Studies on the Performance of ITER90H-P - Asian Journal …ajase-bd.weebly.com/uploads/1/3/4/5/13455174/6.4_43 … · · 2014-07-06Studies on the Performance of ITER90H-P ... REACTIVITY

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



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]



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,



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) .



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.



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



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



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



(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.



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.



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,



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



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



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)



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)



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



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).



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.



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



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.



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) :



(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 :



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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