J. Plasma Fusion Res. SERIES, Vol.7 (2006) 179-182

Magnetic Nuclear Fusion Reactor of New Type: Main Physical Aspects
NASTOYASHCHIY Anatoly
RF SRC “Troitsk Institute for Innovation and Fusion Research”
TRINITI 142190 Troitsk Moscow Reg., Russia.
（Received : 5 October 2004 / Accepted : 10 January 2006）

Abstract
Peculiar properties of a magnetic nuclear fusion reactor of innovative type [1] are discussed where thefunctions of plasma confinement and its thermal insulation are separated. Whereas reducing heat transfer isfulfilled using magnetic field, a hot plasma confinement is maintained by gas of high pressure. In the system
considered the plasma is in a local equilibrium state and, as a consequence, the electron (ion) concentration
is a function of local temperature. In the frames of a the simplified model a approximate stationary solutionof the problem concerning nuclear fusion burning in a D-T mixture is found and the reactor dimensions
are determined. A series of obvious advantages of using high-pressure gas for the confinement of plasmapressure are noted, e.g. absence of interaction fast charged particles and first-wall components, small sizes of
the reactor and opportunity for using other fuel mixtures ( f.e. D+He3 ).
Keywords:
plasma confinement, high pressure gas, thermal isolation, magnetic field configuration
1．Introduction
For about 15 – 20 past years the experimental procedure and techniques in tokamaks have made great
progress that enabled the plasma parameters to be effectively enough controlled and in some cases a number of dangerous instabilities to be suppressed; besides
the plasma confinement was improved. However, theexperimental reactor, ITER, being designed with due
account of the progress made is oversized and considered as an undue expensive facility. Hence there naturally, arise a question: if the chosen way to develop
tokamaks, i.e. permanent increase of their sizes (andcost), the only one correct? In fact, since major physical tokamak concepts were stated [2], main eﬀorts havebeen undertaken in the development of the experimental procedures and techniques and “the arm race”, i.e. acompetition in building larger and larger facilities.
If one lets the “ideology” of the tokamak creation tobe unchangeable, then the only correct way left is to increase its size. As follows from the Lawson criterion
the ignition may be achieved by increasing either theplasma density (this is the case of laser nuclear fusion)or the confinement time. As the plasma density in thetokamaks is limited by the magnitude of the magnetic
field, one needs to increase the time of confinement. In
its turn, this time in the existing tokamaks (stellarators)
is limited because of the fact that their plasma proves tobe in substantially non-equilibrium and suﬀers numerous instabilities.
Below a physical concept of a magnetic fusion reactor is considered where the plasma is in a state close to
local equilibrium.
2．Plasma confinement with high pressure gas
Within large plasma pressures exceeding the magnetic field one the plasma appears to be close to a thermally equilibrium and, hence, must be more stable.
As lots of experiments show with an increase in theplasma density, as a rule, the global confinement time
also rises and at plasma densities which are close or
exceed n ≥ 1014 cm−3 the rate of anomalous electronenergy transfers significantly diminishes and becomescomparable with the ion energy transfer which, in its
turn, close to neoclassical. In addition, increasing bydensity of reacting particles means rising the rate of nuclear fusion reactions and as a result the requirements tothe confinement time and, thus, to the installation size
are reduced. That is why the investigation of possible
methods of increasing plasma density is of vital importance.
In our paper the plasma pressure exceeding the magnetic field pressure (β > 1) is discussed; as a result
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion Research
Corresponding author’s e-mail: anast@triniti.ru179

Magnetic Nuclear Fusion Reactor of New Type : Main Physical Aspects

particles length paths in gas do not exceed ∼ 10 µm.
So these particles are incapable of penetrating throughthe neutral gas shell to the solid surface. The first wall
surface is mainly heated by plasma radiation and neutral gas heat conduction. In order to exclude plasma
polarization in the vertical direction it is necessary thata poloidal field Bθ should be included ( f.e., by using
lasers [3]). Let us estimate the value of bootstrap current JB using the expression for J B from Ref. [4] andtaking into account of p = 2nT = const, where n is ion(electron) concentration; at B ∼ 1 T, n ∼ 1015 cm−3 andT ∼ 10 keV we find JB ∼ 104 A/cm2 that is quite sufficient for maintaining a poloidal magnetic field. Hazard of arising the Relaygh-Taylor instability can be prevented on account of poloidal rotation of the plasma
column at a velocity defined by a “thermal force” RT =−(h × ∇T/ωτe [5] where ωτe is a ratio of cyclotron frequency to collision one for electrons.

