Advanced fusion cycles for high-beta magnetic systems
Power balance analysis of alternative (not D-T) fusion cycles is carried out to find high efficiency and lowradioactivity cycles for fusion reactors based on high-beta magnetic systems, such as field reversed configuration (FRC), spherical tokamak, etc. Cycles based on reactions D-D, D-³He, D-⁶Li, D...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Zitieren: | Advanced fusion cycles for high-beta magnetic systems / A.Yu. Chirkov, V.I. Khvesyuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 36-38. — Бібліогр.: 12 назв. — англ. |
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| author | Chirkov, A.Yu. Khvesyuk, V.I. |
| author_facet | Chirkov, A.Yu. Khvesyuk, V.I. |
| citation_txt | Advanced fusion cycles for high-beta magnetic systems / A.Yu. Chirkov, V.I. Khvesyuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 36-38. — Бібліогр.: 12 назв. — англ. |
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| description | Power balance analysis of alternative (not D-T) fusion cycles is carried out to find high efficiency and lowradioactivity cycles for fusion reactors based on high-beta magnetic systems, such as field reversed configuration (FRC), spherical tokamak, etc. Cycles based on reactions D-D, D-³He, D-⁶Li, D-⁷Be, p-⁶Li, p-⁹Be, and p-¹¹B are considered.
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ADVANCED FUSION CYCLES FOR HIGH-BETA MAGNETIC SYSTEMS
A.Yu. Chirkov*, V.I. Khvesyuk
Bauman Moscow State Technical University, 2nd Baumanskaya Str., 5, 105005 Moscow, Russia
*E-mail: chirkov@power.bmstu.ru
Power balance analysis of alternative (not D-T) fusion cycles is carried out to find high efficiency and low-
radioactivity cycles for fusion reactors based on high-beta magnetic systems, such as field reversed configuration
(FRC), spherical tokamak, etc. Cycles based on reactions D-D, D-3He, D-6Li, D-7Be, p-6Li, p-9Be, and p-11B are
considered.
PACS: 28.52.-s; 28.52.Av
1. INTRODUCTION
We consider fusion cycles based on the following
reactions:
D + D → n(2.45 MeV) + 3He(0.817 MeV) (1a)
D + D → p(3.02 MeV) + T(1.01 MeV)
(1b)
D + T → n(14.1 MeV) + 4He(3.5 MeV) (2)
D + 3He → p(14.68 MeV) + 4He(3.67 MeV) (3)
D + 6Li → n(2.958 MeV) + 7Be(0.423 MeV) (4a)
D + 6Li → n(~0.66 MeV) + 3He + 4He + 1.794 MeV (4b)
D + 6Li → p(4.397 MeV) + 7Li(0.628 MeV) (4c)
D + 6Li → p + T+ 4He + 2.257 MeV (4d)
D + 6Li → 4He + 4He + 22.371 MeV (4e)
D + 7Be → p + 4He + 4He +16.766 MeV (5)
p + 6Li → 3He(2.3 MeV) +4He(1.722 MeV) (6)
p + 9Be → D + 4He + 4He + 0.651 MeV (7a)
p + 9Be → 4He(1.277 MeV) + 6Li(0.851 MeV) (7b)
p + 11B → 34He + 8.681 MeV (8)
In this paper we estimate the potentialities of different
cycles using power balance equation. One can
characterize the power efficiency by high value of the
plasma power gain factor: Q=Pfus/Pext>10 (Pfus is the
fusion power, Pext is the required power of external
heating). In Sec. 2 burning conditions and simple power
balance are studied. Most preferable advanced fusion
cycles for energy production in the magnetic reactor
appear to be D-3He cycles with 3He production.
Calculated parameters of low-radioactivity D-3He
magnetic fusion reactors are presented in Sec. 3.
2. IGNITION AND POWER BALANCE
Under ideal conditions the burn of the fusion plasma
with given Q value is characterised by the criterion
( )n T
k n T n T
Q P P P
i i
i
e e
τ =
+
+ − −
∑
−
3
2
1
2
1
fus br n
, (9)
where k is the Boltzmann constant, n is the total density
of fusion ions and electrons, τ is the energy confinement
time (τ=τE), T=(niTi+neTe)/n, Ti is the ion temperature, Te
is the electron temperature, Pbr is the bremsstrahlung
power, and Pn in the neutron power. Limit case Q→∞
corresponds to the ignition regime. In the calculation of n
τT criterion we assumed, that Te=Ti=T. Reaction rates are
taken from Ref. [1]. For bremsstrahlung losses the results
of numerical calculations [2, 3] are used, which takes into
account of quantum and relativistic effects.
