Abstract
A computational fluid dynamics and plasma model of a collisional (∼ a few Torr) radiofrequency (at 13.56 MHz) argon plasma capacitively coupled in a converging-diverging nozzle (applied to the optimisa- tion of electrothermal plasma thrusters for space use) shows the formation of a strong stationary current-free double layer (CFDL) at the 1.5 mm diameter nozzle throat for a downstream pressure of ∼ 0.1 Torr. The cycle average magnitude of the double layer potential is ∆ΦDL = 77 V and the electron temperature at the high potential edge of the double layer is kBTe = 2.64eV, yielding a strength of ∆ΦDL/(kBTe) ∼ 30. The double layer is 1.2 mm wide which corresponds to ∼ 90 Debye lengths. The axial electric field of the double layer accelerates ions along the nozzle to a maximum drift velocity of 17 km s−1, about 3.3 times the ion sound speed, and their kinetic energy is transferred to neutrals by ion-neutral charge exchange col- lisions. The ion transit time τi through the potential structure spontaneously forming at the nozzle throat is about 5 times the radiofrequency excitation period τRF. These findings are discussed in the broader context of double layer physics and the dynamics of their formation as well as in the context of electrothermal thruster optimisation in which neutral propellant heating via ion-neutral charge exchange collisions is the main source of thrust.
Highlights
Electric double layers (DLs) are transient or stationary localized potential structures which form in space plasmas [1,2,3], laboratory plasmas [4,5,6,7,8,9,10], and numerical simulations of plasmas [11,12,13]
In the present computational fluid dynamics (CFD)-plasma model, the hot ions generated via acceleration through the DL thermalize with the neutrals via charge exchange collisions, as shown by the strong increase and subsequent decrease of uz,i just downstream of the nozzle throat (Figure 4)
The pressure gradient at the nozzle throat is a measure of the geometric expansion and induces significant changes in the plasma parameters as was shown for the resulting potential profile for the reference simulation run for a downstream outlet pressure of 0.349 Torr instead of 0.1 Torr (Figure 3)
Summary
Electric double layers (DLs) are transient or stationary localized potential structures which form in space plasmas [1,2,3], laboratory plasmas [4,5,6,7,8,9,10], and numerical simulations of plasmas [11,12,13]. Current-free DLs were first analytically proposed by Perkins and Sun [32] and experimentally demonstrated by zero-current operation of Qmachines [20], two-electron-temperature plasma expansion in vacuum [9], and lately in low pressure expanding magnetized radiofrequency plasmas in diverging or converging-diverging magnetic nozzles [10, 33,34,35,36]. A computational fluid dynamics (CFD) and plasma simulation of an unmagnetized converging-diverging argon plasma nozzle is developed that shows the spontaneous formation of a current-free stationary collisional electric DL at the nozzle throat when the plasma expands into sufficiently low pressure environment (0.1 Torr). In the present study the millimetric size of the nozzle does not allow a direct comparison with experiments but the main characteristics of the radiofrequency plasma periodic steady state have been previously verified experimentally (via electrical and optical probes), computationally, and analytically in cylindrical geometry [31, 44,45,46] in the context of electric propulsion with the thruster referred to as “Pocket Rocket.” The simulations are performed using the commercial CFD-ACE+ multiphysics package which includes flow, heat transfer, chemistry, electric, and plasma modules described in detail in ESI-Group [47], Kolobov [48], and Kolobov et al [49]1
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