the plasma appears to be close to local equilibrium and,hence, must be more stable.
2.1 Equilibrium plasma state

In conventional tokamaks the plasma pressure p isbalanced by forces arising at interaction of electric currents j with a magnetic field B∇p = 1/c( j × B)

(1)

In the devices with a small aspect ratio of ε = a/R  1
where a, R are the minor and major radii of the plasma
column, respectively, we have∇p + ∇⊥ B2 /8π = 0(2)where p is the plasma pressure At confinement of hotplasma with a gas the second member in the left side(2) can be neglected (β  1), and we have ∇p ≈ 0or p ≈ const, i.e. a hot plasma pressure along theradius is unchangeable. At high plasma temperatures
T  1 eV the quantity of neutral particles in plasma issmall (at T ∼ 10 keV their concentration does not exceed ∼ 10−6 − 10−7 ). In contrast, nearer to the plasmaboundary where its temperature is quite low (T ≤ 1 eV)
the concentration of charged particles is insignificant
and the total pressure is almost entirely defined by neutral gas. In the stationary state the total pressure including that of plasma and neutral gas remains constant,pe + pi + pa ≈ constant, where e, i and a designate
electrons, ions and neutral respectively. The hot plasmapressure in the center of plasma column and the coldgas pressure on the boundary are about equal. Thus,in the center of the plasma column is hot plasma with
its temperature being dropped towards the periphery.
And, correspondingly, a concentration of charged particles increases. However at low temperatures T ∼ 1 eV
plasma changes into a partially ionized gas. In the vicinity of the wall we deal with neutral gas, its temperature is equal to that of the surface. As it is known, atmagnetic confinement plasma pressure is maximum inthe center of the system (“plasma diamagnetism”) with
β = 8πp/B2  1; towards the plasma boundary its
density and temperature fall oﬀ. The plasma in its fullvolume is almost completely ionized and a noticeable
component of neutral particles is revealed only near theboundary itself. The plasma itself being separated fromwalls proves to be highly non equilibrium that is thecause of numerous instabilities. In contrast to this, alocally equilibrium plasma is less susceptible to instabilities.
The conditions and parameters of burning should bechosen such as the wall surface had an acceptable temperature. At gas pressure p ∼ 1 – 100 bar the charged

2.2 Nuclear fusion burning

In lots of experiments it was observed that with increasing the plasma density the global time of confinement increases and the rate of the electron energy transfer becomes comparable with a neoclassical ion energytransfer.
As it was noted, there are two ways to substantiallyreduce the reactor sizes, i.e. to increase the time ofthe plasma confinement or to raise (significantly) theplasma pressure. The second variant appears to be themost optimal as, in addition, the plasma confinement
improves. At an increase in the plasma density the
global time of confinement grows and at large plasma
densities the energy transfer becomes comparable withneoclassical one. Thus it is reasonable to suppose thatat the high plasma densities considered below one canemploy in calculations neoclassical coeﬃcients for ionsin the description of heat transfer in the magnetizedplasma. With increasing the plasma density the rate ofproceeding the reaction (∼ n2 ) rapidly grows. Using asimplified model find a stationary solution to the problem of burning in the D-T mixture assuming the heattransfer due to the neoclassical mechanism:(−1/r)d/dr(rχneo dT/dr) = Qα − Qrad

(3)

where T is the common temperature of electrons andions (in a high density plasma this approximation isjustified) and Qrad is the plasma radiation. Notethat at high temperatures Qrad is mainly defined bybremsstrahlung [6]. And only at temperatures below
ionization potential I, i.e. T < I, recombination radiation becomes prevailing. In its turn, the radiation ofexcited atoms starts playing its part only at the plasma
180

Magnetic Nuclear Fusion Reactor of New Type : Main Physical Aspects

edge where the degree of ionization of atoms is below
100 %. So at high temperatures T  13, 6 eV we have√
Qrad ∼ n2 T [6]. For the boundary conditions wehave:
T = T 0 ; dT/dr = 0 at r = 0
In equation (3) we will use the simplified expression for neoclassic thermal conductivity χneo =χclas q2 ε−3/2 [4,6] where χclas is so called “classical”
thermal conductivity [5]:χclas ∼ n2 T 2 B−2 /T 5/2(4)In the temperature range 5 < T < 20 keV the heatrelease rate Qα , as a result of the nuclear fusion reaction is quite well approximation by the expression(εα = 3.5 MeV is the α- particle energy) [7]:Qα = knD nT T 2 εα(5)where nD and nT are the concentrations of deuterons
and tritons, respectively and k is the numerical coeﬃcient [7]. For the temperature range where Qrad  Qαfrom equation (3) together with the boundary condition（4）we find the approximate solution:
1/T 3/2 − 1/T 03/2 = (3/8) (E/A)r2 /4

Fig. 1 Temperature distribution at nucler fusion burning
using D + T mixture.

