieve
higher
p,
a very compact geometry imposes significant constraints. A high
s
must be balanced against a necessary decrease in magnetic field strength due
to a limit on the maximum allowed B at the coils. Given the scaling of fusion
power with B4 , it is necessary for aspect ratio to be tailored to and optimized
for a given magnetic structure.
This high power density in turn becomes the most significant design restriction in spherical tokamaks because the resulting high neutron fluxes cause major
damage to the in-vessel components [4]. Common fusion tori employ an inner
shield that is ~1m in thickness, the distance typically required for full thermalization and shielding of neutrons. Shielding is necessary for the protection
of the central solenoid and return toroidal field coil legs from neutron damage
and nuclear heating. The external coils of a tokamak confine the fusion plasma
with magnetic fields generated by large electric currents. These magnetic coils
7
are incredibly sensitive to temperature and therefore to nuclear heating, as superconducting materials are functional only when maintained below a certain
critical temperature [5]. Figure 2 shows the configuration of a tokamak's central
solenoid and toroidal field coils. The main area of interest in this study is the
inboard side, where the return toroidal field coil legs and central solenoid are
located.
Central solenoid magnet
Pojoidal4ield
Toroacdal-lield
magnet
Figure 2: The central solenoid, poloidal and toroidal magnetic coils of a
tokamak. [6]
2.2
Plasma-facing Materials & Nuclear Heating
The greatest obstacle to fusion power production is a materials issue.
The
heat and neutron fluxes of fusion plasmsas do extensive damage to the shielding
materials on the inboard surface of the tokamak, located at small distances from
the major axis of symmetry of the torus. The shielding region that immediately
surrounds the plasma consists of a first wall and a blanket, each made of a
different material and each requiring a very deliberate design. Figure 3 shows a
cross-sectional view of a conventional tokamak, with the first wall and blanket
highlighted on the inboard side.
8
DOME PLATE
IVERTOR STRUCTURE
1B DIVERTOR
PLATE
B DIVERTOR PLATE
IB L T-SHIELD
OB FW/BLANKET
OB BLANKET
REFLECTOR
IB HT-SHiIELD---
2,_
STRUCTURAL
RING
OB HT-SHIELD
JIB FW/BLANKET|
OB LT-SHIELD
MAINTENANCE
SEPARATION LINE
Figure 3: A cross-sectional view of a conventional tokamak, with the first wall
(FW) and blanket region on the inboard side highlighted.
The first wall is the outermost section of the shield on the inboard side. While
magnetic fields greatly reduce the extent to which the plasma touches the first
wall directly, there remains a significant amount of contact between the two. As
such, the first wall must be able to withstand plasma contact as well as a high
neutron flux, while meeting a number of other important physical criteria. The
first wall must be compatible with high and fluctuating magnetic fields, allow
for the transfer of a very large heat flux, resist radioactivation, and minimize
contamination of the plasma due to wall erosion. Graphite, molybdenum, boron
carbide, beryllium, and tungsten are among the materials currently being used
to construct first walls.
9
Lying behind the first wall, the blanket serves to slow down neutrons, transforming kinetic energy into heat energy. In the future, this heat energy will be
used for electrical power production. A variety of materials have been used, or
proposed for use, in the blanket. Low-Z materials are traditionally favored, as
they are better at slowing down neutrons, as expected from simple collisional
)
physics. Magnesium borohydride (Mg(BH 4 ) 2 ) and zirconium hydride (ZrH 2
have been shown to perform particularly well as blanket materials [7]. Some
blanket materials, like FLiBe (Li 2 BeF 4 ), contain lithium and are designed to
breed tritium that can be recycled thereafter as fuel for a sustained fusion reaction.
Nuclear heating is of principal concern in a thinly shielded ST configuration.
Approximately 80% of the energy generated in a magnetic fusion reactor is
transported out of the plasma by highly energetic neutrons, resulting in neutron
wall loading on the order of 0.5-2.0 MW m-2 [3].
