An actual fusion reactor will evidently be associated with an external tritium-fuel stockpile, much as a fission reactor needs to have an assured external supply of fissile fuel. We depict such a system in schematic form in Fig. 14.6 where we also show the tritium flows and processes which will affect the inventory of tritium in the external stockpile.

Our preceding discussion involved the description of the tritium destruction rate in the fusion core as well as the tritium production rate and accumulation in the blanket. As suggested in Fig. 14.6, tritium bred in the blanket may decay or it may be extracted for deposit in the external stockpile; once in the stockpile, tritium may also decay, it may also be withdrawn for burning in the fusion core, or it may be lost by transport processes such as diffusion. The dynamical equation for the tritium in the stockpile is therefore

(14.31)

where the F(> terms are the flow rates suggested in Fig. 14.6.

The tritium supply rate to the stockpile may well be taken identical to the tritium extraction rate from the blanket so that according to Eq.( 14.27)

(14.32)

where N, b*(t) is the tritium inventory in the blanket at time t produced by neutron capture in lithium and T,.b is the mean residence of the bred tritium in the blanket.

The prompt removal rate of tritium from the stockpile should-for obvious reasons-be equal to the tritium destruction rate in the core:

f:,,x=r:,. (14.33)

Further, radioactive decay losses from the external stockpile are

(14.34)

Finally, for the present illustration, we assume that the various transport losses from the stockpile are a constant fraction of the inventory such that

= (14.35)

Substituting Eqs.(14.32) to (14.35) into Eq.(14.31) then specifies the dynamical state of the tritium inventory in the external stockpile as

.(a, +ex)N;jt). (изб)

dt Tub

A solution of this equation requires an examination of the various terms and an imposition of some reactor operational modes.

With Єх, C t, and Tt, b as system constants and also taking Rdt* to be constant, the time dependence of the tritium in the blanket Nt, b*(t) is given by Eq.(14.30). Under these conditions, Eq.(14.36) can be specified by the first order differential equation

dNl _ C, R’dtTb dt TtJ>

Here we have also shown an initial condition for the tritium in the stockpile at t = 0. This equation can be cast into the generic form

(14.39c)

While an explicit solution for the time dependence of the amount of tritium in the stockpile, NtjX*(t), can be obtained by solving the above inhomogeneous first — order differential equation, Eq.(14.38), we will find it more instructive to examine the differential equation itself; this will provide for a better understanding of how the various parameters influence the availability of this essential fuel.

Prior to start-up, the tritium in the external stockpile simply decays. Thus, at t=0, when the tritium inventory is Nt, x*(0) = Ntj0, an instantaneous withdrawal from the stockpile to the core takes place and gradual replenishment from the blanket to the stockpile is also initiated; the differential equation thus describes the slope of Nt x (t) at any point in time.

Within a sufficiently short time after startup, e. g. t = 0+, we find from Eq.( 14.38) that

implying that the tritium inventory will initially decrease at a rate dependent upon the magnitude of the initial tritium inventory and fusion reaction rate.

Further, for t sufficiently large, the central term of Eq.( 14.38) will vanish and hence

Slope of Ni(t) =A0-A2N*Joo).

(14.42)

with the general characteristic time variations of tritium suggested in Fig. 14.7. Note that a minimum may exist unless Ct(ib / xtjb) = 1 in which case a zero tritium inventory will be attained.

Problems

14.1 According to Eq.(14.2), an inventory of tritium will become depleted but helium-3 (h) will be produced. This newly bred fuel could supply a fusion reaction based on the d + h —> p + a cycle. If tritium is thus an energy "debit" due to its decay, what is the corresponding energy "credit" for the production of helium-3 as a function of time?

14.2 Compute the Nt = Nd concentration in a fusion core generating 100 kW per litre for various temperatures from 1 keV to 500 keV.

14.3 Determine an explicit solution for Eq. (14.37).

14.4 Examine a self-sufficient tritium breeding fusion reactor such that NtjX—>0 as t—>°°.

14.5 How long, after start-up, until the tritium inventory in the external stocknile attains a minimum?

A number of fusion reactions of interest were listed in the preceding chapter but little reference was made to the conditions under which these reactions might occur. We now consider the fusion process itself and some characterizations of conditions which are fundamental to an understanding of controlled nuclear fusion.

