Analytic expression for the electric potential in the plasma sheath

An expression for the spatial dependence of the electric potential in a collisionless and source-free planar plasma sheath is presented. This expression is derived by analogy with Child's law and approaches Child's law asymptotically as the potential drop φ_W across the sheath becomes large, |eφ_W/kT_e|>10⁴. Here k is Boltzmann's constant, T_e is the electron temperature, and e is the electronic charge. Comparison with numerical solutions of the model equations indicates that the sheath thickness and potential variation predicted by this improved Child's law are accurate for |eφ_W/kT_e|>10. In contrast, the authors find that Child's law is accurate only when |e φ_W/kT_e|>10⁴     

Effect of a high-frequency field on the reflection of ion acousticwaves from the sheath at a grid

Experiments are described which show that the reflection coefficient for ion acoustic waves (IAW) from the sheath at a grid is affected by an HF electric field with a frequency f_HF≲5f_pi(f_pi =ion plasma frequency). For peak-to-peak amplitudes of the HF voltage drop across the sheath Φ₀≲k_B T_e/e and f_HF>f _pi, the energy distribution of the ions passing through the grid develops a hot tail and the reflected wave suffers enhanced Landau damping. If Φ₀≳k_BT_e/e and f_HF<f_pi, a large-amplitude IAW is excited at the grid; a well-defined ion beam is formed; and local growth of the reflected wave is observed. Test waves launched from the grid show the same propagation characteristics as the reflected waves     

Electrical discharge initiation and a macroscopic model forformative time lags

Formative times in electrical discharges in overvoltaged gaps are analyzed with a model having no spatial dependence and with simple assumptions about discharge channel temperature T and discharge voltage. The model treats the early temporal evolution of the discharge. Specifically, the dissipative voltage drop, V*, across the discharge is taken to be a step function of T. Thermal quasi-equilibrium is assumed in the discharge medium, and it is shown that d(In t_d)/_d(In &thetas;)=-1, i.e., &thetas;t_d=constant, where &thetas; is the fractional overvoltage and t_d is the formative time lag, in agreement with measured values of t_d for much of the experimentally explored range of &thetas;. Highly-time-resolved (~92 ps) experimental data are presented for the first 10 ns of electrical discharge initiation; these data suggest that the authors' model should provide a reasonable representation of t _d when t_d>10-100 ns     

A two-electron group model theory for radio-frequency ionization ofnoble gases with turbulent flow

Equations are derived for predicting the current-voltage characteristic curves of axial RF discharges in noble gases, with turbulent flow. The electrons are considered to be made up of two Maxwellian groups: bulk and tail electrons. The bulk electrons are described by a temperature T_b, and have kinetic energies (1/2 mv²=eV) from 0 to eV _l (eV_l=the threshold energy of the first dominant inelastic collision process). The electrons of the depressed tail of the distribution function are described by another temperature, T_t<T_b, and have (eV>eV_l). The terms in these equations correspond to the prevailing processes occurring inside the noble gas discharge. The rate coefficients given are derived, based on the two-electron group model. The effect of the high velocity flow is accounted for by the terms giving the divergence of the flux of particles in the redirection of flow in each of the continuity equations for the primary species and by adding a diffusion coefficient due to turbulence to the static discharge diffusion coefficients of the ions and metastables     

Active species in microwave postdischarge for steel-surfacenitriding

Production of nitrogen atoms has been studied in a 2.45-GHz flowing postdischarge in N₂ and N₂-H₂ gas mixtures with Ar as a buffer gas in the high-pressure regime (5×10³ to 6.5×10⁴ Pa). N atom densities have been measured by NO titration in the 10¹⁴-10 ¹⁵ cm³ range and monitored by the first positive emission resulting from the N atom recombination. The rate coefficient of the N+N+N₂ recombination has been found to be _k=6×10^-33 cm⁶ atom^-2 s ^-1 at T₀=300 K, which agrees with previously published data. The N atom production (or degree of N/N₂ dissociation) in front of an Fe-0.1%C substrate correlates well with the thickness of a γ' Fe₄N layer produced by the postdischarge treatment. The H₂ gas was first introduced in the initial phase of treatment to remove surface oxidizing and then was cut off to keep high densities of N atoms. It is deduced that N atoms are more active nitriding species than NH-type radicals     

