Experimental study on edge energetic electrons in EXL-50 spherical torus

A significant number of confined energetic electrons have been observed outside the Last Closed Flux Surface (LCFS) of the solenoid-free, ECRH sustained plasmas in the EXL-50 spherical torus. Several diagnostics have been applied, for the first time, to investigate the key characters of energetic electrons. Experiments reveal the existence of high-temperature low density electrons, which can carry relatively a large amount of the stored energy. The boundary between the thermal plasma and the energetic electron fluid appears to be clearly separated and the distance between the two boundaries can reach tens of centimeters (around the size of the minor radius of the thermal plasma). This implies that the Grad-Shafranov equilibrium is not suitable to describe the equilibrium of the EXL-50 plasma and a multi-fluid model is required. Particle dynamics simulations of full orbits show that energetic electrons can be well confined outside the LCFS. This is consistent with the experimental observations.

💡 Research Summary

The paper reports a comprehensive experimental and numerical investigation of energetic electrons that reside outside the last closed flux surface (LCFS) in the EXL‑50 spherical torus, a medium‑size, solenoid‑free device that relies on 28 GHz electron cyclotron resonance heating (ECRH) for plasma production and current drive. Using a suite of diagnostics applied for the first time in this context, the authors demonstrate that a population of high‑temperature, low‑density electrons exists in the edge region and can carry a substantial fraction of the plasma’s stored energy.

The diagnostic campaign includes (i) a reciprocating Langmuir probe equipped with two adjacent tips of different material (stainless‑steel and tungsten) to quantify secondary electron emission and back‑scattered electron effects, (ii) two high‑speed visible‑light cameras (M120 and D240) operating at 300 fps that capture the probe’s penetration trajectory and the evolution of a boron‑powder injection plume, and (iii) a hard X‑ray (HXR) detector that monitors bremsstrahlung emission from energetic electrons striking the probe. During a typical discharge (120 kW ECRH, plasma current rising from 90 kA to 130 kA), the probe is inserted from 10 cm outside the LCFS to 20 cm inside. While the line‑integrated density and plasma current remain essentially unchanged, the HXR count rate and the appearance of white‑noise spikes on the camera CCD increase sharply when the probe reaches the deepest position, indicating a dense flux of energetic electrons in the edge region. The tungsten tip shows a less pronounced melting than the stainless‑steel tip, consistent with the larger secondary‑electron emission coefficient of stainless steel, which makes the measured probe current more positive.

A separate experiment injects 70 µm boron particles at 8–10 mg s⁻¹ through a top port. High‑speed imaging shows that the particles become fully ionized within about 0.5 m of penetration, a depth far exceeding what would be expected from ionization by the bulk plasma (density ≈8 × 10¹⁷ m⁻³). The authors infer that collisions with the energetic electron population dominate the ionization process, providing an indirect confirmation of their presence.

Because the conventional Grad‑Shafranov equilibrium reconstruction (e.g., EFIT) assumes that all toroidal current resides inside the LCFS, it fails to capture the observed edge current. The authors therefore employ a multi‑fluid equilibrium model that treats thermal electrons, energetic electrons, and ions as separate fluids. Optical reconstruction of the plasma boundary—obtained by fitting the brightness histogram of the visible‑light images—yields an LCFS radius of ≈0.96 m. The multi‑fluid simulation predicts a second, broader boundary for the energetic electrons at ≈1.2 m. Temperature profiles show that the energetic electrons are roughly three orders of magnitude hotter than the thermal electrons, while their density is about one order of magnitude lower. This separation of the thermal and energetic electron fluids explains why a single‑fluid model cannot reproduce the measured magnetic flux surfaces.

Full‑orbit particle simulations are performed using the magnetic field from the multi‑fluid equilibrium. Scanning initial positions reveals that 2 MeV electrons can remain confined on passing orbits that extend up to R ≈ 1.13 m, i.e., well outside the LCFS but still within the open‑flux region bounded by the limiter. The simulated confinement region matches the experimental observations of probe melting and HXR emission, confirming that the edge energetic electrons are indeed magnetically trapped.

Finally, the authors evaluate the heat load on the probe tip. Assuming a parallel heat flux of 4.2 MW m⁻², a one‑dimensional heat‑conduction model predicts that a tungsten tip reaches its melting point (3410 °C) within 5 s, while a stainless‑steel tip would exceed its melting point (1850 °C) even earlier. This calculation quantitatively explains the observed differential melting of the two probe materials and underscores the importance of accounting for secondary‑electron emission when interpreting probe data in high‑energy‑electron environments.

In summary, the study provides (1) direct experimental evidence of a substantial energetic‑electron population residing outside the LCFS, (2) a multi‑fluid equilibrium reconstruction that captures the distinct thermal and energetic electron boundaries, (3) full‑orbit simulations that validate the magnetic confinement of these electrons, and (4) a detailed thermal analysis of probe interaction with the edge plasma. These findings challenge the adequacy of traditional single‑fluid MHD models for solenoid‑free spherical torus devices and open new avenues for exploiting edge energetic electrons in current drive and plasma control strategies.