Page 4 - Fusion reactivity of the pB11 plasma revisited

Nucl. Fusion 59 (2019) 076018
Electron temperature in equation (4) is evaluated self-con- sistently from power balance equation for electrons retaining only the main and unavoidable terms (as in [5])
Pα,e + Pi,e = PBrem. (8)
Here Pα,e is electron heating by the slowing-down alphas, and Pi,e is electron heating by thermal protons and Borons. We neglect electron energy losses by synchrotron radiation and conduction energy losses assuming that magnetic con- finement device is designed to make them low. Only about 10% of initial alpha particle energy is deposited to electrons at Te = 100–200 keV. The rest is going to the ion components. For more accurate calculations of Pα,e we have to account for additional energy in alpha particle source due to finite kinetic energy of reacting protons and Borons (appendix B)
Energy exchange rate between electron and thermal ions corrected for relativistic effects (appendix C) is:
Pei=3νei(Ti−Te) (9) 2
with »
S.V. Putvinski et al fusion energy release in our case comes out of the system in
the form of Bremsstrahlung radiation.
3. Summary
A re-assessment of the basic features of the hot pB11 plasmas leads us to a more optimistic prediction on the feasibility of the pB11 fusion reactor than the earlier analyses, e.g. [4–6]. The main reasons for more optimistic conclusions are two- fold. First, the appearance of the new, more accurate, measure- ments of the pB11 reaction cross-sections [8, 9] which result in ~20% higher reactivity in a relevant energy range than those used in [5, 6]. The second favorable effect is the kinetic mod- ification of the proton distribution function at energies sig- nificantly contributing to the fusion yield. Combined, these factors bring us to a conclusion that, under the same assump- tion about the plasma confinement as those of [5, 6], the pB11 plasma can come close to the sustained burn and, certainly, can operate as a high-Q system.
One should not of course underestimate the difficulties of reaching an almost perfect plasma confinement assumed both in [5, 6] and in the present paper. However, this belongs with reactor study and should be addressed elsewhere. Here we see that the necessary conditions required for reaching a high-Q performance of the pB11 plasma and even its ignition can be satisfied.
Acknowledgments
Authors are grateful to Dan Barnes, Erik Trusk, and Michel Tuszewski for helpful comments.
Appendix A. Kinetic equation for isotropic distribu- tion function
We used assumptions identical to those made by Nevins and Swain [5, 6]: isotropic distribution functions for all species; Maxwellian distributions at thermal energies; equal temper- atures of the protons, Borons, and slowed-down alphas:
Ä􏰀􏰀 􏰀2ä 􏰀3 1+2Te +2Te πTe/2
ν=ν∗´ ¶√ ©.(10) ei ei ∞exp −( 1+x2−1)/T􏰀e x2dx
0
Here ν∗ is classical, non-relativistic exchange rate ([18], ei 2
equation (2.17)), and Te = Te/mc . The corrected energy exchange is about 10% higher than the classical one (figure 3) and results in somewhat higher electron temperature and thus higher Bremsstrahlung radiation.
2.3. Results of calculations
Distribution function of suprathermal protons had been evalu- ated from equation (3) and used in equation (2) to calculate fusion power. Figure 4 shows comparison of Bremsstrahlung radiation with fusion power as a function of ion temperature. For each ion temperature the electron temperature has been evaluated by equation (8). Calculations are done for optimum Boron concentration, nB/ni = 15%. As in [5], we did not account for He impurity in the ion mix. Increase of fusion reactivity shown in figure 4 is mostly due to higher cross sec- tion (~20%). Kinetic effects contribute additional ~10%. The effect of depletion of the ion tail by the burnout effect is less than 1% at the optimum ion temperature T ~ 300 keV. As can be seen Bremstrahlung radiation does not preclude ignition in pB11 plasmas.
In any steady-state fusion system, an auxiliary power Paux has to be delivered to the plasma for the plasma control, fueling, and compensation of additional losses not included in our model. The relative significance of these external sources
Tp =TB ≡T
different (and lower) self-consistently calculated electron
temperature:
Te < T. (A.2)
Densities: np, nB, ne = np + ZBnB. No spatial dependences are considered.
In difference to Nevins and Swain we include into con- sideration inherently present kinetic effects of proton up-scat- tering on the non-thermal alpha-particles, and higher-energy proton down-draft by colder electrons. These processes can both increase or decrease the fusion yield by ~10%, depending on the details.
The steady-state kinetic equation for the protons is given by equation (3) in section 2. The normalization of the distribu- tion functions is as follows:
can be characterized by the parameter Q defined as Pfus
Q=Paux. (11)
(A.1)
Although ignition in pB11 plasma is marginal, a high Q oper- ation can be reached in a broad range of temperatures. The
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