While the first generation of fusion reactors will evidently be d-t fueled, it is expected that subsequent generations of fusion reactors may use pure deuterium and possibly other "advanced" fuels as discussed in Sec. 1.4; one advantage thus gained is the elimination of the need to breed radioactive tritium. However, even though tritium breeding is not necessary, tritium handling will nevertheless still be required because it is one of the reaction products of d-d fusion, Eq.(1.21).

In comparison to d-t fusion, d-d fusion represents reactions among identical particles. The question of interest is therefore the following: given that for distinguishable ions, we have

a + b^() + () (7.29)

with

Rab= NaNb<GV>ab, (7-30)

what is the corresponding reaction rate expression for

a + a^() + () (7.31)

for the case of arbitrary reaction products? That is, what is Raa for this latter case? These considerations are important not only for d-d but also for t-t and h-h fusion.

Some thought suggests that the product NaNb in Eq.(7.29) represents the number of ways that members of the а-type set of particles can combine with members of the b-type set. As suggested in Fig.7.4, any one of the particles from the Na set could combine with any one from Nb and the total number of possible interactions is therefore equal to the number of (x, y) combinations with x and у identifying any one of the Na and Nb particles, respectively. Hence, all binary possibilities between these two sets are included in the product NaNb; that is, this product represents the totality of matrix elements in Fig.7.4.

For the case of particle indistinguishability, however, we have

a = b. (7.32)

Thus, with the total reactant density being Nj and as suggested by the extension of Fig.7.4, it is necessary to exclude the diagonal elements because a particle cannot interact with itself. However, the remaining Nj2 — N; combinations-that is the total number of matrix elements minus the number of diagonal terms — includes also the transposed pairs (x, y) and (y, x) which clearly represent the identical process and event. Hence, the total number of distinct reaction possibilities is only one half of this, giving therefore

N‘^Ni =}Ni(Ni -1)»-^- . (7.33)

The last approximation is, of course, essentially exact because Nj » 1 for all cases of general interest.

We write therefore for the reaction rate density among identical particles

Raa=<^>aaIY (7-34)

where Na is the total number of indistinguishable ions per unit volume; this number differs by a factor of 2 from the case of distinguishable fusing species, Eq.(7.30).

Magnetic and inertial confinement approaches to controlled nuclear fusion have been shown to involve heating the fuel to high temperature and then confining it long enough for a sufficient quantity of fusion energy to be generated; high temperatures are required in order to counter the effect of Coulomb repulsion among the fuel ions. In contrast, the attainment of fusion energy at low temperature is based on the notion that the effect of Coulomb repulsion can be significantly reduced by a selective and temporary state of pseudo-charge neutrality among the fusile reactants.

The attainment of a sufficiently high reaction-driven energy density is a requirement of all energy systems. For fusion it is essential that the reactant nuclei attain a sufficiently high kinetic energy of relative motion in order to achieve substantial rates of exothermic reactions. These conditions must then be retained for a sufficiently long time in a specified reaction domain. Confining the interacting fuel particles at an appropriate high temperature is thus a most basic consideration of fusion energy systems.

3.2 Necessity of Confinement

Unlike fission reactions which involve a neutral reactant and thus do not experience repulsive effects, fusion reactants are positively charged and must overcome their electrostatic repulsion in order to get close enough for the strong nuclear forces of attraction to dominate. Hence, the essential condition for fusion is the requirement for a sufficiently high kinetic temperature of the reacting species in order to facilitate the penetration of the Coulomb barrier.

The attainment of ion energies in excess of this Coulomb barrier, which is about 370 keV for d-t fusion, poses little technical difficulty. For example, readily available medium-energy accelerators could be used to inject deuterons, of say Ed = 500 keV, into a tritiated target; surrounding neutron and alpha detectors could then be used to identify the reaction products as evidence of whether the reaction d + t—>n + a+17.6 MeV had taken place. Obviously, if each injected deuteron were to lead to d-t fusion, then the energy multiplication would be EoW / Ein = 17.6 / 0.5 = 35 and thus adequate for fusion energy utility purposes.