Important parameters of fusion cycle are neutron yield
ξn=Pn/Pfus, and relative bremsstrahlung losses ξbr=Pbr/Pfus.
Results of calculation of the main parameters of different
fusion cycles are presented in Table 1. The first two
elements in the cycle designations indicate the main
reaction, then, the main reaction products used as the
secondary fuel within the catalysed cycles are shown. For
example, D-D means that the reactions (1), (2) only are
taken into account; D-D-T, the reactions (1)-(3);
D-D-3He-T, the reactions (1)-(4) etc.
The analysis of the power efficiency of fuel cycles for
the magnetic fusion reactor is based on the local power
balance equation
P P P P P
n kT n kT
Pi i e e
E
afus ext n br s+ = + + +
+
+
∑3
2 τ
(10)
averaged over the plasma volume. In Eq. (10), Ps is the
synchrotron loss power (calculated from the Trubnikov
formula [4]), Pa is the loss power of fusion products.
Note that advanced fusion cycles in magnetic reactor
require high value of β µ= 2 0 0
2p B/ (µ0 is diamagnetic
constant, p is the plasma pressure, B0 is external confining
field) to achieve high power efficiency.
Proton reactions p-6Li, p-9Be, and p-11B, where
neutrons are not born, at all, are of a definite interest.
Results of the calculation of the most promising proton
cycle p-11B are presented in Table 2 for the following
ideal conditions: zero densities of ashes (fusion products),
Ps=0, Pa=0, all fusion power and external heating power
transferred to ions. For this analysis we use recently
obtained p-11B reactivity parameter values [5]. Power
flow from ions to electrons calculated using Spitzer’s
formula, that allows calculate Te for given Ti. In Table 2,
B0 corresponds to fusion power value Pfus=5 MW/m3 at β
=1. According our calculations maximal Q value for p-11B
cycle is Qmax≈3.7 at n11B/np=0.1. Under the same ideal
conditions in p-6Li and p-9Be cycles Qmax≈0.33 (at np/n6Li,
Ti=500 keV, Te=225 keV) and Qmax≈0.23 (at np/n9Be,
Ti=200 keV, Te=130 keV), respectively. For these cycles
B0≈14 T for Pfus=5 MW/m3 and β=1.
The highest energy efficiency over all considered
advanced cycles can be obtained in D-3He and catalysed
36 Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 36-38
D-D cycles.
Table 1. Main parameters of different cycles at Te=Ti=T: D-T (nD=nT), D-3He (nD=n3He), D-6Li-… (n6Li/nD=0.3),
D- 7Be-… (n7Be/nD=0.3), p-6Li (n6Li/np=0.2), p-9Be (n9Be/np=0.1), p-11B (n11B/np=0.1).
Cycle Reactions T, keV nτT, m-3×s×keV ξn=Pn/Pfus ξbr=Pn/Pfus Qmax *
D-T 1 14 6.14×1021 0.80 0.013
D-3He 3, 2, 1 70 1.36×1023 0.01..0.06 0.3
D-D 2 100 8.84×1024** 0.38 0.65
D-D-3He-T 2, 3, 1 52 2.17×1023 0.36 0.22
D-D-T 2, 1 61 1.4×1024 0.67 0.23
D-D-3He 2, 3 55 2.58×1023 0.1 0.33
D-D-3He-3He 2, 3 56 1.72×1023 0.06 0.28
D-6Li 4, 2 170*** – 0.21 2.3 0.66
D-6Li-3He-7Be-T 4, 2, 3, 5, 1 130 1.10×1024 0.26 0.51
D-6Li-3He-7Be 4, 2, 3, 5 140 3.01×1024 0.074 0.79
D-7Be 5, 2 500*** – 0.04 1.27 3.22
D-7Be-3He-T 5, 2, 3, 1 375 2.53×1025 0.18 0.79
D-7Be-3He 5, 2, 3 375 1.03×1025** 0.04 0.97
p-6Li 6 210*** – 0 15.6 0.07
p-9Be 7 155*** – 0 8.28 0.14
p-11B 8 200*** – 0 3.56 0.39
* For anburning fuels (Q<10)
** Corresponds to Q=10. (No ignition at Te=Ti )
*** Corresponds to Qmax at Te=Ti.
Table 2. Main parameters of p-11B cycle under ideal conditions. n11B/np=0.1, Pfus=5 MW/m3, β=1.
