Energization of Proton via Beam-Driven Ion Bernstein Waves in p11B Plasmas

Abstract

Energizing background ions plays a pivotal role in all forms of thermal nuclear fusion, as it can increase the fusion reaction rate without affecting the overall mechanical equilibrium. This is particularly critical for p11B fusion due to its exceptionally high operating temperature and substantial energy losses from bremsstrahlung radiation. Here, we report a nonlinear mechanism that efficiently transfers the energy of injected heating beams to background protons in p11B mixed plasmas, via fully kinetic Particle-In-Cell (PIC) simulations. When a proton neutral beam is injected into p11B plasmas, it triggers the excitation of ion Bernstein waves (IBWs) at harmonics of the proton cyclotron frequency. In the initial linear stage, the energy channels to background electrons and protons might be comparable, consistent with theoretical model for the energy transfer. However, in the latter nonlinear stage, the dominant channel transfers to background protons, generating a non-Maxwellian population of energetic protons. This transition is driven by a nonlinear spectral cascade of IBWs toward lower frequencies and longer wavelengths, which strengthens wave proton coupling while suppressing wave electron coupling.

Figures (5)

• Figure 1: Schematic of neutral beam injection into $\mathbf{p\prescript{11}{}{B}}$ plasma. The beam is injected obliquely at an angle $\theta_b$ relative to the background magnetic field $B_0$ and follows an annular distribution perpendicular to the field.
• Figure 2: (a) Temporal evolution of the energy change of each particle species. (b) Energy transfer rate per unit initial beam energy and temporal evolution of the electromagnetic field energy. (c) Temporal evolution of the background protons energy spectra (colored by time).
• Figure 3: (a) Dispersion relation from PDRK/BO. Purple and red dashed lines denote the Alfvén velocities of background boron ions and protons, given by $v_{A\{\text{H,B}\}}=c/\sqrt{\omega _{p\left\{ \text{H,B} \right\}}/\omega _{c\left\{ \text{H,B} \right\}}}$. Green dashed line represents the total Alfvén velocity $v_A=c/\sqrt{\sum_s{\left( \omega _{ps}/\omega _{cs} \right)}}$, while the gray dotted line indicates the beam resonance condition. (b) The dispersion relation for z-component of the fluctuating magnetic field $\delta B_z$. The blue dashed and green dash dotted lines represent $\omega=1.32kv_A$ and the beam resonance condition, respectively. (c) The growth rate versus wave vector. (d) Energy transfer ratio normalized to beam energy. Gray dashed lines indicate $7.5kv_A/\omega _{c\text{H}}$ and $9.96kv_A/\omega _{c\text{H}}$, respectively.
• Figure 4: (a) and (b) are temporal evolution of $\boldsymbol{k}$ and $\omega$. (c) A snapshot of the the phase space of background protons.
• Figure 5: (a) Electron and ion energy transfer rates and phase velocity of excited IBWs as functions of $\theta_b$ at nonlinear saturation. (b) Background proton energy spectra for different $\theta_b$ at nonlinear saturation.