Theory suggests and experiment has confirmed that such a beam-target concept is totally inadequate for the following reasons: as beam deuterons enter a target they lose energy through the processes of ionization and heating the target. As discussed in the preceding chapter and displayed in Fig. 3.5, they are far more likely to scatter-rather than fuse-with an additional attendant energy loss by bremsstrahlung radiation. Thus, very quickly, the projectiles will have slowed down to energies far below the Coulomb barrier rendering further fusion reactions most unlikely. Thus, the overall fusion energy release can not exceed the energy required for beam acceleration. The futility of this approach was

recognized early in fusion energy research.

A more promising approach, however, soon emerged. One begins with a population of deuterium and tritium atoms in some confined space, and by heating one causes both ionization and the attainment of high temperature of the fuel ions. The resulting ensemble of positive and negative charges thus forms a plasma which is expected to attain thermodynamic equilibrium as a result of random collisions. The resultant spectrum of particle energies is then well described by a Maxwell-Boltzmann distribution with the high energy part of this distribution providing for most of the desired fusion reactions. Because the reaction activation occurs here due to random thermal motion of the reacting nuclei, this process is therefore called thermonuclear fusion. The critical technical requirement is the sustainment of a sufficiently stable high temperature (~108 K) plasma in a practical reaction volume and for a sufficiently long period of time to render the entire process energetically viable. Confinement of the fuel ions by some means is thus crucial to maintain these conditions within the required reaction volume.

We add that in contrast to this high-temperature approach to fusion, there exists also a low-temperature approach free of the above type of confinement problems. As we will show in Ch. 12, confinement by atomic-molecular effects may also be exploited.

Having established some characteristics and constraints with respect to particle pressure and magnetic pressure in a magnetic confinement fusion device, we now further examine some properties of the magnetic field itself. In Ch. 5, we discussed the motion of individual charged particles due to a variety of constant and spatially dependent magnetic fields. Here we investigate the case of a simple axially symmetric В-field, the consequent particle motions then recalled with some results from Ch. 5.

Specifically, we consider particle motion in a cylindrically symmetric configuration, i. e. Э/Э9 = 0, with an axial magnetic field В = Bzk, as illustrated in Fig. 9.2. As suggested by electromagnetic theory, we take В to be represented by means of a vector potential A,

В = V x A. (9.12)

This vector potential can be shown to be determined from the electric currents which generate В and is, in the stationary case, given by

A(r) = ^f.^r * .d3r’ (9.13)

4kj r — rl

where r is to be taken in cylindrical coordinates (r,9,z). Since, in the geometry chosen here, the field generating currents point in the poloidal direction e0, it is obvious that A possesses only one non-zero component which is A0 and thus yields

В = V x Aete = + -|-K)k. (9.14)

oz r dr

In the absence of any other external field, the equation of particle motion is then, according to Eq.(5.1), described by

with Ед representing that electrical field which is consistent with temporal variations of В and hence satisfies Maxwell’s relation

ЭА_ .

Ел — ——— ‘Леев

Multiplication of the above equation by r leads to the angular momentum і due to the rotational motion about the z-axis, i. e.

т{г2в + 2ггв^+ r-^-(rAe} = ^-{тг2в + qrAg’j

<9Л9>

dt ‘

= 0.

wherein Ae needs to be determined from

Bz = (VxA)-k = -^(Me).

