Plasma diagnostic experiments are used for understanding the dielectric strength of gaseous cooling media. Plasma measurements on helium-nitrogen gas mixtures with varying composition were conducted with a single-tip Langmuir probe. The data from the measurements were used to derive the electron temperature and electron density. The results suggest that the measured electron temperature is suitable for assessing the dielectric strength variation of the gaseous media as a function of gas composition. However, the results also confirmed that the measured electron density is substantially influenced by the effective wall area of the plasma chamber and thus is inappropriate for being used as the indicator of dielectric strength variation.
I. INTRODUCTION
Liquid nitrogen (N2) has been widely used for cooling high-temperature superconducting (HTS) power applications due to its availability, high heat capacity, and high dielectric strength.1 However, gaseous helium (He) is the preferred cooling media for certain HTS power applications, in which wider operating temperature range and reduced asphyxiation hazard are crucial.2,3 One of the major challenges of using gaseous He is its low dielectric strength, which limits the operation of He-gas-cooled devices to low voltages, compared with that of liquid N2.3 To overcome the challenge, we have been systematically exploring the modified gaseous He media with the addition of small mole fractions of other gases through experimental and theoretical means.4–6 We discovered that the addition of molecular gases such as hydrogen (H2) and N2, even with small concentrations, substantially improves the dielectric strength of the gaseous media.7 According to our analysis on electron kinetics, the main cause for the dielectric strength improvement seen in the gas mixtures was substantial electron energy dissipation (i.e., reduction in mean electron energy) resulting from increased excitation electron-scattering processes as the concentration of molecular gases increased in the gas mixtures.4
To further understand the physics and the fundamental reasons for the observed dielectric strength enhancements of gaseous He mixtures, we introduce a plasma diagnostics experiment. This study involves the Langmuir probe plasma diagnostics method, which observes the fundamental characteristics of plasmas, to estimate the dielectric properties of He-N2 gas mixtures. We measure the electron energy distribution function (EEDF) of the gas mixtures with varying gas composition using the Druyvesteyn method.8–11 Then, plasma parameters including electron temperature (Te) and electron density (ne) are derived from the measured EEDF data.12,13 To validate the measured data, we model the He-N2 plasmas based on the particle balance equation and power balance equation.10,14 The estimated values and the evolution of electron temperature Te and electron density ne agree well with those of the measurements. The results show a decreasing Te with increasing N2 concentration, but an increasing ne with the increasing mole fraction of N2 in the He-N2 plasma. In this paper, we explain the reasons for the opposite trend in the plasma parameters and show how the results can be used for assessing the dielectric strength of gas mixtures.
II. EXPERIMENT
Figure 1 shows the experimental setup established for the plasma measurements conducted for the study. The plasma chamber is made of a cylindrical borosilicate glass (Pyrex) tube with 51 mm in diameter and 600 mm in length, and is equipped with an anode and cathode made of stainless steel on each end. A negative direct current (DC) voltage of –300 to –400 V is applied to the cathode using a DC power supply while keeping the anode electrically grounded. A static gas mixer in conjunction with two mass flow controllers (MFC) is used to vary the composition of the gas mixture containing He and N2. While the chamber is evacuated by a series connected scroll pump and a turbo molecular pump, gas pressure in the chamber is maintained at 30 mTorr (3.99 Pa) by controlling the gas flow using the mass flow controllers. A calibrated absolute capacitance manometer (MKS Baratron) is used to monitor the pressure in the chamber, and the discharge power is maintained at 33 W throughout the study. A Langmuir probe made of a cylindrical tungsten wire that is 0.125 mm in diameter and 10 mm in length was used. The dimension of the probe corresponds to the probe-to-chamber surface area ratio of 1/25000. The tip of the Langmuir probe is placed 200 mm away from the anode, immersed in the He-N2 plasma. The measurements represent the plasma parameters of the entire chamber by maintaining the non-local electron kinetics throughout the study. The distinction between the local and the non-local electron kinetics is based on the electron energy relaxation length (λϵ),12
where λm is the mean free path accounting for momentum transfer collisions, and λ* is the mean free path accounting for all collisions as shown below,
where j represents gas species, ng is gas number density, m is the electron mass, and M is the mass of a neutral. Furthermore, σm, σel, σex, and σiz are momentum transfer, elastic, excitation, and ionization cross sections, respectively. When electron energy relaxation length λϵ is longer than the chamber length, the electron kinetics is non-local. Under such condition, electrons can travel throughout the chamber while losing the similar amounts of energies regardless of spatial location, which indicates that a measurement at a given location in a chamber represents the plasma properties of the entire chamber. Figure 2 shows the calculated energy relaxation length of all He-N2 plasma mixtures at 30 mTorr. Due to the large rotational and vibrational excitation cross sections of N2,15 the energy relaxation length is shortest around 2–3 eV. Nevertheless, for all plasma mixtures, the energy relaxation length is longer than the chamber length, which suggests that non-local electron kinetics is satisfied throughout the study.
