Consideration on Nuclear Fusion in Plasma by the Magnetic...
Transcript of Consideration on Nuclear Fusion in Plasma by the Magnetic...
Consideration the Magnetic
on Nuclear Fusion
Confinement as a in Plasma by
Heat Engine
Yoshio Tsuji
Department ofNuclear Engineering, Faculty ofScience
and Technology, Kinki University, Higashiosaka, 577.
(Received Junuary 22, 1990/Revised Manuscript Received June 4, 1990)
Abstraet
I
In comparing nuclear fusion in plasma by the magnetic confinement with nuclear fission and
chemical reactions, the power density and the function of a heat engine are discussed using a new
parameter G introduced as an eigenvalue of a reaction and the value of q introduced to estimate the
thermal efficiency of a heat engine. It is shown that the fusion reactor by the magnetic confinement
is very difficult to be a modern heat engine because of the lack of some indispensable functions as a
modern heat engine. The value of G and q have the important role in the consideration.
Keywords :
reaction eigenvalue G, practical thermal efficiency, energy loss rate, quantity q, power
density, energy carrier, combustion system, explosive combustion, stationary combustion,
fusion reactor,
l . Introduction Power density as well as the function of
important factor estimating an efficiency of a system as a heat engine should be studied on nuclear fission and chemical combustion systerfrs.
combustion system is a heat engine. Nuclear that basis in comparison
very f usion
with
We introduce a new parameter G, eigenvalue of a reaction, having a role to describe the power density under the function of a certain corribus-tion system. Here~ combustion systems are classified as usual into three types, which are the continuous and explosive combustion, the pulsive and ex-plosive combustion and the stationary combustion. We also introduce the value q to define the practical thermal efficiency as a function of power density together with G. Then we noticed that G values of modern heat engines are very large and nearly about the same value although the G value might not exceed some upper limits to keep nature stable on the earth. Considering these problems, we discuss fusion reaction in the magnetically confined plasma for a heat engine.
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2. Eigenvalue of a reaction. G 2. I Introduction of G
The power density P is, in general, expressed as fo.llows;
P = e <av> nl n2 (1) where e is the generated energy by a reaction, a is the cross section of the reaction at a relative speed v of particles, and n* and n, are the density
l) < av> stands for the of the fuel and the auxiliary material, respectively. value of av averaged over the Maxwell distribution. This equation is usually used for the analysis of fusion in the magnetically confined plasma, but it is possible to apply it to nuclear fission and chemical combustion to compare the power density. For the thermal reactor, n* and n = are the number
n2 ・density of U-235 and thermal neutrons, respectively. Then the role of is to control the combustion. In the case of the usual CH* combustion in air, n* and n, aie the density of CH* and 0= , respectively. O, is supplied to the system together with N, as air and the supply is enough to achieve the perfect combustion in a short time. Although the process of chemical reaction in a gas state is very complicated, eq (1) is reasonable if s is taken to be the total energy generated in the perfect combustion of a CH 4 molecule. Then the characteristic ~nergy generation of a reaction can be defined' for any typ,e of. combtistion, sys,t~Ip as ' follow~;
G = ~<av> [~V, ~n3 s~l]・ , (2) Power den~ity is a product of G, n and n. . The value of G is
proper to a reaction and varies sensitively with the energy of reaction par-ticles. However, if the reaction temperature is settled in a constant range to keep the coinbustion stable for each practical system, ,the power density will be simply controlled by n * and n. .
2. 2 Calculated G values for typical reactions For the evaluation of G, typical reactions are selected in the field of
nuclear fusion, nuclear fission and chemical combustion, as fol,lqws;
III
Table 1 G Value and the data
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~~~7cl ~'~'~'="R~l^~~ Consideration on Nuclear Fusion in Plasma by ~J_+ the Magnetic Confinement as a Heat Engine
D (0.1) + T (0.1)- 42He (3.5) + n (14.1) + 17.6 MeV (3) 2~~U + n ~ 94Sr (90) + I~~Xe (90) + 2n (2) + 208 MeV (4)
38 = CO, (3) + 2H.O (3) + 210.8 kcal/moi (5) CH* + 20,
where the numbers in the parenthesis are particle energy in MeV for eq (3) and (4) and eV for eq (5). Needless to say, eq (4) is one of the probability of fission process. Table I shows the calculated results of G values ac-cording to ~qs. (3), (4) and (5).
2. 3 G value in nature The values of e are plotted against <av> in Fig. 1, where the each
I
11
10
9
s8
>7 06 5
,04 noo
-3 2 1
O
GD
G2
G1
G I ; D-T fusion G2 : U-235 fission G3 ; CH4 combustion GH : H2 combustion G D ; D-Dfusion s : Standard value of G
modern heat engine
3 -1 Gs =1 xlO 14 ~ eVm s
G3
GH
II
-24 -23 -22 -21 -20 -1 9 -1 8 *1 7 -1 6 -1 5 -1 4 -1 3
log < 6v> m 3 s ~1~~-
Fig. I Eigenvalue of reaction
oblique line expresses a constant G value. Prom Fig. l, it is clear that Gl (D-T), G2 (U-235) and G3 (CHL~) exist around the value of 10~14 eVm3 s~l while GD (D-D) is about 11103 times as large as Gl (D-T). The modern heat engine is supported by the large value of G2 or G3. G I i,s also large enough to produce the power density as a modern heat engine. However, GD is so small that the fuel density nl and/dr n 2 should be increased by 103
times to obtain the same power density as D-T reaction. GH rs a little smaller than G3 but H2 is still expected to be usable for the fuel of the modern heat engine, since n I can be large enough to obtain the high power density.