r or

That is, specifically we have

Ae = ~r’ Bz(r’)d’r’ ; r *

roughly assessing, Ae can be approximated to the lowest order by

Ae~LrBz(0) (9.22b)

and inserted into Eq.(9.20) which, recognizing that the rotation is such that sign(в) = sign(q) and further that r6 = vxand here mvjVlqlBz = rg, can then be

written as

These surfaces where rAe = constant may be labeled flux surfaces of the magnetic field and the particle’s guiding centres move on them in the absence of other forces; this follows as a consequence of angular momentum conservation. Even if field gradients exist, which cause particle drifts across В-lines, the particles would, in a cylindrically symmetric plasma, remain on their flux surface since the underlying symmetry here constrains all gradients into the radial direction and, correspondingly, all drifts appear in poloidal directions. In this case, only collisions or anomalous transport processes can drive particles across the flux surfaces, which then is described by the perpendicular diffusion coefficient, Eqs.(6.18b) and (6.19). We further note that, according to Eq.(9.5b), the surfaces of constant В must also be surfaces of constant pressure and consequently, in most cases also of constant density and temperature.

The atoms sputtered from the first-wall into the plasma can lead to considerable degradation of the energy viability of the fusion reaction chain. The reason for this can be summarized as follows. As the sputtered impurity atoms enter the
high temperature plasma, they collide with the plasma fuel ions and electrons and thereby become ionized. Only if these impurities feature a low proton number will they be completely ionized upon entering the plasma. For heavier impurity atoms (e. g. Fe, Ni, …), full ionization will not be possible in the plasma, hence leaving them in states of incomplete ionization, notwithstanding the exhibition of high charge numbers depending on the plasma temperature. Evidently, the overall Z of the plasma is increased, and consequently also the bremsstrahlung radiation which was seen to vary with Z2. Since several types of impurity ions may be present in a plasma at specific concentrations and different charge number, our previous formula for the bremsstrahlung power, Eq. (3.44), should, more correctly, be rewritten as

Ры= Abr^N N efiTe = AbrZeffN2eJkTe (13.14a)

has been introduced.

Additionally, a further important radiation process occurs which is due to the incomplete ionization of impurity atoms. Partly ionized atoms can be collisionally excited to a higher atomic energy level, and subsequently emit electromagnetic radiation by spontaneous transition to a lower energy level. The radiation frequency associated herewith is characteristic for each possible specific transition, and hence this radiation is called line radiation. In the case of a non-negligible impurity concentration in the plasma, the associated line radiation is seen to significantly contribute to the plasma radiation losses.

Since the line radiation PUne is proportional to both N-, and Ne, we introduce an ion-specific radiation parameter |/rad, i by

(Pbr), + (P tme)l

N, N.

which is displayed in Fig.13.7 as a function of plasma temperature. If this parameter is multiplied by the product of the electron density and the density of the i-th impurity, the respective radiation power due to both bremsstrahlung and line transitions is immediately found. Figure 13.7 now makes evident the substantial increase in radiation losses when high Z impurities enter the plasma. Only a very small concentration of such impurities can therefore be permitted in a fusion plasma if it is to be ignited. The straight dotted lines in Fig.13.7 indicate the normalized bremsstrahlung radiation for the case that the atoms of the considered element were fully stripped of electrons. As the plasma temperature increases, such states of complete ionization become more probable and the radiation parameters |/radii are seen to asymptotically approach the respective corresponding straight dotted lines characterizing the bremsstrahlung from fully

Electron Temperature, Te (keV)

Fig. 13.7: Normalized radiation power, |/rad = (Pbr + Pime)/ (N, Ne), as it depends on the
plasma electron temperature. The dotted lines denote the normalized bremsstrahlung
radiation of the completely ionized respective atoms.

ionized atoms.

While a detailed analysis of the adverse effect of the impurity atoms may involve complex transport calculations, an appreciation of some of the implications can be formulated as follows. Consider an initially pure hydrogen — state unit volume of plasma containing deuterons and tritons of equal density and their associated electrons all at temperature Tj. That is, we have Nd = Nt, Nj=Nd+Nt, Nj = Ne and a total thermal energy density in the fusion domain of

£rt, i=i(^ + ^)fc7i — (13.16a)

The contaminated state subsequently contains an additional number of Nz impurity ions and NzZ impurity electrons per unit volume; here Z is the ionization number for the atoms sputtered from the first wall. At thermal equilibrium with a temperature T2 we therefore have

E, h,i = + Xz + Ne + NzZ)kT2 . (13.16b)