Ti, keV 100 200 250 275 300 350 400 500
Te, keV 78 127 147 155 164 178 192 216
np, 1020 m-3 7.17 3.79 3.46 3.25 3.21 3.16 3.12 3.10
ne, 1020 m-3 10.8 5.69 5.19 4.88 4.81 4.74 4.68 4.65
B0, T 8.09 7.91 8.31 8.37 8.62 9.11 9.56 10.43
ξbr 3.29 1.41 1.36 1.27 1.31 1.40 1.48 1.68
Q 0.44 2.44 2.77 3.71 3.22 2.53 2.08 1.47
An attractive feature of D-3He fusion fuel cycle is the
possibility of creating low neutron yield fusion reactor
with a first wall lifetime 30-40 years, which is due to a
low neutron flux to the wall. A serious problem
encountered in realisation of the equicomponent D-3He
fuel fusion cycle is related to the fact that no
commercially significant source of 3He isotope is
available on the Earth. One of the possible solutions is the
delivery of 3He from the Moon [6].
To solve the problem of 3He supply low-radioactivity
cycles with 3He production can be realised [7, 8]. The
light helium to deuterium ratio about 0.1–0.3 can be
obtained in the cycles with complete 3He self-supply. In
Refs. [7, 8] conditions corresponding the low level of a
relative neutron power (5% of a total fusion power) where
obtained.
3. D-3He CYCLES WITH 3He SELF-SUPPLY IN
MAGNETIC REACTORS
In cycles with 3He self supply light helium obtained
any way is stored and than, together with deuterium, is
injected into the plasma, where the neutronless reaction
(3) is used for energy production.
We have considered the following 3He sources:
a) the light helium produced in the reaction (1a) and,
than, released from the gaseous mixture evacuated by
vacuum system;
b) the tritium produced in the reaction (1b), which is
also released from the gaseous mixture and, than,
retained for converting into 3He, as a result of the
decay: T→3He+e–+0.018 MeV;
c) the decay of the tritium produced in the blanket as a
result of the reaction of the type: n+6Li→T+4He+4.8
MeV, and n+7Li→T+4He+n–2.47 MeV.
Thus the 3He production is possible due to reaction
(1a) and (1b) in the plasma and neutron-lithium reactions
in the blanket.
To increase obtainable 3He value in the cycle so-called
selective drift pumping [9, 10] of the fusion products due
to induced weak magnetic field oscillations can be
applied.
In cycles with the selective removal of fusion
37
products, all charged fusion products, 3He and T included,
are moderated in the plasma releasing their energy to it,
than, attaining the energy ε*, their forced removal from
the plasma is expected.
Table 3. Parameters of D-3He reactors with 3He self-supply.
Parameters
D-3He reactors with 3He self-supply
Tandem
mirror
FRC Spherical
tokamak
Classical
tokamak
Plasma temperature T, keV 65 70 40..50 40..50
Vacuum magnetic field B0, T 5..17 8 5 11
Plasma beta β 0.7 0.5..1 0.4..0.6 0.09..0.15
Synchrotron wall reflectivity Γs 0.65 – 0.65 0.92
Required confinement time τ⊥, s 14 2 5 14
Plasma radius a, m 1 2 2 2
Plasma length L, m 40..60 5 – –
Big toroidal radius R, m – – 3 6
Plasma elongation κ – 2.5 3.7 2.5
Plasma current Ip, MA – – 87 38
Total fusion power Pfus, MW 650..900 950 1500 2500
Power gain factor Q 10 20 20 20
Relative bremsstrahlung losses ξbr 0.25 0.21..0.25 0.4 0.4
Relative synchrotron losses ξs 0.1 ~0 0.06 0.33
Neutron yield ξn:
with selective pumping system 0.05 0.04..0.06 – 0.12
with no pumping 0.15 0.12..0.21 0.13 –
First wall neutron flux qn, MW/m2:
with pumping ~0.13 ~0.5 – 0.14
with no pumping ~0.4 ~1.5 ~0.4 –
Selective drift pumping can be used for the forced
selective removal of the charged products moderated to
the energy ε*~200-400 keV. Such a process does not
affect the fuel confinement time. The removed 3He and T
are stored and the obtained 3He is used as one of the D-
3He fuel component. A given cycle has some important
advantages. First, the major part of tritium has no time for
the interaction with deuterium in the reaction (2) that
allows one to obtain a great amount of 3He than that in the
first variant. Second, since the reaction (2) is negligible,
the neutron flux to the first wall is essentially reduced in
comparison with cases with no selective removal. Here, it
is important that the reduction occurs due to the most
dangerous high energy neutrons with the birth energy ε
0=14.1 MeV.