Electron energy relaxation length λϵ of He-N2 plasmas at 30 mTorr compared with the chamber length.
Electron energy relaxation length λϵ of He-N2 plasmas at 30 mTorr compared with the chamber length.
The I-V characteristic curves of He-N2 plasmas are measured by a digital multimeter (Rigol DM3058E) by sweeping the probe voltage. The Druyvesteyn method is used to derive the electron energy probability function (EEPF) from the measured I-V curves8,11
where ϵ is the electron energy, m is the electron mass, e is the elementary charge, Ip is the probe current, Vp is the probe voltage, and A is the surface area of the probe tip. Once the EEPF is obtained, the EEDF is derived from the EEPF through the following relationship:
Finally, the plasma parameters including ne and Teff are derived by integrating the EEDF
where is a symbol for average and F(ϵ) is the EEDF. It should be noted that in the low temperature plasmas, average electron energy is known as effective electron temperature Teff, which is a parameter typically used for representing the overall temperature of a non-Maxwellian EEPF.
III. MEASURED PLASMA PARAMETERS
Figure 3 shows the EEPF derived from the measured I-V curves of He-N2 plasmas. During the measurements, the mole fraction of N2 in the He-N2 mixture was increased in steps of 10% while the gas mixture was balanced with He. As shown in the figure, the electron density increases with the increase in N2 content and the EEPF gradually transitions into a Maxwellian distribution. The Maxwellianization of the EEPF is likely due to increased electron-electron collisions caused by the increased electron density. Although the electron density increases, which is in part due to the lower ionization threshold energy of N2 (15.6 eV)15 than that of He (24.58 eV),16 the high-energy tail of the EEPF decreases as the mole fraction of N2 increases in the plasma mixture. The reducing trend of high-energy tail is an indication of decreasing effective electron temperature and is mainly due to the increasing excitation collisions of electrons with the increasing N2 concentration. Since the excitation cross section of N2 spans over a wide range of energy (from 0.02 eV and above)15 whereas that of He only exists above 19.8 eV,16 more electrons are likely to be involved in the excitation process with higher N2 concentration, which effectively dissipates electron energy.
Measured EEPF of He-N2 plasmas at the gas pressure of 30 mTorr and the discharge power of 33 W.
Measured EEPF of He-N2 plasmas at the gas pressure of 30 mTorr and the discharge power of 33 W.
The effective electron temperature Teff of He-N2 plasmas is calculated from the measured EEDF based on Eq. (6). Figure 4 shows a decreasing trend in the electron temperature as the mole fraction of N2 increases in the He-N2 plasma. The decreasing trend in Teff is primarily caused by the increase in electron-neutral excitation collisions that dissipate electron energy substantially. Molecular gases such as N2 have numerous excitation modes that dissipate electron energy more effectively than the monatomic gases such as He that have fewer excitation modes. Since high-temperature electrons contribute significantly to the ionization processes in gases, maintaining low electron temperature is important in achieving higher dielectric strength. Therefore, increasing the mole fraction of N2 in the He-N2 gas mixture results in higher dielectric strength.
Measured effective electron temperature Teff of He-N2 plasmas at 30 mTorr and 33 W.
Measured effective electron temperature Teff of He-N2 plasmas at 30 mTorr and 33 W.