In the absence of energy injection and the imposition of sharing of thermal energy among all ions and electrons, we may take Eth, i = Eth,2 and obtain

N+ N

:TX (13.17)

for which, evidently, T2 < T b This plasma cooling effect may be more compactly represented by the introduction of an impurity ratio gz defined by

The associated increased bremsstrahlung radiation power losses can be assessed by taking the ratio

Рыл _r{Ne + NzZ)2Zeff

Рыл AbrNeNiJH

with Zeff according to Eq.(13.14b), however noting that the electron density here is Ne + NzZ. Using the definition for the impurity ratio gz of Eq.(13.18) then gives

^ = (l+giZfz*M d3.20b)

ґЬгЛ V

and introducing the temperature ratio of Eq.(13.19) then yields

Pbr,2_ d+gzZf

which shows that bremsstrahlung power losses have indeed increased, even though the temperature was somewhat reduced (T2 < Ti). Hence, this radiation emission, as well as the line radiation previously discussed and which may substantially contribute to plasma power losses, will further cool down the plasma.

Note that those fusion products having Z > 1 (helium) will result in greater bremsstrahlung radiation as well. Therefore, these so-called ash ions should be controlled in a fusion plasma so as not to accumulate to concentrations that are too high. The adverse impurity effect can be controlled by several methods. Two
of the most important are the following: i) the use of divertors which involves magnetic field lines leading out of the plasma chamber to ion collectors so that ions following these lines do not hit the wall and hence do not produce impurities, and ii) the use of low-Z first-wall materials which do not cause such a large increase in the radiation loss even if their concentration in the plasma remains high.

A magnetic field which varies spatially in strength in the direction of the field is of considerable importance in various mirror configurations-Fig. 4.2b. We suggest such a general case in Fig.5.12 and assess its effect on ion motion.

Cylindrical coordinates, (r,9,z) in Fig. 5.12, will serve us well for which Maxwell’s Second Equation, Eq.(5.63), gives

rdrK ’ г дв dz

Axial symmetry is generally expected to hold so that ЭВ9/Э6 = 0 and we obtain

(5.65)

with the boundary condition Br (r = 0) = 0 and dBjdz taken to be independent of r. Then, assuming Be = 0, we write

В = ВгЄг+ Bzez (5.66)

where er and ez are the radial and axial unit vectors in cylindrical geometry, respectively, Fig. 5.12. The corresponding equation of motion of a charged particle in this field is

m<^- = q{vXBzez) + q{vXBrer) — (5-67)

dt

The first term is recognized as the force responsible for particle gyration about Bz and also as that which leads to a grad-B drift, e. g. Eq.(5.51), when the dependence of Bz on r becomes significant. The second term, explicitly written as

q(v x Br er) = — q ve Brez + q vz Br ее (5.68)

contains a force parallel or antiparallel to the field on the axis and an azimuthal force. While the latter urges the particles to drift in the radial direction thus rendering their guiding centres to follow the specific magnetic field lines, the parallel force component will accelerate or, respectively, decelerate ions and electrons along the z-axis depending on the direction of their motion. With the aid of Eq. (5.65) this force component can be expressed as

d R

Fn = jqyer^. (5.69)

dz

We may now recognize the associated effect on the guiding centre by taking again an average Fy over a gyroperiod. Specifically taking the particles to gyrate around the central В-line at r = 0 renders the relation

v0 = — sign(q)v± (5.70)

so that for r = rg, we obtain

= (5.71)

Upon substitution of rg by Eq. (5.17), a generalization of this force can be shown to be given by

F|| (5.72)

Thus a net force acts on charged particles-independent of their sign-in a direction opposite to that of increasing B.

