Page 2 - Fusion reactivity of the pB11 plasma revisited

Nucl. Fusion 59 (2019) 076018
S.V. Putvinski et al
temperature as a parameter and evaluate fusion power, calcu- lated with account for kinetic modification of the ion tail, and compare the result with Bremsstrahlung radiation. Electron temperature shall be estimated self-consistently from power balance for electrons. As in [5], we neglect other loss chan- nels such as particle losses and synchrotron radiation which are device specific. We thereby check only the necessary con- dition for ignition in pB11 fuel. This allows us to make direct comparison of our reactivity calculations with those of [5]. This also provides a basis for formulating specifications of the confinement device.
2.1. Fusion power density
The fusion power density is
Figure 1. Reactivity multiplied by the total yield of fusion reaction, Y (MeV), for DT and aneutronic reactions. Dotted line for DT accounts for the energy of the alpha particle only.
In addition to ion kinetic effects we have accounted for rela- tivistic corrections to the collisional processes involving elec- trons, as the latter typically have temperatures of 100–200 keV in pB11 plasmas. These corrections contribute to enhanced ion–electron energy exchange and thereby to a slight increase of Bremsstrahlung radiation.
We emphasize that our paper is oriented toward magnetic confinement fusion. Accordingly, we assume that the plasma is in a steady state maintained by continuous plasma heating and fueling, balanced against fusion product exhaust. The pB11 reac- tions are of interest also for high-energy density systems driven by intense pulsed lasers, e.g. [10]. A significant number of alpha particles have been detected at high laser intensities [11–13]; the knock-on collisions of just born alphas with protons and Borons have been identified as a factor that increases the yield [14].
The paper is organized as follows. In section 2.1 the fusion power is evaluated accounting for the aforementioned kinetic corrections; in section 2.2 bremsstrahlung radiation is assessed; in section 2.3 the results of calculations presented in the previous two sections are combined to evaluate the plasma energy balance and conclusion is drawn that ignition and high-Q operation are feasible. Section 3 contains sum- mary and discussion. The details of kinetic calculations are presented in the series of appendices.
2. Ignition in pB11 plasma
In this section we shall repeat the analysis of [5, 6] with the new cross sections [9] and with account for kinetic effects. The proton distribution function for the lower energies is close to Maxwellian and can therefore be characterized by the temperature. The proton ‘tail’ that makes significant contribution to the reactivity deviates from the Maxwellian distribution. These deviations depend on the temperature of the bulk ions. Following [5], we shall use this bulk ion
Here
Pfus = npnB ⟨σv⟩ Y. (1) fp (vp) fB (vB) σ (u) ud3vpd3vB. (2)
⟨σv⟩ =
ˆ
u = |vp − vB| and Y is fusion yield, Y = 8.68 MeV for pB11. We shall use the new cross section [7–9] shown in figure 2. Error bars of the new measurements are ~3% [9]. Equation (1) contains only a nuclear energy release, but the reacting proton and Boron transfer to reaction products also their initial kinetic energy ~1 MeV which is more than ten percent of the fusion energy release. In our analysis we assume that fusion alphas are confined long enough to transfer this additional energy to both protons and electrons, i.e. the kinetic energy returns back to the reacting plasma and thus does not affect the overall power balance.
The peak in the cross section lies in the suprathermal tail of the proton distribution function, fp (v). When considering kinetic effects in this energy range, one can neglect collisions of the tail particles with each other, and account only for their collisions with the thermal particles. In other words, we con- sider the energetic ions as ‘test particles’ in the sea of ‘field particles’, which include thermal protons, Borons, energetic alpha-particles, and electrons. We assume that thermalized alphas are efficiently removed from the system. We include also collisions with fast alpha-particles, which cause ‘lift’ of the proton tail. Within this approximation, the kinetic equa- tion for the proton distribution function is:
1 ∂v2ïDp∂fp +Fpfpò−νfus(v)fp+S(v)=0 (3) v2 ∂v ∂v mp
Dp =Dpp +DpB +Dpe +D∗pα (4)
2ˆÅDpp +DpB Dpeã ∗
Fp =mpv T + T +Fpα (5)
2
νfus (v) =
e
fB (vB)σ(u)ud3vB ≈ nBσ(v)v (6)