Modeling and diagnostics for plasma discharge capillaries

In this paper, we show how plasma discharge capillaries can be numerically modeled as resistors within an RLC-series discharge circuit, allowing for a simple description of these systems, while taking into account heat and radiation losses. An analytic radial model is also provided and compared to the numerical model for plasma discharge capillaries at thermal equilibrium, with corrections due to radiation losses. Finally, diagnostic techniques based on visible spectroscopy of plasma emission lines are discussed both for atomic and molecular gases, comparing experimental results with numerical simulations and theoretical calculations.

Figure 1

Plot of the discharge current flowing in the capillary.

Figure 2

Plot of the plasma resistance evolution.

Figure 3

Plot of the average (over the capillary volume) plasma temperature evolution. Superimposed as a dashed curve is the discharge current's profile of Fig. 1 (arbitrary units).

Figure 4

Plot of the electron-ion collision rate evolution.

Figure 5

Plot of the evolution of the average (over the capillary volume) electron plasma density.

Figure 6

Plot of the different contributions on the right side of Eq. (2).

Figure 7

Comparison of the plasma temperature among different gases, given the same input discharge parameters.

Figure 8

Comparison of the discharge current among different gases, given the same input discharge parameters.

Figure 9

Comparison of the electron plasma density among different gases, given the same input discharge parameters.

Figure 10

Function $f\left(\varrho \right)$, expressing the dependence of $T\left(0\right)$ upon the $\varrho$ parameter.

Figure 11

Comparison between the solution $u\left(\xi \right)$ without radiative corrections (dashed line) and with radiative corrections (solid line) for the case $\varrho =3.5\times {10}^{-2}$.

Figure 12

Comparison between the plasma temperature's transverse profile without radiative corrections (dashed line) and with radiative corrections (solid line) for the case $\varrho =3.5\times {10}^{-2}$.

Figure 13

Comparison between the magnetic field's (associated to the discharge current) transverse profile without radiative corrections (dashed line) and with radiative corrections (solid line) for the case $\varrho =3.5\times {10}^{-2}$.

Figure 14

Comparison between the electron plasma density's transverse profile without radiative corrections (dashed line) and with radiative corrections (solid line) for the case $\varrho =3.5\times {10}^{-2}$.

Figure 15

Measurement of the Stark-broadened hydrogen Balmer-$\alpha$ line.

Figure 16

Measurement of a Stark-broadened helium emission line corresponding to the atomic transition $3{}^{1}P\to 2{}^{1}S$.

Figure 17

Measurement of Stark-broadened molecular nitrogen emission lines corresponding to the multiplet $3s^{4}P-4p^4{S}^0$: measurement limited by the spectrometer's resolution.

Figure 18

Schematic of the discharge circuit used for the experiment of electron plasma density measurement. Legend: $R$, resistor; $C$, capacitance; $L$, inductance; $D$, diode; and SCR, silicon-controlled rectifier.

Figure 19

Simulations referring to the experimental data on Stark-broadening for hydrogen, helium, and nitrogen.

Figure 20

Characterization of the electron plasma density for the hydrogen plasma outside the capillary.