As discussed in Sec. 10.1, the confinement of a plasma in a toroidal magnetic field requires a rotational transform of field lines in order to prevent local charge concentrations, plasma polarization and drifts to the wall. Unlike the tokamak which carries an externally induced current in its plasma, stellarator devices do not. They also feature a toroidal geometry but render the confining magnetic field lines helical, i. e. compel a rotational transform, either by a deformation of the torus itself-such early concepts showed poor stability-or by helical or contorted coil currents external to the plasma. These currents, as shown in Fig. 10.13, pass through helical conductors winding around the torus and make the magnetic field lines take on the form of a spiral. A rotational transform produced in this way, as well as the closed magnetic flux surfaces thus rendered, exist in a vacuum field and do not rely on a plasma current induced in a pulsed manner. In stellarators, all magnetic fields providing confinement of the plasma are generated by means of currents flowing in external conductors. Hence, as an important advantage, stellarators allow for steady-state confinement and continuous fusion reactor operation.

In practical terms , a helical winding is a loosely wrapped solenoidal winding and generates, as desired, a toroidal and poloidal field. Furthermore, if viewed from above the torus, it represents also as a loosely wrapped vertical field coil and hence generates a vertical field as well. To eliminate this contribution, currents in adjacent helical windings of the same pitch flow in opposite

directions canceling out one another’s vertical fields and also their toroidal fields, on average. Thus, as seen in Fig. 10.13, a separate set of coils is needed to provide the essential toroidal magnetic field. Therefore, a stellarator still requires toroidal field coils as shown. The poloidal field produced from the helical windings together with the toroidal field from the separate toroidal field coils result in a flux which twists the magnetic field lines as they pass around the torus and thus generate magnetic surfaces of the shape shown in Fig. 10.14. Evidently, the geometrical simplicity of axisymmetry is lost. It is noted that the establishment of closed magnetic surfaces is possible only in a restricted region of the minor cross section of the toroidal tube. For a stellarator with l — 3 pairs of helical coils of opposite currents, we illustrate in Fig. 10.15 the shape of the generated magnetic surfaces. Closed magnetic surfaces are observed within the cross-sectional area embraced by the dashed separatrix line which may be identified also as the last closed magnetic surface. Outside this separatrix the field lines wrap around the individual conductors.

Due to the absence of a current in a stellarator, Ampere’s law (compare with Eq. (9.48)) yields here

— — ds = 0,

К

surface. For this to be true, the poloidal field must change sign and magnitude along s. Hence, unlike in a tokamak, the magnetic field lines in a stellarator do not wrap monotonically around the toroidal tube. Rather, they appear to oscillate periodically according to the qualitative structure given in Fig. 10.16a. Each such so-called fundamental field period incrementally rotates the field lines in the poloidal direction. Yet another inhomogeneity of the magnetic field is to be considered, which is due to the curvature associated with torus geometry. The resulting variation of the magnetic field along the toroidal direction is illustrated in Fig. 10.16b where the deep and more frequent oscillations of В are caused by the helical windings alternately carrying currents of different direction, and where the slow modulation of В corresponds to the toroidal curvature. It is obvious that in addition to the magnetic mirrors in the toroidal field which lead to particle trapping as in Sec. 10.3, there are also local mirrors of the helical field.

Analyzing the particle motion in such magnetic field configurations yields three distinctive types of orbits: (i) circulating particles which pass entirely around the torus without encountering a reflection, (ii) so-called ‘helically trapped’ particles reflected in the local mirrors of the helical field, and (iii) ‘toroidally trapped’ particles tracing banana orbits as they are reflected in the toroidal magnetic mirrors known from Sec. 10.3. It is possible that a helically trapped particle appears to be toroidally trapped as well. Such a particle is then called a ‘superbanana particle’.

Another approach to establish a rotational transform for toroidal plasma confinement is to partially rotate non-circular toroidal field coils, one with respect to the other. Further, specific designs-with their general principle demonstrated in Fig. 10.17-allow for practical modular composition. For reasons of simplification, in Fig. 10.17 the helical windings of a stellarator are reduced to consist of only two conductors with currents of opposite sign. Such an t — 1 configuration permits replacement by modules which combine parts of the helical coils with additional meridian-ring conductors. Advanced modular designs utilize non-planar twisted coils, that are sophisticated spatial elements as illustrated in Fig. 10.18. Modular coils are favourable from an engineering standpoint of view because they allow for assembly and disassembly of the coils without having to unwind or disconnect helical conductors encircling the major torus axis.

