Khokan C. Paul

Transient response of the radio frequency inductively coupled plasma to a sudden change in power

A two-dimensional, axisymmetric model was developed to study the response of a radio-frequency inductively coupled plasma to a sudden change in its active power. The time-dependent equations for the conservation of mass, momentum, and energy, along with Maxwell’s equations were solved numerically. Results were obtained for a pressure range of 200–760 Torr, a frequency range of 1–3 MHz; torch diameters between 40 and 75 mm; and, argon/hydrogen flow rates of 40–75 slpm. Initially, the plasma was assumed to be under steady-state condition at 20 kW. The plasma power was then reduced to 10 kW for 35 ms and, the response of the plasma fields and the coil current were predicted numerically. When power was reduced, the coil current reduced significantly in 2 ms. It then increased to a maximum before smoothly decreasing to its new steady-state value. The response of the plasma depended, to different degrees, on all the parameters considered here. Depending on the position within the torch, it could vary from 2 ms ...

Experimentally diagnosed transient behavior of pulse modulated inductively coupled thermal plasma

An argon/hydrogen (argon: 89% molar) pulse-modulated radio-frequency inductively coupled thermal plasma was generated at adequate power level (active plasma power up to about 15 kW) and has features such as control of thermal flux in time domain and introduction of nonequilibrium phenomenon. These characteristic features have ample attraction for thermal plasma materials processing. A solid state power source, which supplies the electric power at a nominal frequency of 1 MHz with high matching efficiency of 90%, was used as the pulsing generator to generate the induction plasma. Experimental measurements were carried out to analyze the transient responses of ArI (at 751 nm wavelength) line and current intensities for the imposed pulsing signal. Results were obtained for pressure range from 200 to 760 Torr, with a power on time in the range from 2 to 20 ms while the power off time ranged from 5 to 12 ms. The plate power level was varied from 11 to 17 kW though the results presented in the present article a...

Self-Consistent Model of HID Lamp for Design Applications

This paper describes a robust and self-consistent high-intensity-discharge (HID)-lamp model implemented on a vendor-supplied computational platform. The model includes a one-dimensional representation of the sheath in the near-cathode region, which allows one to join solutions in the plasma and in the cathode body and thus to self-consistently determine the cathode fall and temperature and current density distribution along cathodes surface. The model has the capability to predict direct-current-operated-lamp properties from the first physical principles without relying on the experimental information (except the confirmation purpose of the predicted results). The P-1 method is used to model radiation transfer, where the mean absorption coefficient for spectral bands is being used to calculate the mean incident radiation for each band. In the scheme developed, the lamp body is divided into a number of domains that are coupled through boundary conditions (for example, boundary conditions for energy and current continuity equations in the plasma depend on the solutions of the cathode and anode models). The complete global solution is obtained iteratively. Properties of interest of the cathode body, the adjacent sheath, the gas-filled region, and the anode body are computed for a typical HID lamp. Results are presented for a discharge medium consisting of an argon-mercury mixture at an operating pressure of 0.11 MPa. The lamp current is 10 A. The predicted maximum temperature and plasma velocity are 10 700 K and 8 m/s, respectively, for this particular lamp. Adequate accuracy (experimental validation) occurs under the following operating conditions: a dc current between a few amperes and a few tens of amperes flows in a discharge medium with a pressure from one to a few tens of atmospheres

Predicted results of a HID DC current lamp considering a P-1 radiation model

This paper presents a numerical model that can be used for designing and/or improving a high-intensity DC discharge lamp. For purposes of illustration, we present results for the plasma subregion considering a 10 A discharge in a mercury-argon mixture (91:9 mass concentrations) operating at 1.1 atm. Calculation is carried out for a simple geometry of lamp, which consists of spherical vessel and ellipsoidal electrodes with a 15 mm interelectrode gap. The steady-state transport equations for mass, momentum, and energy, Laplaces equation for electrostatic potential, Amperes law for magnetic field intensity, the species continuity equation, and the P-1 radiation equation are solved simultaneously for a simple two-dimensional axisymmetric geometry. The buoyancy effect is introduced and the lamp is placed vertically with the anode at the top. We have found a maximum plasma temperature of 10 000 K and a maximum velocity magnitude of 6 m/s near the cathode surface. The values of maximum temperature and velocity are also predicted to be relatively high near the anode surface compared to the values calculated around the middle of the interelectrode gap.

