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Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 43
Studies on the Performance of ITER90H-P
Fusion Reactor Considering the D-T and D-3He
Fuel in the Steady-state
S. N. Hosseinimotlagh1, S. Kianafraz2
1Department of Physics, Shiraz branch Islamic Azad University, Shiraz, IRAN
2Department of Physics, Payam Noor University of Mashhad, Mashhad, IRAN
ABSTRACT
In this work, the performance of fusion reactor ITER90H-P with considering D–T and D-3He fuels areexamined by writing the dynamics equations on thesystemreactor. Therefore, we solve these equations analytically in thesteady state. In this state we determine the optimum conditions for achieving the maximum fusion gain. In addition, we ignore the impurities because we need to high performance points without impurities. Our calculationsinthis papershow that we have maximum fusion gain for D-T and D-3He fusion reactions in steady state at resonance temperature Kev70 for D-T fusion reaction respectively .Their maximum values of fusion gain are equal to 6.01for D-T fuel-and the 0.012 for
3D He , respectively. Therefore, currently, using 3D He as a fusion fuel is
not recommended. Key words: steady, fusion gain, power, helium, tritium.
INTRODUCTION
The aim of fusion research is to utilize the energy source of the sun and stars here on earth:
A fusion power plant is to derive energy from fusion of atomic nuclei. Under terrestrial
conditions this can most readily be achieved with the two hydrogen isotopes, deuterium
and tritium. These fuse to form helium, thus releasing neutrons and large quantities of
energy: One game of fuel could yield in a power plant 90,000 kilowatt-hours of
energy, i. e. the combustion heat derived from 11 tons of coal. The basic substances
needed for the fusion process, viz. deuterium and lithium, from which tritium is produced
in the power plant, are available throughout the world in almost inexhaustible quantities.
Like a coal fire, a fusion fire does not happen on its own, but only when the appropriate
ignition conditions are present. As regards the fuel – a low-density, ionized gas, a
“plasma” it needs an ignition temperature of 100 million degrees. This high temperature
precludes the plasma from being directly confined in material vessels. Any wall contact
occurring would immediately cool the hot gas. Instead, use is made of magnetic fields,
which confine the fuel as thermal insulation and keep it away from the vessel walls. The
principle of deriving energy in this way was first realized in the JET (Joint European
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 44
Torus) device at Culham, UK, the world’s largest fusion experiment at present. It
was jointly planned and built by Europe’s fusion scientists and has also been jointly
operated since 1983. All scientific and technical objectives specified in the
planning have meanwhile been attained or even exceeded. In 1997 a transient fusion
power of 16 megawatts was achieved. More than half the power needed to heat the
plasma was regained through fusion. However, the JET plasma with its volume of
80 cubic meters is too small to provide a net energy gain. This will be the role of the
ITER (Latin for the “way”) international experimental reactor. In its plasma volume of
about 830 cubic metres a fusion power of 500 megawatts is to be produced, this being
ten times as much as is needed to heat the plasma.
Humanincreasing needfor energyhas ledtosignificant progresses to be doneinachieving
the values of temperature, density and confinement time and required parameters to
builda fusion power plant. One of themajor projectsin which scientists,
designersandengineers fromdifferent countriesare doing ,to design anuclear fusionreactor,
is ITERtokomak.The ITER project itself began at the Geneva Summit in 1985,
with a device designed to be capable of a steady-state, self-sustaining fusion reaction
with a significant net energy gain. ITER Conceptual Design Activities (CDA) began in
1988 and were completed in 1990, carried out jointly by the U.S., E.U., Japan and Russia
under the auspices of the IAEA. Engineering Design Activities (EDA) commenced in 1992
and finished in 1998 resulting in a complete design. Financial constraints
demanded a reduced-cost approach, though, and a second EDA period of 1999-2001
completed the current ITER-FEAT (Fusion Energy Amplifier Tokamak) design
(Figure 1).
Figure 1: The ITER-FEAT device and major components[9,10,11]
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 45
With these improvements, it is hoped that ITER will also allow for the possibility
of reaching a more important goal, one that will be essential for a fusion power plant.
For a deuterium-tritium plasma, once heating of alpha particles (the Helium nuclei
product of fusion), not by external input but by the fusion process itself, is equal to the
heat loss through the vessel walls and diverter, the plasma becomes self-sustaining
and is said to be ignited, or burning. External heating can be turned off, and the
plasma will continue to exist and induce fusion. With no heating (energy input), the Q
factor ratio tends to infinity and the fusion process is controlled in steady state only by the
fuelling rate to the torus.
