Effect of Dimensional Changes on Plasma Characteristics in Electrothermal Capillary Discharges for Optimized Performance in Fusion Pellet Injection

Abstract

Geometrical changes in capillary discharges influence the plasma properties and can control exit parameters to certain desired values. For a fixed capillary radius of 2 mm and a 72-μs 43.9-kA peak discharge current, the plasma temperature is about 2.7 eV for different capillary lengths due to the constant input energy, while the number densities tend to saturate for capillary lengths greater than 12 cm. The electrical conductivity reaches 4.02 × 104 Ω⁻¹ m⁻¹ and then tends to saturate for 9-cm capillary length. The maximum bulk velocity at the capillary exit slightly increases with the increase in the capillary length from 6.15 to 6.26 km/s for lengths below 18 cm and decreases to 5.88 km/s for longer capillaries due to the higher amount of ablated mass and increased drag forces. For a 9-cm length with the same 72-μs 43.9-kA peak discharge current, the increase in the capillary radius reduces the energy density, which in turn reduces the total ablate mass, plasma density, electrical conductivity, and exit pressure. It is shown that the plasma temperature decreases from 4.6 to 2.1 eV by increasing the capillary radius and radiant heat flux also drops from 463 to 18.1 GW/m². The exit bulk velocity drops from 8.7 to 5.3 km/s as the radius increases from 0.5 to 3.6 mm, respectively. The design features of a capillary discharge can be adjusted for the radius and length, to produce specific plasma parameters for desired applications. Scaling laws relating exit peak plasma parameters to radius and length are obtained to facilitate quick estimate of plasma parameters. The validation of this model has been confirmed by confronting with experimental measurements.