Electron beam–plasma discharge in GDT mirror trap: particle-in-cell simulations

Abstract

The paper presents the results of numerical simulations of the collective relaxation of an electron beam in a magnetized plasma at the parameters typical to experiments on the ignition of a beam-plasma discharge in the Gas Dynamic Trap. The goal of these simulations is to confirm the ideas about the mechanism of the discharge development, which are used to interpret the results of recent laboratory experiments [Soldatkina et al 2021 {\it Nucl. Fusion}]. In particular, a characteristic feature of these experiments is the localization of the beam relaxation region in the vicinity of the entrance mirror. A strong mirror magnetic field compresses the beam so that its transverse size becomes less than the wavelength it excites. In addition, near the mirror, the electron cyclotron frequency is much higher than the plasma one, which can significantly affect the possibility of propagation of the most unstable waves outside the beam. Particle-in-cell simulations make it possible not only to find how efficiently intense plasma oscillations penetrate the rarefied periphery, but also to prove that the turbulent zone in a realistic nonuniform plasma has regions dominated by transverse electric fields. This creates the necessary conditions for efficient acceleration of the trapped particles to energies much higher than the initial beam energy.

Electron beam-plasma discharge in GDT mirror trap: experiments on plasma start-up with electron gun

“…Since x-ray radiation begins to reduce only when the mirror field becomes lower than the value B output = 10.2 T (which shifts the stopping points of trapped electrons by 2.6 cm from the plug (figure 13(b)), we conclude that large-E oscillations driven in the mirror occupy an area with a characteristic size of 5 cm. The same estimate for the beam relaxation length is obtained in PIC simulations [31]. Since the x-ray signal drops by half when the mirror field B output = 5 T prevents the trapped particles from approaching the plug closer than 11 cm, we conclude that half of the total kinetic energy is acquired by fast particles during their interactions with oscillations concentrated at distances of 2.6-11 cm from the plug.…”

“…In the first experiments, rather weak magnetic fields (Ω e < ω p ) with a small mirror ratio of 2-4 were used, and the distance between the mirrors was comparable to the relaxation length of the beam, so the question of the spatial localization of plasma oscillations along the trap was not of a fundamental importance. On the contrary, in the GDT setup, the magnetic field changes along the axis by a factor of more than 30, and the distance between the mirrors is so great that, according to simple estimates and the results of particle-in-cell simulations [31], the beam relaxation region should lie entirely in the vicinity of the entrance mirror with a strong magnetic field (Ω e /ω p ∼ 10). Since plasma during beam injection is successfully created in the entire volume of the trap in our experiments, it is required either to experimentally confirm the localization of plasma oscillations in the region of a strong magnetic field, but then to question the adequacy of geometric optics for describing the radial propagation of the most unstable modes to periphery, or to demonstrate the possibility of effective beam relaxation in the central part of the trap, where Ω e < ω p , explaining what effects breaks the instability in the input mirror.…”

Summary of the 3rd International Workshop on Gas-Dynamic Trap based Fusion Neutron Source (GDT-FNS)

“…This observation is critically important for the neutron source design as it enables us to loosen the requirements to capacity of its pumping system. The method of initial plasma build up was developed using an injection of low energy electron beam into a gas target through the end mirror [22]. The attained plasma parameters were adequate to provide efficient trapping of the injected neutral beams and accumulation of fast ions.…”

Numerical simulations of a continuously injected relativistic electron beam relaxation into a plasma with large-scale density gradients

“…Under laboratory conditions, plasma mechanisms for EM radiation generation are currently studied as promising sources of high-power narrowband THz radiation [13]. Also injection of non-relativistic electron beams into a gas is a perspective technique for creating a target plasma in open magnetic traps for plasma confinement, while beamexcited transversely polarized whistlers can lead to the formation of electron populations accelerated to energies an order of magnitude greater than the initial energy of the beam particles [14,15].…”

“…The first effect was the formation of plasma in a volume much larger than the area occupied by the beam, and the second one was the appearance in the system of electrons accelerated to energies of the order of 300 keV. To interpret the observed effects, 2D3V PIC simulations of the electron beam injection into the region near the input magnetic mirror have been carried out, taking into account the growing longitudinal and decreasing transverse density gradients and magnetic field curvature [15]. Numerical experiments have demonstrated the acceleration of electrons in the region of beam-plasma turbulence up to a value of the order of 100 keV in one act of interaction with a plasma wave.…”