In order tonuclear fusionreactoriseconomicallyaffordable , thesystem must stay for a long
time in the burning plasma steady-state with performance points athighQ .HereQisthe
ratio ofauxiliary power to fusion power which is calledfusion. Thus, in this paper,
underthese conditions we will have study on the behaviorofITER 90 HP fusionreactor in
the steady- state fortwo fusion fuel such as D - T and 3D He with taking into account
thesystemtemperature variations. Finally, wedetermine the required conditionsto
achievehighfusion gain. The rest of the paper is organized as follows: in section 2,
Reactivity parameter for D-T and 3HeD fusion reactions is presented.in section
3,Nonlinear point Kineticequationsgoverning on the ITER 90 HP fusion reactor ITER 90
HP for the D - T and 3D He fuel are stated, and these equations are solved analytically.
Section 4 is concerned with these equations are solved analytically .Section 5 discusses
the results of the Calculation andcomparison of required parameters forstudy of ITER90H-
pfusion reactoratsteady stateforbothfuel D T and 3D He Finally, section 6 contains
some conclusions concerning this work and further extensions and research suggested
in this direction.
Table 1: ITER machine parameters[1,2,6].
SYMBOL QUANTITY VALUE
I Plasma Current 22.0MA
R Minor Radius 2.15m
A Major Radius 6.0m
B Magnetic Field 4.85T
𝑘𝑥 Elongation at X 2.2
𝑘𝛼 Alpha particle confinement Cte 7
𝑘𝐷𝑇 DT particle confinement Cte 3
𝑘𝐼 Impurity particle confinement Cte 10
𝛽𝑚𝑎𝑥 Beta limit 2.5I/aB=5.3%
V Plasma volume 1100m^3
REACTIVITY PARAMETER FOR D – T AND 3HeD FUSION REACTIONS
This paper , presents a strategy for the development of 3D He fusion for terrestrial and
space power .the approach relies on modest plasma confinement progress in alternate
fusion concepts and on the relatively less challenging engineering, environmental and
safety features of a 3D He fueled fusion reactor compared to a D - T fueled fusion
reactor. The 3D He benefits include full-lifetime materials reduced radiation damage,
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 46
less activation, absence of tritium breeding blankets, highly efficient direct energy
conversion, easier maintenance and proliferation resistance. The main fusion fuels are :
D + T 4He + n + 17.6 MeV
D + 3He 4He + p + 18.4 MeV
Also another important parameter is reactivity of D - Tand 3HeD which depends on the
temperature.
a) Bucky Reactivity is temperature dependent (T (keV)) and isgiven by:
2 3 4152 3 4 6exp (1)rDT
av a aT a T a T a T
T
Here ia and r are given in the Table 2.
Table 2: Numerical values of ia and r parameters for D - Tand 3HeD fusion
reactions using Bucky formula.[3]
DT D-3HE
2.7764468×101 2.1377692×101 a1
3.1023898×101 2.5204050×101 a2
2.7889999×10−2 7.1013427×10−2 a3
5.5321633×10−4 1.937545×10−4 a4
3.0293927×10−6 4.9246592×10−6 a5
2.5233325×10−8 3.9836572×10−8 a6
0.3597 0.2935 R
b) Bosch-Halereactivity is given by the following formula
3
1 2 3(2)
r
C em C T
، and GB are:
12 3
4(3)GB
2 4 6
3 5 7
(4
1
)
1
TT C T C TC
T C T C TC
2
1 2 2 (5)G rB Z Z m c
Theconstants values of 1C to 7C in theseequations for different fusion reactions are
given.inTable(3) .
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 47
Table(3): The constants values of 1C to 7C for different fusion reactions[4]
D3HE DDP DDN DT
5.51E-10 5.66E-12 5.43E-12 1.17E-09 1C
6.42E-03 3.41E-03 5.86E-03 1.51E-02 2C
-2.03E-03 1.99E-03 7.68E-03 7.52E-02 3C
-1.91E-05 0.00E+00 0.00E+00 4.61E-03 4C
1.36E-04 1.05E-05 -2.96E-06 1.35E-02 5C
0.00E+00 0.00E+00 0.00E+00 -1.07E-04 6C
0.00E+00 0.00E+00 0.00E+00 1.37E-05 7C
1124572 937814 937814 1124656
2
rm c
keV
According to theabove equations and the data in Tables(2) and (3) we plotted the v
versus temperature for the fusion reaction of D – T and 3HeD for both of Bucky and
Bosch-Hale formulae.