(6)

fuel mixtures) can be used in the reactor. One more important aspect should be noted. As it follows from theequality of the pressure nT = const at a plasma temperature falling along the radius the plasma density, on thecontrary, should rise (at least in the central “hot” area).
It means that the cyclotron radiation will be blocked inside the plasma and the main danger in building a reactor on the working mixture D + He3 , i.e. extremely
high losses by cyclotron radiation, does not exist in thecase considered. On the basis of the model equation(3) employed above one may also estimate a characteristic size of the area of burning when D + He3 is used
as fuel. Taking into account that a dependence of thereaction cross-section D + He3 → He4 + p is similar
D + T reaction and the reaction cross-section D + He3
at T = 100 kev coincides with that of DT at T = 10 keV,but the energy release (18,65 MeV) is about five times
greater, from (3) we find that the size of the area ofburning in the D + He3 mixture is about 4-5 times larger(∼ 1 m). To start burning when a high pressure gas interlayer is available in the tokamak chamber seems tobe possible with using, e.g. CO2 - lasers [3]. By the author’s estimate 5 − 6 MJ in a pulse of ∼ 100 ns are thenecessary parameters for the CO2 - laser. Creation of aCO2 - laser with a similar parameters is an engineering
problem which can be resolved, if necessary, for 3 − 5years. Besides, the HF plasma heating is possible whichshowed good results in tokamaks.

where E/A = B2 /100 (at q2 ε−3/2 ≈ 30), with the magnetic field measured in units of 5 T. An example in thefigure shows the temperature profile for B = 0.3 andT 0 = 10 keV; as is seen, the burning area has a smallenough radius and of about the same thickness are boththe plasma with a lowered temperature T < 4 keV fromwhere the energy is removed by radiation and the neutral interlayer between the plasma and chamber “wall”.
At the same at B = 0.3 cyclotron radius of α-particles
is compared with the thickness of a burning area andconsequently the α-particle energy will be “spread” onplasma column radius. Note, that in the temperature
range where the approximate relation for the velocity ofheat release by α- particles (5) is true, solution (6) does
not depend on nT. It means that the reactor power canbe regulated by reducing or raising the plasma pressure.
Note that at the aspect relation ε ∼ 1/3 for the mainradius we have estimate R ∼ 1 m. Since the plasmapressure stays on constant along the plasma turn crosssection, it follows that the plasma density should be a
growing function of the radius. The neoclassical coeﬃcient of heat conductivity at nT = const is proportional
to χneo ∼ n2 T 2 /T 5/2 , i.e. it reduces with the plasma temperature. Thus the burning mode considered can be unstable with the plasma transition into a state with a hightemperature of T ∼ 70 − 100 keV. So D + He3 (or other181Magnetic Nuclear Fusion Reactor of New Type : Main Physical Aspects

3．Conclusion
The results of the approximate analysis show that thesuggested innovative concept of a fusion reactor with its
plasma confined by a high pressure gas is characteristicof some properties:(1) plasma is in a local equilibrium state and, hence,
it is less susceptible to hazardous instabilities;(2) in reactor a high pressure of plasma can be easily established, i.e. heat transfer, in accordancewith existing knowledge will have a neoclassicalcharacter;(3) reactor can have quite moderate sizes, about ∼1 m;(4) energy released in the process of burning is carried away by neoclassical thermal conductivity,
bremsstrahlung produced radiation and recombination radiation (low temperatures);(5) in the reactor D + He3 mixture can be used asfuel. A very useful feature of the reactor is thata powerfull cyclotron radiation is trapped inside
hot plasma.
In the author’s opinion the creation of a reactor withplasma confinement by using of high-pressure gas appears to be a quite real problem. Desired gas pressuresof ∼ 10 to 100 bar are within the pressure range well
worked out. The construction of lasers with desired parameters does not look like a serious engineering problem. Besides, the existing powerful HF generators canbe used for plasma heating.
Essential is the fact that the reactors under consideration can be used for burning diﬀerent fuel mixtures,such as D + He3 , etc.

[1]
[2]

[3]

[4]
[5]
[6]
[7]

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