These neutrons deposit a
fraction of their energy upon collisions with nuclei in other reactor materials,
resulting in nuclear heating [8]. Nuclear heating is calculated as the product
of the number of neutron-nuclei interactions in the target material and the
amount of energy released by these interactions. The nuclear heating, H, of a
target material is found to be
H = ,Da-NAE.,
where <D is the incident neutron flux in units of neutrons/cm 2 s,
(2)
ac
is the
microscopic cross section for reaction x in units of cm 2, NAis the total number
of target nuclei, and Exis the energy transferred by interaction x in Joules. The
nuclear heating is in units of watts (W). The photon field generated by these
neutrons also contributes to the heating. These effects cause a temperature
field to form within the target material, which in extreme cases can lead to
10
material failure. However, as the proposed device will serve merely as a proof of
principle and generate only short-term fusion power, the lifetime of the shield
and in-vessel components need not be maximized as they are in designs such as
ITER. As such, the traditional 1 meter thick inner shield can hypothetically be
made much thinner and still provide protection for the device to sustain a fusion
plasma and demonstrate net-gain for a short time before experiencing critical
failure.
3
3.1
Methods
MCNP Model
To investigate the potential for the use of very thin shields in a low aspect
ratio D-T fusion tokamak, a model of the inboard section of such a device has
been constructed using the MCNP (Monte Carlo N-Particle) transport code.
MCNP is a software package distributed by the Radiation Safety Information
Computational Center and is used to simulate nuclear processes. The model
itself, as shown in a cross sectional view in Figure 4 at two different shield
thicknesses, includes all material structures relevant to the inboard shielding of
the central components from fusion neutrons. The model consists of a central
cylinder of superconducting material, a blanket region, an outer first wall, and
a surrounding neutron source. In MCNP, exchanging materials to occupy any
geometric cell is simple. The model constructed is therefore robust and can be
used to simulate tokamak neutronics with any combination of desired materials.
11
R=.16m
R=.23m
R=.16m
R=
R=.33m
R=O
R=.26m
R=.36m
Figure 4: An MCNP model of the inboard section of a low aspect ratio tokamak,
including the first wall (blue), blanket (green), and an approximation of the
materials that make up the central solenoid and return toroidal field coil legs
(orange and red). A monoenergetic D-T fusion 14.1 MeV neutron source exists
in a cylindrical ring (white) around these materials.
3.2
Materials
This study focused on a few particular first wall and blanket materials, each of
which have been shown in existing literature to perform well in their individual
shielding functions. The materials of interest are shown in Table 1, along with
their relevant thermal and physical properties.
Magnesium borohydride and
zirconium hydride are of particular interest for use in the blanket because of
their high hydrogen densities (13.2x10 28 /m
3
and 7.2x10 2 8/m 3 , respectively) [7].
This is attractive because hydrogen atoms and neutrons are roughly the same
mass, resulting in maximum energy transfer during collisions. Molybdenum has
been used for the first wall in a number of fusion tori, including Alcator C-
12
Mod at MIT [9]. Full tungsten first walls have been considered on a number of
devices, including the ASDEX Upgrade [10].
Table 1: First wall and blanket materials investigated for use in sub-meter
shielding in a low aspect ratio D-T fusion tokamak.
Section
Material
Formula
Mol. Wt
p [g/cm 31
Melting Pt
_
FW
FW
Blanket
Blanket
Blanket
tungsten
molybdenum
magnesium
borohydride
zirconium (II)
hydride
FLiBe
[K]
_[g/mol]
W
Mo
Mg(BH 4)2
183.84
95.94
53.99
19.3
10.8
1.45 [7]
3695
2896
587 [11]
ZrH 2
93.24
5.56 [7]
1073
Li 2BeF 4
98.89
1.92
Boil: 1703
The dimensions of each individual cell can also easily be manipulated. For
the purposes of this study, each shielding combination of first wall and blanket
have been simulated at varying thicknesses. A 30mm first wall layer is used,
and the size of the blanket is varied from 70mm to 170mm in increments of
10mm. The result is a range of shield thickness from .lm to .2m, each simulated
separately using every combination of shielding materials of interest.
The central components of a tokamak can be made from a variety of materials. Traditionally, the solenoid and field coils are composed of a super conducting
material and steel for reinforcement and structural support. To approximate the
material composition of the central components, this MCNP model includes a
central cylinder composed of niobium-tin (Nb3 Sn) and stainless steel, at a mixture of 50%-50% by mass. Niobium-tin is a type II superconductor capable of
handling magnetic fields of up to 13 T, and will be used to construct the toroidal
field coils and solenoid of ITER [12, 1, 13].