Figure2: Comparison of the graphs of fusion reactions reactivity variations for a) D - Tand
b) 3HeD versus temperature by the two methods, Bucky 3 1
.( . )
DT Bcm s
،
3
3 1
.( . )
D He Bcm s and Bosch-Hale ( 3 1
.( . )
DT B Hcm s
3
3 1
.( . )
D He B Hcm s
As shown in Figure2-a , the reactivity of D – T fusion reaction is greater than 3HeD .
Because < 𝜎𝑣 >DT at 70 kev temperature has a maximum value thus 70 kev is temperature
resonance.the value of D – T reactivity at this temperature approximately 10 times is
greater than 3HeD .By viewing the obtained numerical values and Figure2-b we find
that the difference between the two ways of calculating reactivity is minimal and since that
the method of Bucky is newer than Bosch-Halein our calculations we use this.
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 48
NONLINEAR POINT KINETIC EQUATIONS GOVERNING ON THE ITER 90 HP FUSION
REACTOR ITER 90 HP FOR THE D - T AND 3D He FUEL
Inthiswork, wehave used fusionreactor in which approximately particle energy
balanceequationsfor two D - T and3D He fuel are given by:
a)Nonlinear point Kineticequationsgoverning on the D – T fuel
2α α DT (6)dn n n
( ) dt τ 2
DTv
2DT DT DT n
DT d
(7)dn n n n
2 ( ) dt τ 2 τ
DTv
n n
d
(8)dn n
sdt τ
I II
I
(9)dn n
sdt τ
auxohmic rad
E
(10)dE E
P P P Pdt τ
b) Nonlinear point Kinetic equations governing on the 3D He fuel
3
3
2α α D He
α
ndn n ( ) (11)
dt τ 2 D Hev
3 3 3
3
3
2D He D He D He n
dD He
dn n n n2 ( ) (12)
dt τ 2 τD Hev
n n
d
(13)dn n
sdt τ
I II
I
(14)dn n
sdt τ
auxohmic rad
E
(15)dE E
P P P Pdt τ
In these equations, nI و nn , 3D Hen , nDT , nα are the alpha particle, deuterium-tritium,
deuterium-helium3,and the neutral fuel (defined as the number of fuel atoms divided by
the core volume) and impurity densities, respectively. is the confinement time for the
alpha particles, S is the refueling rate , τDT , 3D Heτ are the confinement time for ionized
fuel particles of D , T and 3 ,He D , respectively.τd is the controller lag time ,E is the
plasma energy,τE is the energy confinement time,τI is the confinement time for the
impurities,SIis the impurity injection rate, Q∝= 3.52MeV is the energy of the alpha
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 49
particles. P , Paux , radPohmic
,P , iP and fu
P are the alpha power, auxiliary power ,
Ohmic power, radiation loss, the net plasma heating power and fusion power
,respectively that are given for D – T and 3D He fuels in the following:[5]
2DTnP ( ) (16 )
2DT DT DTv Q a
3
3 3 3
2D Hen
P ( ) (16 )2D He D He D He
v Q b
2
(17 )
2
2
24
3
DTauxDT DTDT
E
DTohmic bDT
DTDT
DT
a
nEP v Q
P A n n
En n
N
3
3
3 3
3 3
3
3
3
2
(17 )
2
2
24
3
D He
D HeauxD He D HeE
ohmic bD He D He
D He
D He
D He
b
nEP v Q
P A n n
En n
N
,
iE i
Nare the total energy and
density for 3( , )i DT D He
:
(18 )3
2DT DT aE N T
3 3 (18 ) 3
2D He D HebE N T
and
( (19) )12 3DT I IDT DT Z anN n n
33 32 3 ( 1 (19) )I ID He D He D Hen bN n Z n
2 (20 )bDTradDT eeffDTaA Z n TP
3 3 3
2 (20 )bD HeradD He eeffD He
A bZ n TP
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 50
where
3
37 (21 )4.85 10bDT
Wma
keVA
3
337 (21 )5.35 10
bD He
Wm
keVbA
The effective charge (ieff
Z )and electron density(ien ) for D – T and
3D He are:
(22 )4
2DT DT
effDT
DT DT
an n
Zn n
3
3
3
3
3
(22 )4
2D HeD He
effD He
D HeD He
bn n
Zn n
eDT DT αDT I I (23 )n n 2n Z n a
3 3 3 I IeD He D He αD He(23 )n n 2n Z n b
Where ZI Is the atomic number of impurities.