Transport and thermodynamic properties of SF/sub 6/ gas contaminated by PTFE reinforced with Al/sub 2/O/sub 3/ and BN particles

The computational approach in which time-dependent balance equations of mass, momentum, and energy are solved numerically is becoming an important technique for analyzing electric arcs in a gas circuit breaker (GCB) or gas-insulated switchgear (GIS). In this paper, the transport and thermodynamic properties of SF/sub 6/ gas necessary for this approach as basic data are calculated under multimixed condition by PTFE(-C/sub 2/F/sub 4/-) reinforced with alumina (-Al/sub 2/ O/sub 3/-) or BN particles. Calculations are carried out for a wide range of temperatures from 1500 to 30000 K, of pressures from 0.1 to 0.4 MPa, and of concentration ratios from 0 to 50%. The results show that the change of electron density is significant for alumina-reinforced PTFE, but insignificant for BN-reinforced PTFE contamination. Henceforth, the electrical conductivity varies only for alumina-reinforced PTFE contamination. The thermal conductivity, however, changes distinctly by mixing alumina-reinforced PTFE as well as by mixing BN-reinforced PTFE. Up to three characteristic peaks (T<3600 K), the thermal conductivity decreases, but above this temperature, augmented thermal conductivity is noticed until 7000 K for alumina and until 12000 K for BN. All thermodynamic properties and viscosity vary only at a higher level of contamination, at or above 10% admixture ratio.

Three-dimensional modeling of a direct current operated Hg-Ar lamp

This paper describes a three-dimensional (3-D) numerical model, first of its kind, for predicting the plasma behavior of high pressure (viz. high-intensity discharge (HID) and ultra high pressure) lamps. Two-dimensional (2-D) and axisymmetric plasma models are widely used as these are less complicated and fairly available. But 2-D and axisymmetric models are not useful for any lamp operation other than vertical burning. There are many systems where HID lamps are horizontally oriented and/or inclined. Therefore, a universal 3-D model is a must for the proper predictions of such lamp behavior. The developed plasma model solves the complete set of magnetohydrodynamic (MHD): transport equations of mass, momentum, and energy along, with the vector potential form of Maxwells equations to account for the electromagnetic effects. Radiation of the energy balance is calculated using the P-1 radiation method by dividing the electromagnetic spectrum into several graybands. For presenting the model performance, calculations are done for a lamp having arbitrary geometry and operating conditions. The glass-bulb of the lamp is assumed ellipsoid and the interelectrode gap is taken as 5 mm. Although the model has the features of predicting properties of the whole domain (electrodes with nonequilibrium cathode-sheath, 3-D plasma region, 2-D glass bulb, and stems), we limit the presentation for the electrodes and plasma region only to control the article size. Operating conditions of the lamp are chosen as a direct current (dc) of 20 A, a discharge medium of Hg and Ar mixture, and an operating pressure of 0.11 MPa. Current levels of 30 and 40 A have also been used to predict the current effect on radiation output. Calculated plasma results show a clear deviation from axisymmetry for horizontal operation of the lamp. Temperature and other plasma fields are found as the strongest near the cathode tip. Effect of Lorentz forces on the plasma velocity is found very significant. For the case of 20 A, maximum temperature is found as about 11000 K and the maximum velocity as 6 m/s.

Development of Xe‑and Sn‑fueled high‑power Z‑pinch EUV source aiming at HVM

Discharge-produced plasma (DPP) based EUV source is being developed at Gotenba Branch of EUVA Hiratsuka R&D Center. Among the several kinds of discharge scheme, Z-pinch is employed in our source. An all-solid-state magnetic pulse compression (MPC) generator is used to create a Z-pinch plasma. Low inductance MPC generator is capable of producing a pulsed current with over 50 kA of peak amplitude and about 100 ns of pulse duration at 7 kHz of pulse repetition frequency. In order to obtain sufficient output radiation power, tin-containing gas is being used as well as xenon. Due to the high spectral efficiency of tin, demonstrated EUV output power reached 645 W/2πsr within 2% bandwidth around 13.5 nm. A novel scheme of fuel gas supply led to as good output energy stability as xenon can achieve. Using a nested grazing-incidence collector, EUV power at intermediate focus point which is defined as an interface to the exposure tool reached 42 W with 3.3 mm2sr of etendue.