Closely related to the stellarator configuration is the so-called ‘torsatron’ in which the rotational transform is produced again by helical windings, however with like current directions. In this design there is no need for toroidal field coils, but, instead, equatorial ring conductors may be applied to generate a transverse field which can compensate the vertical magnetic field produced by the torsatron as a result of like helical current directions. This necessity of a compensating vertical field may be avoided by specifically winding the helical conductors according to

тв = ф + a sin ф + P sin(20) (10.52)

with m being an integer and a, (3 denoting chosen constants. Such a device is

Much theoretical and experimental investigation is still devoted to the determination of the maximum plasma-beta in a stellarator/torsatron for which stable equilibrium can be sustained. It is thought that (3’s of several percent, perhaps up to 10%, can be stably achieved if the configuration exhibits a helical magnetic axis.

Non-axisymmetric configurations such as the stellarator may lead-in comparison with axisymmetric devices-to more complex transport processes due to the greater variety of particle orbits. The quality of particle and energy confinement is dominantly determined by the trapping of particles in the various

ripples of the magnetic field and by the frequency of collisions occurring in the plasma. Collisions may scatter particles from one region of trapping to an adjacent region and thereby alter the type of trapping. Interestingly, in non — axisymmetric toroidal systems, the electron and ion components of the confined plasma diffuse independently of each other.

Fig. 10.17: Depiction of replacement of helical conductors by modular elements: (a)
helical stellarator windings; (b) modular coils generating a stellarator magnetic
configuration much the same as established by (a).

For very high collision frequencies Vc= 1/XC (see Eq. (6.17)) in a stellarator or a torsatron, the particles do not travel sufficiently long distances without a scattering encounter to be reflected by either the helical or the toroidal mirrors. As a consequence, particle and energy transport in a stellarator operated in this collisional regime is similar to that in collisional tokamaks. However, differences between these two configurations arise for lower collision frequencies, that is when the mean collision time xc appears to be in the order of the average time needed by a particle to bounce between the mirrors. If Vc is such that particles can be trapped helically but do not precess entirely around the minor torus axis before undergoing a collision, the helically trapped particle will drift from one magnetic surface to another. This spreading of particles obviously enhances particle diffusion. For vc lower than the frequency of precession around the magnetic axis, i. e. the single line around which the magnetic surfaces appear to be nested, these particle spreadings tend to cancel out, and the diffusion coefficient in this regime is expected to decline with decreasing collision frequency. If, however, superbananas are present, as featured by stellarators, the diffusion coefficient will not decline immediately with a reduced vc, but rather it remains constant at its high value over a limited collision frequency interval and thus exhibits the so-called superbanana plateau. Finally, as Vc becomes smaller than the superbanana bounce frequency, the diffusion coefficient is observed to decrease in stellarators as well.

Thermal energy diffusion appears to follow a dependence on vc similar to that seen for particle diffusion. The plasma-energy-confinement time of stellarator/torsatron devices is thought to scale similarly to that found for tokamaks, except for the weak-collision regime where the spreading of helically trapped particles enhances the diffusion. Suppressing this contribution is the objective of advanced stellarator designs.

In conclusion, we summarize some potential advantages of the stellarator/torsatron concept: Steady-state magnetic fields simplify the magnet design. Unlike in tokamak reactors, there is no need for pulsed superconducting coils and corresponding energy storage to drive these pulsed coils. Since a toroidal plasma current is not needed, a potential source of instabilities is eliminated. Early predictions of enhanced transport losses and increased instability have not materialized. Stellarator and torsatrons appear to be operating as effective plasma confinement machines, with dimension and performance parameters comparable to those of similar toroidal magnetic devices. The high aspect ratio, the absence of transformer coils and, particularily, modular construction make stellarator/torsatron devices well accessible. Further, steady — state operation of an ignited plasma would allow for a simplified blanket design due to reduced material durability requirements.