2ohmicDT
(24 )P η jDT a
3 32
ohmicD He(24 )P η j
D Heb
j is the plasma current density and n is electron density such that
5 65 10 1.5 10j mA and 3 190 14 10en m . η is the Spitzer resistivity in
which for D – T and 3D He we have:[7,8] 3
4 2
3
2
3(25 )
1.03 10
ln3.14
DT effDT
effDT
a
T Z
T
z e n
3 3
3
34 2
32
3(25 )
1.03 10
ln3.14
D He effD He
effD He
b
T Z
T
z e n
Here T and e are the electron temperature and charge such that :
191.6 10e C
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 51
(26)i ii i
i auxrad ohmicP P P P P
Where i=DT,D3He. and
2
DT
fuDT(27)
nP σv
4 DT DTQ
3
3 3 3
2
D He
fuD He(28)
nP σv
4 D He D HeQ
Also,the gain (Q)ofthistype of reactorfor theD - Tand 3 HeD reactionsD - Tare given in
the following:
(29)DTfuDT
auxDT
P
PQ
3
3
3
(30)D He
fuD He
auxD He
P
PQ
Also from the plotting of equations (24-a) to (25-b) )we have two-dimensionalandthree-
dimensionalgraphs of resistivity and Ohmic power variations for ITER 90 HP fusion
reactor in terms of electron density and temperature for D – T and 3D He in the
temperature interval 0-100 kev.(see figures (3) and (4)).
Figure3: Comparison of two-dimensionalresistivitycurvesof twofuels a) D T b) 3D He at three
temperaturesT = 10 keV, T = 70 keVandT = 100 keVin terms of electron density variations.
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 52
a)
b)
Figure 4: Comparison of two-dimensionaldiagramsoftheOhmicpower for two fuel a)D-T
b) 3D He at threedifferentcurrent density, 6
2( )0.5 10
A
mj ، 6
2( )1 10
A
mj and
6
2( )1.5 10
A
mj
in terms of the electron densityvariations.
From viewing oftwo-and three-dimensional graphs of resistivity and Ohmicpowerfor both
D T and 3HeD fuelwe findthatbothresistivity ( ) andOhmicpower )( ohmicP decrease by
increasing of electron density ateach temperature but increase by
decreasingtemperature.Energyconfinementtimeof the reactor ITER90H-P is given by:[2]
τE = f 0.082 I1.02R1.6B0.15Ai0.5 kX
−0.19p−0.47 (31)
Where the isotopic number for 50:50 D-T mixture percentage is 2.5. The factor scale f
depends on the confinement situation. I ، R ، Band Pare plasmacurrent, plasmaradius,
toroidal plasma field and net plasmaheating respectively, in which its numerical values
are given in Table(4) .
Table(4): Numerical values of ITER90H-P fusion reactor[6]
f 0.425 B Tesla 4.85
mAI 22 i
A 2.5
mR 6 Xk 75
MWP 75
Confinement times in terms of different values are scaled with energy confinement time τE
as τd = kdτE ,τα = kα τE ,τDT = kDT τE and 3 3 ED He D He
τ k τ.
Inaddition, inourcalculations we ignore of impurities because we interested to free
conditions of impurities.
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 53
RESULTS AND DISCUSSION
Note that , the values ofvariables in which obtain inthe steady-state for fusion reactor
ITER90H-p are shown withalineabove them.So,thenumerical valuesof thesevariables
3n αI DTn n ,n, ,n وD He
n and energy state variable E atrefueling S and auxiliary power
auxP at steady state from solving of nonlinear point kineticequationscan be calculate with
the inserting leftsidenon-linearequations(6) to (15) equaltozero. Our obtained figures are
given in the following for both D T and 3D He fuel at steady-state in temperature
range 0 to 100kev. It should be noted that the two parametersd
and used indrawing
the graphs are considered constantand its numerical values are 3d
k and 7k
a) b) Figure 5: Comparison of variations of neutral fueldensity, a)deuterium and tritium and alpha
particles of D T b) deuterium and Helium and alpha particles of 3D He in the steady state at
temperature range of 0 to100 Kev.
From Fig.5 we see that particledensity of D and T is declining becausedue to nuclear
fusion of D – T, D and T particles are consumed and its amount are decreased.