An increasing trend in electron density ne, calculated based on Eq. (7), with the increase in N2 concentration in the He-N2 plasma is shown in Fig. 5. The trend seems to suggest a decreasing dielectric strength as N2 increases because, from the electron kinetics perspective, higher electron density indicates higher ionization process. However, it is important to notice that the ionization process is not the only factor that determines electron density in a plasma chamber. In a confined plasma, the chamber wall is where the loss of electrons and ions occurs. Between the chamber wall and bulk plasma, there exists a plasma sheath. Depending on the sheath geometry, which depends on the mean free path of ions (λi), the effective chamber wall area (Aeff) is determined. If the effective chamber wall area is decreased due to the variation of gas composition, the loss of electrons would also decrease, and thus, the plasma density could increase even if the ionization process decreases in the bulk plasma. To confirm the measured results and to further understand the cause of the increase in ne, the parameters of the He-N2 plasmas are estimated with the use of the particle balance equation and the power balance equation.
IV. ESTIMATED PLASMA PARAMETERS
A. Particle balance equation
The particle balance equation describes the temporal variation of the particle density in plasmas, and it is used to estimate the electron temperature Teff of a plasma. The equation describes the variation of electron density ne by balancing the ionization and attachment processes as well as the loss of electrons at the plasma chamber wall. The following particle balance equation describes the mixtures that consist of more than one constituent gas:
where Kiz,j and Katt,j are the rate constants of ionization and attachment of gas j, ng,j is the number density of gas j, uB,j is the Bohm velocity of gas j, and Aeff,j is the effective chamber wall area of gas j. According to this equation, electron density ne increases with the ionization process, but decreases with the attachment process and with particle loss at the chamber wall. Ionization and attachment processes are described by rate coefficients Kj, which are calculated by using the EEDF and the electron-scattering cross section data of constituent gases. Note that electron attachment is not taken into account in this study since neither He nor N2 are electron-attaching gases
The process of particle loss at the chamber wall depends on the Bohm velocity (uB) and the effective area of chamber wall Aeff. The Bohm velocity uB is given by the following equation:
where Mi represents the mass of ions that is calculated by for gas mixtures: xj is the mole fraction of constituent gas j. Moreover, the effective chamber wall area of a cylindrical chamber is calculated as follows:
where R and L are the radius and length of a cylindrical chamber, hl,j and hr,j, which alter the chamber surface area, and are defined as the ratio of the sheath edge plasma density to bulk plasma density12
Both hl,j and hr,j depend on the type of the plasma since ion mean free path is involved in the calculation
where σj is the cross section for the ion-neutral collisions of He and N2.12,17
Figure 6 shows the results of the estimated Teff obtained by solving the particle balance equation. A decreasing trend in Teff similar to that shown in Fig. 4 is observed in Fig. 6. Although both the measured and the estimated results agree on the decreasing trend, discrepancies exist between the values of the results. The probable cause of the discrepancy is in the particle balance equation of this study, which mainly accounts for the kinetic reactions between electrons and the original gas species, but not for the possible kinetic reactions involved with particles such as ions, metastables, and dissociated neutrals.
Effective electron temperature Teff of He-N2 plasmas estimated from the particle balance equation.
Effective electron temperature Teff of He-N2 plasmas estimated from the particle balance equation.
B. Power balance equation
The power balance equation equates the power input Pin and power loss Ploss of plasmas and is used to estimate the electron density ne. Ploss consists of Pc and Pk, which are collisional loss and kinetic loss, respectively. Pc involves energy losses occurring from elastic and inelastic collisions, and Pk involves energy losses occurring from electron and ion loss at the chamber wall
where e is the elementary charge, uB is the Bohm velocity, εtot is the total energy loss, and Aeff is the effective chamber wall area. The total energy loss εtot consists of kinetic energy loss and collisional energy loss
where εk is the kinetic energy loss and εc is the collisional energy loss. εk consists of ionic energy loss εi and electronic energy loss εe, where εi and εe are given by the following equations:
The collisional energy loss εc is derived from the energy loss involved in an electron-ion pair generation, which is given by the following equation:
where k represents the type of excitation collision process. The right hand side of the equation describes the sum of energy losses involved in all collisions per ionization. Based on the Bohm velocity uB, the total energy loss ϵtot, and the effective chamber wall area Aeff, the electron density ne is derived from the power balance equation
The calculated values of ne from the power balance equation are shown in Fig. 7. As shown in the figure, ne increases with the mole fraction of N2 in the He-N2 plasma. A comparison of the data in Figs. 5 and 7 shows a close agreement between the measured and the calculated values of ne. The measured ne values of the bulk plasma increases with the mole fraction of N2 mainly because the Bohm velocity uB and the effective chamber wall area Aeff decreases even though the total energy loss εtot increases as the mole fraction of N2 increases in the plasma.