13
3.3
Neutronics Simulations
The MCNP model is programmed to tally a number of key neutronics phenomena in the material structure. The neutron current through each surface is
tallied, along with the average neutron flux through each material. The most
important tally for this investigation is the measure of the energy deposited in
each material. As mentioned previously, nuclear heating is measured in units of
W (or J/s). MCNP measures energy deposition, a time independent yet analogous quantity for the sake of comparison, in units of MeV/g. A comparison of
the energy deposited per gram in each material at varying shield thickness will
serve to differentiate each unique configuration, allowing for the selection of an
optimal design that minimizes nuclear heating in the central components. The
full MCNP code created for this investigation can be found in the Appendix.
4
Results & Discussion
Each configuration of the MCNP input file for this model was run with at least
10 million source particles to reduce variance and ensure precision in the tallies.
Energy deposition in the first wall, blanket, and central component materials
are shown as functions of shield thickness in Figures 5-9. As a change in shield
geometry leads to a change in first wall surface area, the number of source
particles in each run were adjusted such that the neutron wall loading was kept
constant at 0.7 MW/m 2 . This allows for an assessment of the feasibility of thin
shields for this particular reactor setting.
14
1.60E-07
1.40E-07
>-
1.2013-07
01.0013-07
-
*W-Mg(BH4)2
*W-ZrH2
0 8.0013-08
-W-FLiBe
.Mo-Mg(BH4)2
"Mo-ZrH2
Mo-FLiBe
4.00E-08
2.00E-08
0.OOE+00
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Shield Thickness [m)
Figure 5: Energy deposition in the first wall is plotted against shield thickness
for six different shielding compositions. W-Mg(BH 4) 2 (dark blue line) cannot
be seen, as it lies just beneath Mo-FLiBe (orange).
It is shown in Figure 5 that more energy is deposited in a molybdenum first
wall per gram than in a first wall made of tungsten. There are two key factors
underlying this result, both relating to the difference in mass between these two
first wall materials. Tungsten's large mass leads to neutrons transferring less
energy per collision than they do in molybdenum, as it is known that collisional
energy transfer is maximized when the colliding objects are of similar mass. In
addition, the normalization of this energy quantity by mass results in tungsten,
the heavier element by nearly a factor of 2, experiencing significantly less energy
deposition per gram.
Of particular interest is the fact that a magnesium borohydride blanket is
shown to minimize energy deposition in the inboard first wall, regardless of
the first wall's composition. This is likely due to the high hydrogen density
of magnesium borohydride, which serves to maximize the degree of neutron
15
moderation that occurs in the blanket.
7.OOE-06
6.00E-06
5.00E-06
4E6W-Mg(BH4)2
4.0013-06
.W-ZrH2
"W-FLiBe
3.OOE-06
*Mo-Mg(BH4)2
Mo-ZrH2
2.00E-06
-Mo-FLiBe
1.00E-06
0.00E+00
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Shield Thickness [m)
Figure 6: Energy deposition in the blanket is plotted against shield thickness
for six different shield compositions.
It can been seen in Figure 6 that energy deposition in the blanket is maximized with the use of a shield composed of a molybdenum first wall and a
magnesium borohydride blanket. As previously stated, magnesium borohydride
is an excellent blanket material for moderation because of its high hydrogen
content.
Neutrons are more likely to scatter and deposit more energy when
colliding with particles of similar mass, such as the hydrogen atom. As shield
thickness shrinks to .1m, the blanket energy deposition for shields employing
magnesium borohydride is up to 4-5 times that of shields employing zirconium
hydride or FLiBe.
16
1.40E-07
1.20E-07
1.OOE-07
"W-Mg(BH4)2
8.00E-08
"W-ZrH2
"W-FLiBe
6.00E-08
"Mo-Mg(BH4)2
"Mo-ZrH2
d
4.00E-08
Mo-FLiBe
2.OOE-08
O.OOE+00
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Shield Thickness [m]
Figure 7: Energy deposition in the stainless steel of the center section of a low
aspect ratio tokamak is plotted against shield thickness for six different shield
compositions.
Figure 7 shows the energy deposited in the stainless steel plotted against
shield thickness. This stainless steel, which is used as a structural support to
the superconducting magnetic coils and central solenoid, is extremely sensitive
to neutrons. Once again, the first wall and blanket combination of tungsten and
magnesium borohydride is shown to be optimal for minimizing the energy deposition, and by extension the nuclear heating, of sensitive central components.