Thensystemgo toward relativeequilibrium and the value of densities could beafixed
amount. Density of thealpha particlesis increasingbecausedue to D - T fusion reaction
alpha particlesare produced thus the value of themamountincreases. Then since that they
mayhaveescaped from system thus the value of them are reduced and then
sincethesystemgoestoward to arelative equilibrium the numerical values of densities could
beafixed amount. Neutralparticledensity ofthe fuelis injectedat a constant rate
19 37 10 m atalltemperatures. Also, for the 3D He reaction in temperature rangeof 0
to100kev,we see that alpha particle density, at first is increasing because as shown in
Figure(2) to a temperature of60 (keV), 3D He
and therefore number offusion reactions
increase. As the temperature increases 3D He
andthus number of fusion
reactionsdecrease.therefore alpha particledensityisdecreased. Initially theparticledensity of
D and 3He decrease because according of Figure(2) till temperature 70 (keV), 3D He
and thus number of fusion reactions increase therefore more fuel is consumed. Therefore,
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 54
theparticledensity of D and 3He is reducedwhoseits decreasing processes in this
temperature range is perfectly obvious. Then in thetemperature range70 to100 (keV),
3D He and thus number of fusion reactions of
3D He are reduced. Therefore
low 3D He fuel is consumed ,thereforegradually is increased. Neutralparticledensity
ofthe fuelis injectedat a constant rateatalltemperatures. Since that the magnitude of
neutraldensity versus temperature is order of 17 36.98 10 m therefore in comparison
with thealpha particle ,D, and T densities ( 1910 3m ) is very low, that can be seen in the
Figure(5).Also Figure (6) shows variations of energy density in terms of temperature for
bothfuel D T and 3D He atsteady state.
a) b)
Figure 6: Energy density variations of a) D T and b)3D He c) comparison of D T and
3D He inthe steady-stateat the temperature range0 to100 Kev.
From Figure 6 for D T and 3D He fuel we observe that initially the energy density of
these fuel increases with increasing temperatureuntilthetemperaturereachestheresonance
and then graduallyreduced.Its reason is that with increasing temperature number
offusionincreases and thusmore energyis produced such that in 70KeV which known as
resonance temperature of D T fusion reaction we have maximum energy. Then with
increasing temperature, DT
is reduced. Therefore, the number of fusion reactions are
reduced and thus energy is decreased. The sametrendcan be seenfor the 3D He reaction
except that since 50KeV is the resonance temperature of 3D He .Therefore, at the
resonance temperatureof 3D He fusionreaction we will havethe maximum energy. With
having the values of 3
3 3, , , , ,
DT DT D He D HeDT n nD He
n n n n n n
and ignoring of impurities and
using equations (17)to (20) ,(22)and (26) to (30) respectively ,quantities of auxiliary power (
auxP ),total energy density ( E ),total density( N ),radiative power loss (rad
P ),effective
charge of all ions (eff
Z ),net power heating (i
P ),fusion power(fu
P ),and fusion gain(Q )of
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 55
fuel D T and 3D He are calculatedin terms of temperature variations andtheir
curves are given in theFigure(7) to (15).
a) b)
Figure 7: auxiliary power ofa) D T and b) 3D He at the steady stateinthe temperature range
of 0 to100 (keV)
According to Fig.7 can be concluded that auxiliary power of D-T fuel initially is reduced
and the temperature about12( )keV is minimized then with increasing temperature is
increased and at the 100( )keV temperature is maximized. For 3D He this power is
maximized at low temperatures then by increasing temperature auxiliary power is
reduced and the temperature near 20( )keV is minimized and then by adding to
temperature 100( )keV gradually grows .
Figure 8: Comparison ofthe total energyoftheD-T and 3
HeD fuelin thesteadystate and
temperature rangeof 0 to100 (keV).
According to the figure 8 we can find that the total energyof bothD-Tand 3 HeD fuel
with increasingtemperature has increasedlinearly. Becauseaccording toequations(18 -a),
and (18 -b) thetotal energy, directlyproportional totemperature(T).Since from figure9we
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 56
can see the total densitiesofDTN and
3D HeN are nearly equal therefore according to
therelations(18 -a), and (18 -b), we can conclude thatthe totalenergyDTE and
3D HeE will be
the same.
Figure 9: Comparison of total density of theD-T and 3
HeD fuelin thesteadystate and temperature
rangeof 0 to100 (keV).