A nuclear fusion core may be surrounded by a blanket in which the neutrons from the fusion reactions sustain tritium breeding as well as fissile fuel breeding and — to a varying extent-fission energy production. The fissile fuel bred in such a hybrid is to supply the fuel requirements for "client" fission reactors and, by the consequent energy credit generated, alleviate some energy balance constraints on the fusion component.

15.1 Conceptual Description

The potentially recoverable energy from a fusing domain consists of electromagnetic radiation, the kinetic energy of charged nuclear particles, and the kinetic energy of neutrons.

The neutron is of particular interest for the following reasons: while its kinetic energy can be utilized-that is converted into thermal energy as it slows down by nuclear collisions in the blanket-the neutron itself remains a valuable particle to induce selected nuclear reactions. As previously discussed, the tritium for fuel self-sufficient d-t fusion reactors must be bred by neutron capture in lithium. Hence, for d-t fusion, one essential use of the fusion neutron is to breed tritium in order to close the fuel cycle. The reactions and reaction linkages involved are

(15.1)

Further thought suggests other productive uses of the 14.1 MeV fusion neutron. With its high kinetic energy, the fusion neutron has access to numerous (n, xn) neutron multiplying reactions, Fig. 15.1, and these reactions can result in a number of neutrons in excess of what is required for tritium breeding. Consequently, the spare neutrons can be used for other purposes; alternatively, if a fuel cycle such as catalyzed-D described in Ch. 7 is used, tritium breeding is not required so that the entire neutron population is available for other purposes. An interesting system concept is to surround the fusion chamber with a blanket of fertile nuclear fuel, that is 238U or 232Th, so that the neutrons can breed fissile fuel and/or aid in sustaining fission reactions in the intrinsically subcritical blanket.

Since each fission event yields -200 MeV, the blanket serves the function of energy multiplication and can also serve as a "fuel factory" for fission reactors. This concept can be further clarified by considering three dominant classes of neutron reactions which, for illustrative purposes, are assumed to occur in separate regions of the blanket.

Immediately adjacent to the fusion core, a region is envisioned with a high concentration of isotopes possessing a significant (n, xn) neutron multiplication cross section (i. e., x > 1) as shown in Fig. 15.1; the dominant reaction is therefore of the type

n+ AZ^>xn + A~X+1Z, X>1 (15.2)

where AZ represents a typical neutron multiplier. A location close to the fusion core capitalizes on the high energy of fusion neutrons to increase the neutron population by (n, xn) reactions which require neutron energies in excess of specific thresholds.

The next blanket layer is taken to contain fertile materials (232Th, 238U) which transmute into fissile materials ( U, Pu) by the processes
(15.3a)

or, more simply

n + g-^f (15.3b)

with g representing the fertile fuel and f denoting the fissile nuclei bred, some of which may be fissioned by neutron absorption and thereby generate significant amounts of energy.

The outer most blanket region is used for tritium breeding by neutron capture in lithium via

(15.4a)

or

n + £->t, (15.4b)

where £ denotes the lithium fuel.

It is thus evident that the hybrid blanket produces both energy and fissile fuel, and depending on the design objectives, one of these functions can be emphasized. The ratio of fissile fuel nuclei bred per unit fusion energy released is therefore an important parameter for the characterization of such a system. For example, in designs emphasizing the fuel factory approach where energy production is de-emphasized so the plant need not be a key contributor to an electrical network-and thereby also freeing it for a more flexible operating schedule-this ratio would be maximized. This may be accomplished by selecting materials in order to minimize fission reactions in the blanket while maximizing fissile breeding reactions.

These three dominant processes and the corresponding blanket domains are depicted in Fig. 15.2. Other arrangements are possible, but the order chosen here for the various regions follows a functional pattern intended to make enhanced use of the fusion-source neutron energy: (i) neutron multiplication is most productively accomplished with high-energy neutrons and hence the blanket section designed for this process occurs close to the fusion core for immediate access to the 14.1 MeV fusion neutrons before they slow down; (ii) next, fissile fuel breeding is best accomplished with intermediate energy neutrons; (iii) finally, after the neutrons have slowed down, the 1/v-dependence of the neutron capture cross section of 6Li ensures efficient tritium breeding.