2. 4 Power density and introduction of q value Consider the Carnot cyc, Ie, in which energy Ql is given to a system
at the temperature Tl [K] and energy Q2 is removed from the system at T2 [K]. Then, the thermal eff.iciency rl is expressed as follows;
n = (Tl-T2)/Tl' (6) 73
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When it is provided that a practical heat cycle needs more energy Q 3 than Q I of the Carnot cycle ( Ql + Q3 is given to the system at Tl and Q 2 + Q 3 is removed from the system at T2), then the thermal efficiency of this cycle nR could be expressed as follows;
Ql+Q3-Q2-Q3 Ql-Q2 Ql Tl-T2 ( I Q3 ) (7) Ql ~Q 2
n R X. = Ql+Q 3 Q I Ql+Q3 Tl Q l+ Q3 Ql+ Q 3
As shown in eq (7), nR is a product of the thermal efficiency for the Carnot cycle and a factor less than unity representing the differenc~ frlom the Carnot cycle. Supposing that the generated power density P eVm s and the energy loss rate L eVm~3 s~1 originated from Q3 are homogeneous and stationary in the burning area V m3, we obtain the following equations.
P - ( Ql+Q3)/(Vt), L - Q3/(Vt), (8) where t(sec) is the tim~ for adding or removing energy. Then the quanuty q is introduced.
q = Q3/(Ql+Q3) = L/p (9) Substituting q =L/P, the relation between Tl and T)R can be described by
the following equation.
nR= n(1-q). (10) The temperature of the construction material, including safety factor,
could not exceed 900K in general. Assuming that the atmospheric tempera-ture is 300K, the therma, efficiency of the Carnot cycle becomes n ・= 213. However, nR of the conventional power plants, the obtained value in prac-tice, is about 0.4,5) which is 60b/o of the ideal n . On the other hand, the
maximum temperature of LWR is limited to be about 600K because of the boiling of the moderator water. When the Carnot cycle (Tl = 600K, T2 = 300K) is assumed as the LWR system, n = 1/2 should be obtained. nR of LWR is about 0.32~) which is 640/0 of the ideal n . It is supposed that the difference between 600/0 and 640/0 comes from the difference of q related to the ower densit . The ower densit of the conventional plant and LWR is p y p y 3 e) about the order of 10MW/m3 7) 100MW/m , respectively. The value of q decreases with increase of P , since L is partially a function of P but also includes a constant value regardless of P. The power density of a heat en-gine is composed of two parts, G and nl n2 in eq (1). The former is a proper value of a reaction but the latter depends on the combustion system. For a reaction having small G value, special consideration is necessary to ob-
Comparing the fusion reaction of D-D with that of tain the large nl n2. D-T, nl n2 of D-D must be 103 times larger than that of D-T. Is the magnetic confinement of plasma possible to achieve this difficult task ? 2.5 Temperature coefficient of G value
G value varies with the energy of reaction particles. The variation of G in the operation temperature range is shown in Fig. 2. This figure was conducted from Table I and the published data.8) The nuclear fission in eq (4) is controlled by the thermal neutron density, and G2 is supposed to be constant in the operation temperature range, since the thermal neutron cross section complies with 1/v law.9) The chemical reaction shown in eq (5) is a combustion in a gas state. The cross section of a molecule was es-
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研究論文Consideration on Nuclear Fusion in Plasma by
the Magnetic Confinement・as a Heat Engine辻
timated by4πr2,where r 蓋s the radius of a m’olecule,and the cross sectionis proportional to T1〆2 .10》 Therefore,G changes a 董itde in the operation
range of temperature,that is,G3 does have the poss董tive temperature coef-ficient. The nuclear fusion in eq (3》seems to be achieved by the magnet重cconfinement of the plasma at about O.001MeV. However,Gl ste6ply risesup in the operatlon range(0.001to O.01MeV》and the temperature coefflcientseems very difficult to be compensated by the value ofη1 n2which in-creases with increase of the magnetic force. Only the way to control thecombustion by the magnetic confinement is to keep the p豆asma stationary atthe top of the curve,that is about O。08MeV(Fig.2)。 Is lt possible to ob-
tain a far stronger magnet孟c field than the present experimental use?
