Spin Polarized Fusion

Our discussion of fusion bum thus far would seem to suggest that only simple collision considerations are relevant. However, fusion phenomena may include other intrinsic processes thereby increasing the fusion reaction rate, and a possible suppression of less-desirable side reactions. We consider one such process next.

Neutrons and protons are known to possess an intrinsic spin. Quantum mechanical considerations characterize this spin as y2h with ti representing Planck’s constant. Then, when nucleons combine to form nuclei, the constituent spins add vectorially assigning a spin to the entire nucleus. The nuclides involved in d-t fusion possess spins as follows in units of the Planck constant h: deuteron : 1 triton : Уг neutron : Уг alpha : 0 .

The direction of a nuclear spin is determined by reference to an external magnetic field with the convention that the (+) sign represents a direction parallel to the magnetic field, (-) refers to the anti-parallel direction and (0) is for the transverse direction. We suggest these spins for a deuteron and a triton in Fig.7.6 where we also introduce the notation f 0 0 for the fraction of the respective nuclei oriented in the allowed directions; quantum mechanical considerations permit no

other directions.

Triton

 

В Deuteron

 

(+)-fi/2 (-)^/2

image327

 

(+)* (-)’fi (0)-fi

image328

 

image329

fd + *d + fd = 1 ft++ ft =1

Fig. 7.6: Spins for deuterons and tritons.

 

image330

It is known that spin conservation characterizes nuclear transformations. The maximum spin for 5He, produced momentarily as a compound nucleus when the reaction

г/ + г->(5Яе) ->n + a (7.54)

occurs, is 3/2 in units of fi — occurring when the deuteron spin and triton spin are aligned. The microscopic fusion cross section for this process will be represented by Go and constitutes a maximum.

It is possible to write an expression for the d-t fusion cross section Gdt in terms of G0 and the various fractional concentrations of deuterons and tritons in their allowed spin states, i. e., in terms of fd+, fd’, fd°, ft‘, and ft" as depicted in Fig.7.6. Referring to some specialized aspects of nuclear reaction theory, this cross section can be well represented by

(7.55)

 

Odt~

 

(Jo

 

and can be used to evaluate the extent to which Gdt approaches the maximum possible fusion cross-section, G0, for various mixtures of polarization of deuterons and tritons in a magnetic field.

Evidently, an equal fraction of fuel nuclei in each of their allowed spin states constitutes an overall completely depolarized state; such random polarization is defined by the ratios

f+ = L f’ = 1

J t 2 ’ J t 2

and the corresponding d-t fusion cross section (Gdt)r, r is therefore given by

Thus, for this case of random spin polarization, the Gdt cross section equals 2/3 of the maximum possible value, G0-

Consider now a parallel alignment of the deuterium and tritium nuclei. For this case we have

fd = l. fd = 0, fd = 0, f* = l, ft = 0 (7.58)

and hence

M+ + = {l + 0 + 0 + 0 + 0)oo=Oo ■ (7.59)

Comparison of this result with Eq.(7.57) indicates that a 50% increase in the d-t fusion reaction rate density is achieved if the deuterons and tritons all possess a spin alignment in the direction of the magnetic field. By inspection, the same result occurs if the spins all point in the opposite direction, i. e.,

{ел)+ + = {о<к)__ ■ (7.60)

A further question of interest then is to consider a plasma for which the tritons spins are random and the deuterons are injected with a specified spin polarization. Setting therefore

f>i> fd=o, rd=o, /:=j, r=i (7.6i)

gives

M+, = [і + О + о + Щ) + оа0-= }СТ0 (7.62)

as for Eq.(7.57).

Accelerators exist which could supply spin polarized deuterium or tritium ions into a plasma. Then, since the spin polarization can be sustained for time periods up to 10 s, a 50% increased fusion power density could be sustained. Additionally, it has been found that under conditions of polarized fusion, the neutron and alpha reaction products emerge with a preferred directional distribution requiring therefore special containment-wall considerations.

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