In this work we consider the possibility of high
efficiency operating of D-3He reactors based on different
magnetic systems: tandem mirror, field reversed
configuration (FRC), classical and spherical tokamaks.
Parameters of magnetic reactors using D-3He cycles with
3He self-supply are presented in Table 3. Parameters of a
tandem mirror system we calculate according the model
developed in Refs. [2, 3]. For the FRC power balance
model [11] is used, and for classical and spherical
tokamaks calculation model of Ref. [12] is used.
4. CONCLUSIONS
In the framework of presented study the most optimal
low-radioactivity fusion cycle appears to be D-3He cycle.
Problem of 3He supply for D-3He reactors can be solved
by the use of D-3He cycles with 3He self-supply.
According to carried out calculations highest power
efficiency of magnetic fusion reactors with D-3He cycles
corresponds the high-beta confinement systems such as
FRC and spherical tokamak.
REFERENCES
1. Feldbaher R. Nuclear Reaction Cross Sections and
Reactivity Parameter. IAEA, 1987.
2. V.I. Khvesyuk, A.Yu. Chirkov // Tech. Phys. Letters,
2000, v. 26, No. 11, P. 964.
3. A.Yu. Chirkov, V.I. Khvesyuk // Fusion Technol.,
2001, v. 39, No. 1T, P. 402.
4. B.A. Trubnikov, in Reviews of Plasma Physics, Vol.
7 (Ed. M.A. Leontovich), Plenum, New York, 1979
5. W.M. Nevins, R. Swain // Nucl. Fusion, 2000, v. 40,
P. 865.
6. L.J. Wittenberg, J.F. Santarius, G.L. Kulcinski //
Fusion Technol., 1986, v. 10, P. 165
7. V.I. Khvesyuk, A.Yu. Chirkov // Tech. Phys. Letters,
2001, v. 27, No 8, P. 686.
8. V.I. Khvesyuk, A.Yu. Chirkov // Plasma Phys.
Control. Fusion, 2002, v. 44, No. 2, P. 253.
9. N.V. Shabrov, V.I. Khvesyuk, // Fusion Technol.,
1994, v. 26, P. 2.
10. V.I. Khvesyuk, N.V. Shabrov, A.N. Lyakhov //
Fusion Technol., 1995, v. 27, No. 1T, P. 406.
11. A.Yu. Chirkov, V.I. Khvesyuk // Fusion Technol.,
2001, v. 39, No. 1T, P. 406.
12. A.Yu. Chirkov // Voprosy Atomnoi Nauki i Tekniki,
Fusion Ser., 2001, No. 2, P. 36. (in Russian)
38
39
Qmax *
ne, 1020 m-3
Q
Tandem mirror
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-77873 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T19:03:21Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Chirkov, A.Yu. Khvesyuk, V.I. 2015-03-08T20:09:14Z 2015-03-08T20:09:14Z 2002 Advanced fusion cycles for high-beta magnetic systems / A.Yu. Chirkov, V.I. Khvesyuk // Вопросы атомной науки и техники. — 2002. — № 5. — С. 36-38. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 28.52.-s; 28.52.Av https://nasplib.isofts.kiev.ua/handle/123456789/77873 Power balance analysis of alternative (not D-T) fusion cycles is carried out to find high efficiency and lowradioactivity cycles for fusion reactors based on high-beta magnetic systems, such as field reversed configuration (FRC), spherical tokamak, etc. Cycles based on reactions D-D, D-³He, D-⁶Li, D-⁷Be, p-⁶Li, p-⁹Be, and p-¹¹B are considered. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники ITER and fusion reactor aspects Advanced fusion cycles for high-beta magnetic systems Article published earlier |
| spellingShingle | Advanced fusion cycles for high-beta magnetic systems Chirkov, A.Yu. Khvesyuk, V.I. ITER and fusion reactor aspects |
| title | Advanced fusion cycles for high-beta magnetic systems |
| title_full | Advanced fusion cycles for high-beta magnetic systems |
| title_fullStr | Advanced fusion cycles for high-beta magnetic systems |
| title_full_unstemmed | Advanced fusion cycles for high-beta magnetic systems |
| title_short | Advanced fusion cycles for high-beta magnetic systems |
| title_sort | advanced fusion cycles for high-beta magnetic systems |
| topic | ITER and fusion reactor aspects |
| topic_facet | ITER and fusion reactor aspects |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/77873 |
| work_keys_str_mv | AT chirkovayu advancedfusioncyclesforhighbetamagneticsystems AT khvesyukvi advancedfusioncyclesforhighbetamagneticsystems |