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一2 -1 11095caleCH4c・mbustionandU-235fissioneV一ひ 9鞠レ D-T reac亀ion MeV
Fig.2VariationofGintherangeofthe controltemperature
3Combustion3.1Combustion system Combustion systems of heat engines can be classified into three types,as fol10WSl (1)continuous and explosive combustion(bo孟ler bumer》 (2》pulsive and explosive combustion(intemal combust垂on engine) (3)gentle and stationary combustion(thermal neutron reactor).(1)and (2)are the explosive thermal reaction in a gas state and t紅e com-
bustion itself can not be controHed, in general. Then, the power dens童tyshould be controlled by nユ and n2. A constant power dens重ty is supportedand also limited by the total Iatent heat of the fuel supplied to the combus-
tion area per second. On the other hand,(3)is the sohd state combustionand it is possible to control the combustion itself accord孟ng to the neutrondens重ty n2 with the control rods. Fusion by the magnetic confinement ofplasma is the thermonuciear reaction in a gas state,and that should be the
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核融合研究第64巻第1号 1990年7月
explosive combustion. Provided that the combust重on is controlled only by themagnetic confinement,the force should be strong enough to keep the plasmatemperature at O.08MeV as mensioned before(See Fig.2).392St6rage fuel in Oombustion area A ¢onstant quantity’of CH再, sent into the combust玉on area succes-sively,releases all the latent energy in a short time,bUt the released energy
will be limited to a constant value. However,thermal neutron reactors storethe fuel for 3 to 5 years in the combustion area and very sman portionbums gendy and stationarHy because of the solid state combustion as men-tioned before. The fuel is necessary to keep the criticality and the powerdensity. Large fuel quantity is also necessary to nuclear fusion as well asfissi・n,alth・ughthebumingratepersec・ndis・nly10伽6P・rti・n・fthestorage fueL Hdwever, the 星ack of the εuaranty to suppress the powerbelow a constant value 玉s a serious problem,since it is the explosive com-bustion.3.3 Share of generated energy The generated energy is so large that those particles which carry theenergy should not directly contact with the construction materia1. In eq(5),
one CO2 molecule carries about3 eV,and-this is 40 times of O.075 eV(900K). The molecules of the reaction product repeat comsion with otherparticles, and a cluster is produced around the reaction center. The par-ticles shared the energy in the cluster wm diffuse to outside of the cluster,
thus the generated energy wiH be shared among many carriers in smallenergy in a short time before contact to the wall of the co“tainer. In eq(4),a sma藍l portion of the generated energy is carried out from the cluster
by Y ray, electrons, neutrons and neutrinos, but a maJor portion of theenergy is carried by the two fission products,e.g.』Sr and Xe. The clusterthus produced by the reaction products is supposed to be extremely small insize, since they are heavy chafged part蓋des. The state, 藍nside of theduster, may be 孟n an ultra high temperature plasma because the energyshould be released only in a shQrt range of sintered UO2? The energy inthe cluster wm diffuse w量thin the sintered UO2 by phonon and transf¢rred to
the water flowing outside of the sheath can. The sintered UO2 fuel and thesheath can 童5 used to be changed every 3 to 5 years. In eq (3》, no
reasonable carr蚤er can be ,to share the into small produced
energies because aU the partic監es
temperature. This mechanism ofengine but the combustion of themechanism. The failure of thereason.11)12) The problem 藍sof 孟ncident partic塾es.
4Conclusions Introducing parameter G and
magnetlc confinement in terms of量t is expected that the fusion
engine for the reasons (1)Reaction eigenvalue G has a
theoperat孟onrange. (2》The thermonudear fusion by combustion,that is similar to (3》Only a small portion of the burnt iれ an explosion。 There is
power of the chemical the fuel inserted to the burning
generatedenergy
are already heated up to an ultra high
shar量ng energy is ind重spensab監e to a heat
plasma fus量on system does not have this first wall (disruptioη》 is caused by this
not on量y the energy fluence but the energy
q value,we discussed the fusion by the
function of a heat engine. As the result,
system is very d孟fficult to operate as a heat
mentioned below. large possitive temperature coefficient in
the magnetic confinement is an explosive the thermochemical react董on in a gas state. storage fuel in the combustion area 玉s
no guar3nty of the power limitation. The
combustion 五s h血量ted by the whole latent heat of area,at the time of each explosion.
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Consideration on Nuclear Fusion in Plasma by
the Magnetic Confinement as a Heat Engine 7~t
<4) In the case of the chemical reaction, sharing the geneirated energy to the carriers, the small energy of a carrier does not give a serious damage to the wall of the furnace or cylinder liner. This is one of the functions to make the large energy available in a heat engine, and the thermal neutron reactor has the same function. However the fusion system has no such a function.
(5) G value of D-D reaction is about l0~3 times as large as that of D-T. To obtain the similar density, n I n 2 of D-D system must be 103 times for D-T system, otherwise the q value becomes large and the thermal ef-ficiency will be too small as a modern heat engine. By consideration of these reasons, Solid State Fusion Fission Combined Reactor (SFCR) is pro osed to make nuclear fusion reaction available for a modern heat engine. 13
Acknowledgment
The author would like to thank Professor W. Unno <Kinki Uni'versity) and Dr. H. Atsumi (Kinki University) for the discussion.
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