It is noteworthy that the energy deposition in the stainless steel appears to be
strongly dependent on the first wall composition. It should also be noted that
across the range of shield thicknesses, shields with tungsten first walls perform
only marginally better than shields with molybdenum first walls. At .2m shield
thickness, the shields employing hydride blankets experience roughly the same
energy deposition in the structural stainless steel (~2.Ox10-
8
MeV/g). The same
is true at lower thicknesses, where the hydride blanketed shields each receive
17
between 6.0x10-8 and 7x10- 8 MeV/g. A different trend is observed in Figure 8,
where energy deposition in the superconducting material (in this case Nb 3 Sn)
is shown to be more dependent on blanket composition than on first wall composition.
Shield configurations employing a magnesium borohydride blanket
outperform those using zirconium hydride or FLiBe. Once again, the combination of a tungsten first wall with a magnesium borohydride blanket is shown to
minimize energy deposition in the target material.
1.40E-07
1.20E-07
1.00E-07
W-Mg(BH4)2
8.00E3-08
"W-ZrH2
"W-FLiBe
S6.00E-08
-Mo-Mg(BH4)2
"Mo-ZrH2
4.00E-08
"Mo-FLiBe
2.OOE-08
0.00E+00
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Shield Thickness [m]
Figure 8: Energy deposition in the inboard superconducting material (Nb 3Sn)
of low aspect ratio tokamak is plotted against shield thickness for six different
shield compositions.
The nuclear heating of the inboard Nb 3 Sn in a 100 MW, R=1m D-T fusion
tokamak with neutron wall loading of .7 MW/m2 is shown in Figure 9 for each
shield composition, once again plotted as a function of shield thickness. It is
demonstrated that a W-Mg(BH 4 ) 2 first wall and blanket combination minimizes
nuclear heating and keeps the magnetic coils of a low aspect ratio D-T fusion
tokamak operational longer than the other shield configurations explored in this
18
study.
Nuclear heating of the magnetic coils on the order of 0.01 MW presents a
significant problem to the operation of a 100 MW, R=1 low aspect ratio D-T
tokamak.
The heat resulting from the energy deposited in the magnets must
be removed at the temperature of the superconducter. Niobium-tin superconductor operates at around 4 K. This heat must be rejected at 300 K, however,
leading to a considerable Carnot penalty. A 100 MW tokamak may produce 25
MW of electrical power, as dictated by the thermal efficiency of the blanket, but
the operational feasibility of the reactor is ultimately at the mercy of thermodynamics. Superconducting materials operate only below a critical temperature,
and so must be actively cooled in order to function properly. If a significant
portion of the electrical power produced by this device is needed to cool the
coils, it is clear that it very quickly becomes difficult to reach and sustain net
electricity.
Thus, what may seems like a small amount of nuclear heating in
the central components of a tokamak will actually greatly affect the power cycle
of the reactor.
As an energy source, nuclear fusion has relatively low power
density and high recirculating power. This thermodynamics problem is just a
small part of what makes nuclear fusion one of the most difficult engineering
projects ever attempted.
19
0.12
0.1
0.08
W-Mg(BH4)2
W-ZrH2
0.06
W-FLiBe
Mo-Mg(BH4)2
Mo-ZrH2
0.04
Mo-FLiBe
Z 0.02
0
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Shield Thickness [ml
Figure 9: Nuclear heating in the superconducting magnets of a 100MW, R=1m
D-T fusion tokamak is plotted against shield thickness for six different shield
compositions.
20
5
Conclusions
Upon successful simulation of the use of .1-.2m shielding on a very low aspect
ratio D-T fusion tokamak with MCNP, a number of conclusions are made. First
and foremost, the MCNP model is proven to be robust and extremely efficient,
producing precise reaction and energy deposition tallies with minimal variance.
Secondly, it is made quite clear that, of the materials tested using this model,
tungsten and magnesium borohydride are the best candidates for first wall and
blanket materials, respectively, for use in a very low aspect ratio D-T fusion
tokamak proof of principle device. This shielding composition is shown to minimize nuclear heating in the sensitive superconducting materials of the central
solenoid and toroidal field coils. A thin shield composed of a tungsten first wall
and a magnesium borohydride blanket is shown to be a promising design that
may make a highly compact proof of principle fusion device possible. However,
it remains to be seen whether such thin shields will be thermodynamically compatible with tokamaks to the extent that the superconducting magnets can be
maintained below critical temperature and net electricity can be sustained.
