Stimulated Emission of Fast Alfvén Waves within Magnetically Confined Fusion Plasmas

A fast Alfvén wave with a finite amplitude is shown to grow by a stimulated emission process that we propose for exploitation in toroidal magnetically confined fusion plasmas. Stimulated emission occurs while the wave propagates inward through the outer midplane plasma, where a population inversion of the energy distribution of fusion-born ions is observed to arise naturally. Fully nonlinear first-principles simulations, which self-consistently evolve particles and fields under the Maxwell-Lorentz system, demonstrate this novel “$\alpha$-particle channeling” scenario for the first time.

Figure 1

Stimulated emission of 10%–20% of the energy of the $\alpha$-particle population over a few gyroperiods, when subjected to resonant fast Alfvén waves that have much lower energy density. Temporal evolution of the minority $\alpha$-particle population energy density (the dashed traces) and deuteron energy density (the solid traces) in response to applied waves with a range of energy densities. Marked pairs of traces for $\alpha$ particles and deuterons show energy change in the presence of waves with energy densities ranging between ${10}^{-2}$ and ${10}^{-8}$ that of the energy initially in the $\alpha$ particles, and the null case, labeled 0, without an imposed wave. Energetic minority $\alpha$ particles transfer energy to thermal majority deuterons on shorter time scales when subjected to higher amplitude fast Alfvén waves. The eventual level of energy transfer is broadly the same. Vertical dashed lines annotated (i)–(iv) indicate the snapshots in time displayed in Fig. 4. The change in energy density (the ordinate) is plotted in units of the initial $\alpha$-particle energy density ${\epsilon }_{\alpha 0}$, and the time (the abscissa) is plotted in units of the $\alpha$-particle cyclotron time period ${\tau }_{c\alpha }=2\pi /{\omega }_{c\alpha }$.

Figure 2

Dominant waves, and their linear and nonlinear interactions, identified from Fourier transforms of the computed $E_x$ field in the simulations. These are obtained by computing the fast Fourier transform of the whole spatial and temporal domain from a simulation with an imposed Alfvén wave with an initial energy of ${10}^{-5}{\epsilon }_{\alpha 0}$. (a) $(\omega ,k)$ amplitudes. (b) $(t,k)$ amplitudes.

Figure 3

Coherent field oscillations persist through, and beyond, the sudden transition to strong nonlinearity in $\alpha$-particle dynamics. Linear (early time) and nonlinear (late time) propagation and evolution of energy wave packets at the imposed frequency ${\omega }_i$ and wave number $k_i$. Shading indicates the spatiotemporal amplitude of the 2D wavelet DFT at $({\omega }_i,k_i)$ of (a) the $E_x$ field and (b) the $\alpha$-particle number density for a wavelet window of the size $2\pi ({\omega }_i^{-1},|k_i^{-1}|)$ (see the text). Data are from the simulation shown in Fig. 2.

Figure 4

Sudden transition to nonlinear $\alpha$-particle dynamics at $t\simeq 4{\tau }_{c\alpha }$. Linear and nonlinear wave-particle interactions shown in the perpendicular velocity space of a randomly selected sample of 10% of $\alpha$ particles at four times, (i)–(iv), which are marked in Figs. 1, 2, 3. Shading represents the value of $x$ modulo $2\pi /k_i$ at $t=3{\tau }_{c\alpha }$, $4{\tau }_{c\alpha }$, $5{\tau }_{c\alpha }$, and $10{\tau }_{c\alpha }$. The dashed vertical trace shows the phase speed of the imposed fast Alfvén wave, ${\omega }_i/k_i$. Velocity is in units of the initial $\alpha$-particle speed, $v_{\alpha 0}$. Data are from the same simulation shown in Figs. 2 and 3.