Electron density ne of He-N2 plasmas estimated from the power balance equation.
V. DISCUSSION
A. Dielectric strength and plasma parameters
When only the electron kinetics of a bulk plasma is considered, the increasing dielectric strength of a non-electron-attaching gas mixture can be represented by the decreasing trend of ne and Teff. This is because gas mixtures with low Teff values show low ionization processes and result in low ne values. However, the results of the study show that the measured ne and Teff values vary with the opposing trends: ne increases while Teff decreases with the increase in mole fraction of N2. The increasing trend of ne is mainly due to the direct influence of the varying effective chamber wall area Aeff caused by the varying N2 composition of He-N2 plasmas. The trend suggests that ne values do not accurately represent the electron kinetics of the gas mixture itself since particle loss at the chamber wall, which depends on uB and Aeff, has a substantial influence on ne. Hence, assessing the dielectric strength variation based on the values of ne is not appropriate. If ne is independent of the processes at the chamber wall and dependent only on the electron kinetics of gas mixtures, the varying trend of ne would be suitable as a means of evaluating the dielectric strength of gas mixtures. However, in actual experiments, plasmas interact with the chamber wall, and thus, ne is not solely dependent on the electron kinetics of the gas mixture. Therefore, we suggest using Teff as a means to evaluate the dielectric strength of non-electron-attaching gas mixtures with varying composition.
B. Using low-pressure plasma parameters for evaluating the dielectric strength of high-pressure gas mixtures
The typical operating pressure of any HTS power application is between 1.0 and 2.0 MPa. Under such high-pressure conditions, a gaseous dielectric breakdown would become an arc discharge that has a higher degree of ionization and higher electron density than a low-pressure glow discharge. Due to these conditions, the characterization of high-pressure arc discharges should account for the influence of electron-ion collisions, which are not the main focus of this study. Therefore, it is important to understand that the parameters of the low-pressure discharges discussed in this paper are not intended for representing the characteristics of high-pressure arc discharges. Although the measured parameters of low-pressure plasmas may not be suitable for describing high-pressure arc plasmas, the parameters can still be used for predicting the dielectric strength variation of high-pressure gas media. The prediction is possible because the initiation of a gas dielectric breakdown depends on the ionization process of electron-neutral collisions regardless of whether the breakdown would develop into an arc or glow discharge, and also because the low-pressure plasmas can be described mainly by electron-neutral collisions due to their low degree of ionization. Since preventing gas media from breaking down is more crucial in HTS power applications than describing the characteristics of the type of discharge it develops into, we estimated the dielectric strength variation mainly based on electron-neutral collisions.
Furthermore, the Maxwellianization shown in Fig. 3 is related to the increasing electron density shown in Fig. 5 and should not be hastily generalized to high-density arc discharges. In general, increasing electron-electron collisions with increasing electron density is a phenomenon that is more pronounced in low-pressure discharges that are inherently low in electron density. Unlike in low-pressure discharges, variations in electron-electron collisions are less pronounced in high-pressure arc discharges due to its inherently high electron density.
VI. CONCLUSIONS
The utilization of plasma diagnostics to assess the dielectric strength of gas media was demonstrated using the He-N2 plasma mixtures with a varying composition. The results of the experiments showed that the measured electron density in the plasma is not suitable for accurately estimating the dielectric strength because the variation of the chamber wall process and the effective chamber wall area associated with gas composition are substantial. However, it was confirmed that the trend in the variation of electron temperature is suitable as a surrogate to dielectric strength when developing the new gas media for the high-voltage insulation applications or for assessing the potential influence of the purity of gas media on the dielectric strength. The discussed plasma experimental technique is useful in studying gas mixtures with varying composition obtained by a combination of mass flow controllers and vacuum pumps.
ACKNOWLEDGMENTS
This work was supported by the Office of Naval Research (ONR) through Grant Nos. N00014-14-1-0346 and N00014-16-1-2282.