Page 3 - Fusion reactivity of the pB11 plasma revisited

Nucl. Fusion 59 (2019) 076018
S.V. Putvinski et al
Figure 2. The ‘new’ and ‘old’ pB11 cross-section as function of center-of-mass (CM) energy.
where the symbols D and F stand for the diffusion and dynamic friction. νfus (v) is the rate of proton burnout (proton loss in fusion reactions), and S(v) is net source of protons (including fueling and loss from the system).
Note that Maxwellian field particles produce diffusion coefficient and dynamic friction that are related by the detailed balance principle. For the collisions with the non-Maxwellian particles (in our case, fast alphas) this relation does not hold. We use an asterisk to distinguish the contribution of the non- thermal alphas. Diffusion coefficients and dynamic frictions are evaluated in appendix A. We consider all the plasma spe- cies as isotropic.
Three kinetic effects are important in estimates of devia- tion of fp (vp) from the Maxwellian and thus must be taken into account.
– The first one is depletion of proton energy tail by cooling on colder electrons (Te < Ti). This effect leads to a reduc- tion of reactivity.
– The second effect is heating of the tail by energetic alpha particles resulting in an increase of tail density and thus the reactivity.
– The third one is depletion of proton energy tail by burnout at maximum cross section. The burnout leads to a small reduction of reactivity.
All these effects are encapsulated in equations (3)–(6) and the distribution function fp is found with the corresponding corrections included. With regard to the first two effects the net result (suppressing or enhancing of the ion tail) depends on the parameters of the system. For the typical parameters considered in this paper, the net effect is positive and adds ~10% to the reactivity on top of 20% increase related to new cross-section data.
2.2. Bremsstrahlung radiation and ion–electron energy exchange
For the power density of bremsstrahlung radiation we shall use fitting formula from [15] which describes with accuracy
Figure 3. The ratio of the relativistic energy exchange rate to the non-relativistic one, ν∗, as function of normalized electron temperature, t = Te/mc2. ei
Figure 4. Fusion power density produced in pB11 plasma and bremsstrahlung radiation as a function of the ion temperature. Fusion power calculated from reaction rates of [5] and coinciding with results of Nevins [5] is shown by dashed curve. Both curves are calculated for ion density ni = 1020 m−3and both scale as n2i .
better than 1% the quantum mechanical calculations [16] in a wide range of electron temperature and Zeff.
3
PBrem/W0 = 8.511t1/2 􏰃Zeff 􏰂1 + 1.78t1.34􏰁
􏰂 2 2.5􏰁􏰀
+2.12t 1+1.1t+t −1.25t . (7)
Here t = Te/mc2, W0 = e6n2e/mc2􏰄. The popular Rider’s formula [17] used in the paper [5] does not give accurate dependence on Zeff (although, accidentally, it gives a good fit with Te at Zeff ∼ 3 as in pB11 plasmas!).