According to Figure9 can be seen that the total density of the fuel D - T and 3 HeD
similar trends with temperature variations and with temperature increasing, their values
rapidly increase and then reach to a constant value also from 80 (keV) to 100 kev grows
gradually but at all temperatures, the density of 3HeD is greater than D – T. This
behavior is due to the kinetic equations governing the system and the shape of equations
(20-a) and (20-b).
Figure 10: Comparisonof theradiativelosspowerfor both fuel of D – T and 3 HeD in steady state
at temperature interval 0 to100 (keV)
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
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Accordingto figure 10can be found that radiative power loss of both fuel D - Tand3 HeD with temperature increasing, grows. Because, as the temperature increases, the
ions of the plasma, obtain more energy and thus these power increase. Also wecan see that
radiative power loss of 3 HeD variations at all temperature range is greater than D – T.
Figure 11: Comparison of effective charge of all ions for both D-T and 3
HeD fuelin the steady
state and temperature range of 0 to100 (keV).
According to figure 11 can be found that effective charge of all ions for D – T with increasing of
temperature increase and its maximum value is about 1.99 at 5 kev then with increasing
temperature its value is fixed . For 3 HeD similar performance is occurred except that its
maximum value at 24 kev is about 1.99 then with increasing temperature till 76 kev its value is
fixed and after that with growth of temperature its value is reduced very slowly.Also we can
see that in the temperature interval 30 to 80 keveffDT
Z and 3effD He
Z are coincidence.
Alsofromequation (26)netheating power for both fuel D – T and 3 HeD in the
temperature interval 0 to 100 kev are plotted (see fig 12).
Figure 12: Comparison of the net heating power of D – T and 3 HeD in steady state at
temperature interval 0 to100 (keV)
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
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According to figure12 can be found that the value of net heating power of the D - T
increases with increasing temperature such that its value changes from 7 ( )4.12 10 W to 7 ( )4.31 10 W , and then its value slowly and gradually decreases with increasing
temperature. But from this figure you can see that the 3 HeD total net heating power is
always greater than D – T, in the temperature range0 to100 keV)) .
Figure 13: comparison of fusion power for both of D – T and 3
HeD fuel in the steady state in
terms of temperature variations
Accordingto figure13 canbefound that the fusion power of both fuels D-T and 3 HeD grows with temperature increasing. Since that the number of fusion reactions isenhanced
thereforethe fusionpowerincreases.Also ,we can seethatthe fusion power of D-3He fuel is
higher than D T .
a) b)
Figure 14: fusion gain variations of a)D - T, b) 3 HeD and fuel in the steady state at the
temperature range 0 to100 (keV)and 3.3( )EDT
s ,3 16( )
ED Hes
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
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Accordingto Figure 14 can be found that initially fusion gain of D T fuel is enhanced
with temperature increasing ant its maximum value is about 6,then with temperature
growing its value gradually reduced such that at 100kev temperature its Q value reaches
5.However , 3 HeD fusion gain with temperature increasing enhances such that at 20
kev temperature reaches to the value 0.012,than with increasing temperature up to 100 kev
its value is fixed.in general from this figure we see that fusion gain of D-T is greater than 3 HeD . So in thesteady stateis not recommendedto usethe 3 HeD fuelfor the reactor
ITER90H-P. For having more realisticinformation about Q for both fuel-D - T and 3 HeD
itis better to enter E changes on the fusion gain. (see Fig.15)
Figure 15: Three dimensional variation offusion gain for D - Tand 3 HeD fuel, in the steady
state at temperature range of 0 to100 (keV) andE range of 0 to 30 seconds.
Also if in determining of physical quantities such as radiative power loss ,total energy
,net heating power, auxiliary power ,power and fusion gain of both fuel D – T and
3 HeD we enter the variations of dK K و parameters in the range of 0 25K ,
0 4dK and also by considering fusion power variations for both fuel D T and
3D He versus energy confinement time ( E ) the discussion is wider (see figs.16 to 20).
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 60
Figure16: Three dimensional comparison of radiative power loss for D – T fuel in steady state at
three temperature 10,70 and 100 kev in terms of and d
variations
With seeing Fig.16we find that ttheradiationpowerloss of D-T fuel increasedwith
increasing temperature and andd
.
Figure17: Three dimensional comparison of total energy for D – T fuel in steady state at
three temperature 10,70 and 100 kev in terms of and d variations
From Figure17can be seen thatthe total energyof the D T fuelincreaseswith increasing
temperature as and d change.
