Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas

P. Liu, D. Wu, T. X. Hu, D. W. Yuan, G. Zhao, Z. M. Sheng, X. T. He, and J. Zhang

Phys. Rev. Lett. 132, 155103 – Published 11 April 2024

Abstract

Electromagnetic turbulence and ion kinetics in counterstreaming plasmas hold great significance in laboratory astrophysics, such as turbulence field amplification and particle energization. Here, we quantitatively demonstrate for the first time how electromagnetic turbulence affects ion kinetics under achievable laboratory conditions (millimeter-scale interpenetrating plasmas with initial velocity of $2000 km / s$ , density of $4 \times 10^{19} {cm}^{- 3}$ , and temperature of 100 eV) utilizing a recently developed high-order implicit particle-in-cell code without scaling transformation. It is found that the electromagnetic turbulence is driven by ion two-stream and filamentation instabilities. For the magnetized scenarios where an applied magnetic field of tens of Tesla is perpendicular to plasma flows, the growth rates of instabilities increase with the strengthening of applied magnetic field, which therefore leads to a significant enhancement of turbulence fields. Under the competition between the stochastic acceleration due to electromagnetic turbulence and collisional thermalization, ion distribution function shows a distinct super-Gaussian shape, and the ion kinetics are manifested in neutron yields and spectra. Our results have well explained the recent unmagnetized experimental observations, and the findings of magnetized scenario can be verified by current astrophysical experiments.

Received 4 June 2023
Revised 18 December 2023
Accepted 12 March 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.155103

Physics Subject Headings (PhySH)

Nonlinear phenomena in plasmas Nuclear fusion Plasma instabilities Plasma turbulence

Particle-in-cell methods Plasma kinetic theory

Plasma Physics

Authors & Affiliations

P. Liu ¹, D. Wu ^2,*, T. X. Hu ^1,2, D. W. Yuan³, G. Zhao³, Z. M. Sheng ^1,†, X. T. He¹, and J. Zhang ²

¹Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou 310058, China
²Key Laboratory for Laser Plasmas and School of Physics and Astronomy, Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
³Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China

^*Corresponding author: dwu.phys@sjtu.edu.cn
^†Corresponding author: zmsheng@zju.edu.cn

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Vol. 132, Iss. 15 — 12 April 2024

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Images

Figure 1
(a) Schematic diagram of two counterstreaming plasmas generated by laser-ablation targets. There are three possible unstable modes: the filamentation mode (labeled with “FI”) with $k ⊥ v_{0}$ , Weibel mode (labeled with “WI”) with $k ∥ v_{0}$ , and two-stream mode (labeled with “TS”) with $k ∥ v_{0}$ , where $v_{0}$ is the flow velocity. Maps of filamentous current density along the $\pm y$ directions (denoted by red-blue colors) in $z − x$ (b) and $y − x$ (c) simulation planes.
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Figure 2
Top: unmagnetized case with $B_{0} = 0 T$ . Bottom: magnetized case with $B_{0} = 50 T$ . Snapshots of magnetic field [(a),(b)] and electric field [(c),(d)] at $t = 800 ps$ . (e) and (f) are 2D Fourier transforms of magnetic field shown in (a) and (b), respectively. [(g),(h)] Distribution functions of the deuteron beams at $t = 6 ns$ , where the blue dots and solid (dashed) lines respectively represent the simulation data and Gaussian (super-Gaussian) fitting curves with the form of $\exp [- (v_{y} / v_{t h})^{α}]$ for high-energy ions. The inset of (g) represents the case without considering electromagnetic effects, i.e., the electromagnetic fields are not applied to the particles. We also perform another magnetized case where $B_{0} = 10 T$ , and the simulation results about the distributions of electromagnetic fields, Fourier transform, and velocity distribution function can be seen in the Supplemental Material [26].
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Figure 3
Temporal evolution of work done by turbulent electric field for sampled deuterons in the unmagnetized case with $B_{0} = 0 T$ (a) and magnetized case with $B_{0} = 50 T$ (b), where the colored curves represent different tracked deuterons. Temporal evolution of the deuteron energy spectra (colored by time) for three scenarios of excluding electromagnetic field effects ( $w / o$ EMF) (c), $B_{0} = 0 T$ (d), and $B_{0} = 50 T$ (e). (f) Neutron yields as the functions of time in different $C D$ - $C H$ cases. (g) Average reactivity of $D$ - $D$ thermonuclear fusion as the function of temperature [45, 46], where the marks of blue circle, magenta pentagram, and red diamond, with $6.31 \times 10^{- 20}$ , $2.20 \times 10^{- 19}$ , and $1.88 \times 10^{- 18} {cm}^{3} s^{- 1}$ , correspond to three temperatures in (c)–(e), respectively.
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Figure 4
Temporal evolution of neutron yields (a) and energy spectra at $t = 6 ns$ (b) in different $C D$ - $C D$ cases of without considering electromagnetic effects ( $w / o$ EMF), $B_{0} = 0 T$ , $B_{0} = 10 T$ , and $B_{0} = 50 T$ . The blue line in (a) represents the yield difference between the cases of $w / o$ EMF and $B_{0} = 0 T$ as the function of time. Neutron velocity shifts as the function of emitted angle $θ$ in the cases of $w / o$ EMF (c) and $B_{0} = 0 T$ (d), where the red dashed lines represent $Δ V_{n} = m_{r} v_{r}^{2} / (2 v_{n 0} m_{⋆})$ , $v_{n 0}$ is the velocity of a neutron created from a cold and stationary deuterium plasma, $m_{r} / m_{⋆} ≃ 0.748$ , and $v_{r} = 2 v_{0}$ .
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