21
References
[1] P.H. Rebut. Iter: the first experimental fusion reactor. Fusion Engineering
and Design, 30:85-118, 1995.
[2] Tokamak Aspect Ratio Comparison. http://www.ccfe.ac.uk/assets/images/research/aspect
[3] J. Freidberg. Plasma Physics and Fusion Energy. Cambridge University
Press, 2008.
[4] R.D. Stambaugh. The spherical tokamak path to fusion power. Fusion
Technology, 1996.
[5] R. T. Santoro. Radiation shielding for fusion reactors. In 9th International
Conference on Radiation Shielding, 1999.
[6] Tokamak Schematic. https://www.llnl.gov/str/janfeb02/gifs/nevinsbox.jpg.
[7] T Hayashi. Neutronics assessment of advanced shield materials using metal
hydride and borohydride for fusion reactors. Fusion, 81:1285-1290, 2006.
[8] D. Richter K. seidel S. Unholzer H. Freiesleben, K. Merla. Measurements
of nuclear heating in fusion reactor mock-ups. SPIE, 2867:453-456.
[9] B. Lipschultz. A study of molybdenum influxes and transport in alcator
c-mod. Nuclear Fusion, 41, 2001.
[10] V. Rohde. Tungsten as first wall material in the main chamber of asdex
upgrade. Technical report, Max-Planck-Institut fur Plasmaphysik, 2002.
[11] Daniel Thomas Reed. An Investigation into the Synthesis and Characterisation of Metal Borohydridesfor Hydrogen Storage. PhD thesis, University
of Birmingham, 2009.
[12] K. Tomabechi. Iter conceptual design. Nuclear Fusion, 31:1135, 1991.
[13] N. Mitchell. The iter magnets: Design and construction status.
Transactions on Applied Superconductivity, 22, 2012.
22
IEEE
6
6.1
Appendix
MCNP Input File
MCNPX Visual Editor Version X_24E c
Cells
c
//W-MgBH42
1
489
-5.9 -1
-9 8
2
488
-7.92 -2 1 -9 8
3
1
-1.45 -3 2 1 -9 8
4
272
-19.3 -4 3 2 1 -9 8
5
0
-11 10 -9 8
6
0
5
7
0
-5 9
8
0
-5 -8
9
0
-5 11 -9 8
10
0
4 -10 -9 8
c
//W-FLiBe
c
1
489
-5.9 -1 -9 8
c
2
488
-7.92 -2 1 -9 8
c
3
3
-1.92 -3 2 1 -9 8
c
4
272
-19.3 -4 3 2 1 -9 8
c
5
0
-11 10 -9 8
c
6
0
5
c
7
0
-5 9
c
8
0
-5 -8
c
9
0
-5 11 -9 8
c
10
0
4 -10 -9 8
c
//W-ZrH2
c
1
489
-5.9 -1 -9 8
c
2
488
-7.92 -2 1 -9 8
c
3
2
-5.56 -3 2 1 -9 8
c
4
272
-19.3 -4 3 2 1 -9 8
c
5
0
-11 10 -9 8
c
6
0
5
c
7
0
-5 9
c
8
0
-5 -8
c
9
0
-5 11 -9 8
c
10
0
4 -10 -9 8
c
//Mo-FLiBe
c
489
1
-5.9 -1 -9 8
c
2
488
-7.92 -2 1 -9 8
c
3
-1.92 -3 2 1 -9 8
3
c
4
416
-10.28 -4 3 2 1 -9 8
c
5
0
-11 10 -9 8
c
6
0
5
c
7
0
-5 9
c
8
0
-5 -8
c
9
0
-5 11 -9 8
23
Cameron French,
22.THU
MIT
10
0
//Mo-ZrH2
1
489
2
488
3
2
4
416
5
0
6
0
7
0
8
0
9
0
10
0
//Mo-MgBH
1
489
2
488
3
1
4
416
5
0
6
0
7
0
8
0
9
0
10
0
c
c
4 -10
-9
8
-5.9 -1 -9 8
-7.92 -2 1 -9 8
-5.56 -3 2 1 -9 8
-10.28 -4 3 2 1 -9
-11 10 -9 8
5
-5 9
-5 -8
-5 11 -9 8
4 -10 -9 8
42
-5.9 -1 -9 8
-7.92 -2 1 -9 8
-1.45 -3 2 1 -9 8
-10.28 -4 3 2 1 -9
-11 10 -9 8
5
-5 9
-5 -8