Figure 18: Three dimensional comparison net heating power for D – T fuel in steady
state at three temperature 10,70 and 100 kev in terms of and d variations
From Figure 18 can be seen that the net heating power decreases with increasing
temperature as and d change.
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 61
Figure 19: Three dimensional comparison auxiliary power for D – T fuel in steady state
at three temperature 10,70 and 100 kev in terms of and d variations
We have seen form Fig.19 ,by increasing temperatureaxillary power ( auxP ) will rise as
and d change.
Figure20: Three dimensional variation of fusion gain for D - T and 3 HeD fuel in the
steady-state at temperature range of 0 to100 (keV) and energy confinement time range0
to30seconds
According to figure 20 we can say thatin all temperature and confinement time variations
the fusion power 3D He is greater than D-T.
CONCLUSIONS
With studying and analyzing ofITER90H-p fusion reactor sand solving the non-linear
point kinetic equations governing on the two- fuel D - Tand 3D He at steady,
dynamical and perturbation states, we find that the main quantities in determining the
fusion gain are the densities of alpha particles, deuterium, tritium, helium, neutral fuel,
electron , fusion energy and the total energy, and density of total particles, the effective
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 62
charge of all ions, radiative powerless, auxiliary and fusion power ,respectively. In order
to be commercially competitive, a fusion reactor needs to run long periods of time in a
stable burning plasma mode at working points which are characterized by a high Q ,
where Q is the ratio of fusion power to auxiliary power. Active burn control is often
required to maintain these near-ignited or ignited conditions ( Q = ∞ ). Although
operating points with these characteristics that are inherently stable exist for most
confinement scaling, they are found in a region of high temperature and low density. Our
studies show that in the steady-state above quantities are only a function of temperature
and each has its own specific variations and also at the temperature70 (keV) these
quantities produce the maximum fusion gain for both of fuels D – T and 3D He ,such
that their values are equal to 6.01for D - T fuel-andthe0.012 for 3D He , respectively.
Fusion using 3D He fuel requires significant physics development particularly of
plasma confinement in high performance alternate fusion concepts. Countering that cost ,
engineering development cost should be much less for 3D He than D – T , because 3D He greatly ameliorates the daunting obstacles caused by abundant neutrons and
the necessity of tritium breeding. A 3D He fusion fueled fusion reactor would also
possess substantial safety and environmental advantages over D –
T.CurrentlyrecommendedforreactorITER90H-p is used D - T fuel and still need more
research to be done on the fuel 3D He .
REFERENCES
[1] N. A. Uckan, J. Hogan, W. Houlberg, J. Galambos, L. J. Perkins, S. Haney D. Post and S. Kaye, “ITER design: physics basis for size, confinement capability power levels and burn control”, Fusion Technology, vol.26, (no.3, pt.2), pp. 327-30, Nov (1994).
[2] N. A. Uckan, “Confinement Capability of ITER-EDA Design”, Proceedings of the 15th IEEE/NPSS Symposium on Fusion Engineering,vol.1, pp. 183-6, (1994).
[3] L. M. Hively, “Convenient Computational Forms for MaxwellianReactivities,” Nucl. Fusion, 17, 4, 873 (1977)
[4] H.S.Bosch, G.M.Hale,Nuc.Fusion,32,611(1992) [5] A.V. Eremin , A.A. Shishkin ,”Fusion D+T And D+D Products Dynamics for the Different
Fueling Scenarios in Toroidal Magnetic Reactors”,ssn 0503-1265. UKR. J. Phys. V. 53, N 5,(2008). [6] E. Schuster, M. Krstic´ , and G. Tynan,”Burn Control in Fusion Reactors Via Nonlinear
Stabilization Techniques”,Fusion Science and Technology ,VOL. 43 , (2003) [7] L. Spitzer, Physics of Fully Ionized Gases ~ Interscience, New York, (1956 ) [8] F. Trintchouk,M. Yamada, H. Ji, R. M. Kulsrud, and T. A. Carter,”Measurement of the transverse
Spitzer resistivity during collisional magnetic reconnection”,PHYSICS OF PLASMAS,VOLUME 10, Number 1, (2003).
[9] Kadomtsev, B.B.: Tokamak Plasma: a Complex Physical System, Institute of Physics, Bristol (1992).