The dynamic behaviour of wall-stabilized arcs contaminated by Cu and PTFE vapours

The transport and thermodynamic properties of gas under contaminated conditions with Cu and PTFE vapours have been determined taking into account the new introduction of molecular particles, produced by chemical interactions between gas and impurities like CuF, , and , making in total 25 species. The main concern of this work is to predict, from the obtained material properties data, the transient behaviour of gas wall-stabilized arcs with these types of contamination that inevitably happen in gas circuit breakers during arc interruption. The results indicate that the electron density and the electrical conductivity increase with Cu vapour contamination, especially below 9000 K, due to the lower ionization potential of Cu atoms, but are almost invariant with PTFE contamination. The thermal conductivity changes only at higher admixture ratios above around 10% for both impurities. Typical increases in due to molecular dissociation have been found at temperatures around 4000 K for Cu vapour and at 3000 - 8000 K for PTFE vapour contamination. The transient behaviours of contaminated gas arcs have been analysed for step-current modulation in the wall-stabilized arcs under the condition of no gas flow. The greater value of arc conductance with Cu vapour contamination broadens the arc current channel, exposing possible disturbance of the current interruption function in gas circuit breakers. PTFE vapour contamination does not affect the arc decay process in wall-stabilized arcs significantly.

Copper vapor effect on RF inductively coupled SF/sub 6/ plasmas

Considering inductively coupled plasma (ICP) as an alternative way to study the copper (Cu) vapor effect in SF/sub 6/ circuit breaker arcs, a two-dimensional, axisymmetric model was solved, for a torch of 82-mm inner diameter, to predict the change of plasma properties: temperature, velocity, electric and magnetic fields, joule heating, and Lorentz force. For the four considered sets of thermophysical properties with 0%, 0.1%, 1%, and 10% Cu concentration (molar) ratio in SF/sub 6/, plasma properties were calculated for 130-slpm gas flow: 80-slpm SF/sub 6/ in the sheath channel and 50-slpm argon in the intermediate channel at pressure 100 and 200 torr. The radial temperature distribution as well as the Lorentz force and the joule heating broadened along the torch diameter by Cu vapor admixture. This predicted elongation of plasma for Cu vapor inclusion was confirmed experimentally determining the radial temperature distribution.

A comparative study of transient characteristics of argon and hydrogenated-argon pulse-modulated induction thermal plasma

Solving a time-dependent two-dimensional local thermodynamic equilibrium (LTE) model simulation of Ar and Ar-H/sub 2/ atmospheric pressure, a high-power RF-induction thermal plasma was performed. The effects of shimmer current level (SCL) in pulse-modulated mode and hydrogen concentrations on different flow fields were predicted. The radiation intensities of Ar I (751 nm) for different SCL were calculated from the temperature fields. For the same operating conditions as simulation, plasma was successfully generated in pulse-modulated mode and spectroscopic measurements were carried out to investigate the effects of SCL upon temporal plasma properties. Response times (rising, falling, on-delay, and off-delay time) of temporal radiation intensity were crosschecked for both experimental and simulated ones. The rising time increased gradually with the decrease of SCL, though the falling time remained almost unchanged with SCL. For example, for Ar plasma at 86%, 79%, 72%, 65%, 50%, and 40% SCL the rising times were 2.7, 3.0, 3.4, 3.4, 3.6, and 3.8 ms, respectively. And for Ar-H/sub 2/ plasma (2.4% H/sub 2/), at 87%, 77%, 72%, 63%, 55%, and 45% SCL, rising times were 2.5, 3.0, 3.0, 3.4, 3.7, 3.9, and 4.0 ms, respectively. Hydrogen inclusion slowed down the plasma response during the off-to-on pulsing transition at lower SCL and constricted the plasma axially. Finally, part of the simulated results was compared with experimental determinations and acceptable agreements were found. The discrepancies, in few cases, explicated mainly that the LTE assumption did not prevail in pulse-modulated plasma, especially around the on-pulse transition.