-5 11 -9 8
4 -10 -9 8
Surfaces
//.20m
1
cz 12
2
cz 16
3
cz 33
4
cz 36
5
so 250
8
pz 0
9
pz 200
10
cz 40
11
cz 50
//.19m
1
cz 12
2
cz 16
3
cz 32
4
cz 35
so 250
5
8
pz 0
pz 200
9
10
cz 39
11
cz 49
//.18m
1
cz 12
2
cz 16
3
cz 31
4
cz 34
24
8
8
5
8
9
10
11
so
pz
pz
cz
cz
250
0
200
38
48
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
30
33
250
0
200
37
47
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
29
32
250
0
200
36
46
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
28
31
250
0
200
35
45
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
27
30
250
0
200
34
44
cz
cz
cz
cz
12
16
26
29
//.17m
1
2
3
4
5
8
9
10
11
//.16m
1
2
3
4
5
8
9
10
11
//.15m
1
2
3
4
5
8
9
10
11
//.14m
1
2
3
4
5
8
9
10
11
//.13m
1
2
3
4
25
so 250
pz 0
pz 200
cz 33
cz 43
5
8
9
10
11
//.12m
1
2
3
4
5
8
9
10
11
cz 12
cz 16
cz 25
cz 28
so 250
pz 0
pz 200
cz 32
cz 42
1
2
3
4
5
8
9
10
11
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
24
27
250
0
200
31
41
cz
cz
cz
cz
so
pz
pz
cz
cz
12
16
23
26
250
0
200
30
40
//.lom
1
2
3
4
5
8
9
10
11
mode
m272
n
74182.70c
74183.70c
-0.289615
m416
42092.70c
42094.70c
-0. 166756
42097.70c
-0.100286
ml
1001.70c
5011.70c
0.0718809
12025.70c
m2
1001.70c
-0.260586
$Tungsten
-0.142269 74184.70c
-0.142179
$Molybdenum,
-0.090549 42095.70c
-0.096469 42098.70c
-0.307531
74186.70c
-0.1575
42096.70c
-0.246262 42100.70c
0.727
$Mg(BH4)2 Magnesium Borohydride
0.145964 5010.70c
0.036036 12024.70c
0.0091
0.667
12026.70c
0.0100191
$ZrH2 Zirconium Hydride
26
40090.70c
0.0571095
40091.70c
m3
4009.70c
9019.70c
0.2642926
m488
14028.70c
14029.70c
-0.007095
24052.70c
-0.004171
25055.70c
-0.601748
26057.70c
-0.080873
28060.70c
-0.004546
28064.70c
-0.002264
42095.70c
-0.002412
42098.70c
m489
41093.70c
50120.70c
0.03635
50119.70c
0.014475
50122.70c
0.00165
imp:n
1 4r
nps 10000000
sdef x=dl y=d2 z=d3
sil -36 36
spi 0 1
si2 -36 36
sp2 0 1
si3 0 200
sp 3 0 1
f16:n 1
f26:n 2
f36:n 3
f46:n 4
f14:n 1
f24:n 2
f34:n 3
f44:n 4
*f54:n 1
*f64:n 2
*f74:n 3
*f84:n 4
0.1713285
40094.70c
0.0578754 40092.70c
0.0373626
0.143
$FLiBe (Li2BeF4)
0.571 3006.70c
0.0217074
3007.70c
-0.009187
-0.000482
$Steel,
Stainless 316,
14030.70c
-0.000331
24050.70c
-0.142291
24053.70c
-0.016443
24054.70c
-0.02
26054.70c
-0.037326
26056.70c
-0.014024
26058.70c
-0.001903
28058.70c
-0.031984
28061.70c
-0.001408
28062.70c
-0.001189
42092.70c
-0.003554
42094.70c
-0.003937
42096.70c
-0.004169 42097.70c
-0.006157 42100.70c
-0.002507
0.75
$Nb3Sn Niob ium-Tin
0.08145 50118.70c
0.06055
0.021475
50117.70c
0.011575
50112.70c
0 3r
1
cel=5
27
50116.70c
0.0192 50124.70c
0.002425
$ 1,
50114.70c
10
f11:n 1
f21:n 2
f31:n 3
f41:n 4
*f51:n 1
*f61:n 2
*f71:n 3
*f81:n 4
print
prdmp 10000000
10000000
1
28