[10] Wesson, J.: Tokamaks, 2nd edition, Clarendon Press, Oxford, 1997. [11] T. Pinna, C.Rizzello,”Safety assessment for ITER-FEAT tritium systems”,Fusion Engineering
and Design 63 – 64, 181 – 186, (2002). [12] Ahmad M and Alam MS. 2014. Non-Associativity of Lorentz Transformation and Associative
Reciprocal Symmetric Transformation International Journal of Reciprocal Symmetry and Theoretical Physics, 1, 9-19.
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 63
APPENDIX A:
To obtain thenumerical valuesof the density state 3n αI DTn n ,n, ,n وD He
n variables we solve
analytically point kinetic nonlinear equationsgoverning on the two fusion fuels D – T and 3D He .
Because,the equationsof the twofuelsare similartherefore we solve only the equations (6) to (9) forD - Tfuel. We put theleftsides ofequations(6) to(9) equal tozero
α DT n I 0dn dn dndn
dt dt dt dt
So, from putting theequation (1) equal to zero, ,we have:
(A-1 )2DT DT n
DT d
0n n n
2 ( ) τ 2 τDTv
(A-2 )2 αDT nn( )
2 τDTv
According to equation(A-1)and(A-2), DTn isas follows:
(A-3)
1
2
DT
4
n
τDT
n
v
1
2
21
2
DT
2
n
d
4
4
τ
0
1
τ τ
2 ( )2
n
τ
1
DT
DT
DT
v
n
n
v
v
1
2α n
DT d
40
n n12
τ τ τ τDT
n
v
(A-4)
T
2
D
1
α
d
n12
τ
4
τ ττ
DT
nv
nn
we put equation (8) equal to zero
(A-5) n
d
n s=0
τ
By inserting equation (A-4) inside to (A-5) the following relation is given:
α
DT
1
2
dd
n12
τ τ τ
41 τ s=0
τ DTv
n
(A-6)
1
2α
DT
121
n2 τ τ τ
2
DTv
ns
We define x as follows and insert it into the equation (A-6) :
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
Copyright © 2012, Asian Business Consortium | AJASE Page 64
(A-7)
12
τ
nx
1
22
DT
1
2
τ
2
DTvx x s
1
22
DT
1
2
τ
20
DTvx x s
The aboveequationisaquadratic equation, by solving this equation x is determined and by replacing into eq (A-4) we have
T
2
D
1
α
d
n2
τ
42
τ ττ
DT
nv
nn
And using equation (A-7) nn can be written as :
(A-8)1
12
T
2
D
d
12
2
ττ
DT
n x xv
n
Here the variableydefinedas follows and insert it inequation (A-9)
D
2
T
1
2
τ
1
DT
yv
(A-10)
1
2
d
2τ
n yx xn
we put the equation (7) equaltozero:
(A-11) 2DT DT n
DT d
0n n n
2 ( ) τ τ2 DT
v
Then by insertingequation (A-10)intoequation (A-11)we getthefollowingquadratic equation in terms
of DTn : 12
2DT DT
DT
2 0n n
τ2 DT
yx xv
by solving this equation we have
(A-12)
1
1
2
2
2
DT
DTDT
221
τ
1
1
n2τ
2 DT yx xv
By replacing the densities DTn inequation (A-2) n is calculatedas follows:
2 αDT
n n( )
τ2 DTv
By inserting Relation (A-12) into equation (A-2) n is given by :
Asian Journal of Applied Science and Engineering, Volume 3, No 2 (2014) ISSN 2305-915X
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21
2
D
1
2
T D
2
T
α
12
4 2 2
1
τ
12
τ
1
n
τ
DT
DT
yxv x
v
(A-13)
21
2
DT DT
1
22
ατ
4
2 2τ 2 τ
1 1 12
n
DT
DT
yx xv
v
Electron densityin thesteady stateis
obtainedfromthe relationship:eDT DT αDT I I
n n 2n Z n .
Ifweignoretheeffectsof impuritiestheelectron densityequationisas follows:
(A-14) eDT DT αDTn n 2n
Bysubstitutingequations (A-12and (A-13)inequation (A-14), the steady-stateelectrondensity is given by (A-15)
(A-15)
DT
1
2
DT
21
2
DT
1
22
2
DT
1
2
eDT2τ
2 2 τ
2 2 2τ 2 τ
1
1 12
1 12
1
n
DT
DT
DT
yx x
yx x
v
v
v
It should be notedthatthe aboverelationshipisalso truefor 3D He fuel except that in the
mentioned relations the index DT must be replaced by 3D He
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