Pressure limits for the vacuum arc deposition technique

Observations of the cathodic copper plasma expansion at low pressures of He, Ar, and SF₆ showed that, for background gas mass densities of ρ_g=1 to 4×10^-4 kg/m ³ and higher, the plasma and gas are separated into two volumes. A shock wave acts as a boundary between the two volumes. The boundary attains a stationary position once its expansion velocity decreases to the velocity of sound in the background gas. This position corresponds to a distance R_c to the cathode that agrees with a snowplow expansion model, giving R_c ^βf=E_r, where f is a function of the arc current and background gas characteristics, E _r is the erosion rate of the cathode, and β varies between 2.1 and 2.5. The interaction model is based on kinetic energy exchanges between two gas-like volumes without other energy losses. A maximum pressure limit for vacuum arc deposition is set for ρ_g /I=2 to 9×10^-6 kg/m³ A     

Stimulated acceleration and confinement of deuterons in focuseddischarges. II

For pt.I see ibid., vol.16, no.3, p.368-73, June 1988. Methods of increasing, by a factor greater than five, the neutron yield/short Y _n from D-D fusion reactions in a plasma focus (PF) enhance both the D⁺-ion acceleration to energy values E _d>1-8 MeV and the ion confinement in the pinch region. Nuclear activation of C and N in the (doped) filling gas of the discharge chamber and of solid targets of C and BN bombarded by the ion beam in the direction of the electrode axis (0°) confirms earlier determination of the energy spectrum of the trapped ions (dφ_t/dE∝φ_0tE ^-m) and of the ejected beam (dφ_b/dE∝φ_0bE _d^-m, m=2.5±0.5 for 0.1 MeV≲E≲3 MeV). A Thomson (parabola) spectrometer with nanosecond time resolution determines the time of emission t( E) of the beam at 0°. Ion acceleration and trapping occur within the small (filamentary) elements of the magnetic fine structure of the pinch, which can be dispersed on a relatively large confinement volume after the pinch disintegration. It has been found that φ_t/φ_b≳10-10³ for E_d≳1 MeV, depending on Y_n     

Superheat turbulence in gas discharged plasma

The influence of the electron concentration and temperature fluctuations on local thermodynamic equilibrium (LTE) in a gas-discharge plasma due to superheat turbulence development is analyzed. Data for the noble-gas atmospheric plasmas Ar and He (T=6-18 kK) and air ( T=4-9 kK) are given. It is shown that superheat turbulence causes deviation from LTE when parameter-space gradients are absent. As a result, the influence of superheat turbulence for weakly radiative gases (He, H₂) is considerably greater than for strong radiative gases (Ar, Xe, etc). The artificial excitement of superheat turbulence in plasma without any current by means of external electric field fluctuations is demonstrated     

Analytical solution for capacitive RF sheath

A self-consistent solution for the dynamics of a high voltage, capacitive radio frequency (RF) sheath driven by a sinusoidal current source is obtained under the assumptions of time-independent, collisionless ion motion and inertialess electrons. Expressions are obtained for the time-average ion and electron densities, electric field and potential within the sheath. The nonlinear oscillation motion of the electron sheath boundary and the nonlinear oscillating sheath voltage are also obtained. The effective sheath capacitance and conductance are also determined. It was found that: (1) the ion-sheath thickness S _m is √50/27 larger than a Child's law sheath for the DC voltage and ion current density; (2) the sheath capacitance per unit area for the fundamental voltage harmonic is 2.452 ϵ₀ /S_m, where ϵ₀ is the free space permittivity; (3) the ratio of the DC to peak value of the oscillating voltage is 54/125; (4) the second and third voltage harmonics are, respectively, 12.3 and 4.2% of the fundamental; and (5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 (λ_D/S_m)^2/3 (e ²n₀/mu_e), where n ₀ is the ion density, λ_D is the Debye length at the plasma-sheath edge, and u_e is the mean electron speed     

Experimental study of a plasma-filled backward wave oscillator

Experimental studies of a plasma-filled X-band backward-wave oscillator (BWO) are presented. Depending on the background gas pressure, microwave frequency upshifts of up to 1 GHz appeared along with an enhancement by a factor of 7 in the total microwave power emission. The bandwidth of the microwave emission increased from ⩽0.5 GHz to 2 GHz when the BWO was working at the RF power enhancement pressure region. The RF power enhancement appeared over a much wider pressure range in a high beam current case (10-100 mT for 3 kA) than in a lower beam case (80-115 mT for 1.6 kA). The plasma-filled BWO has higher power output than the vacuum BWO over a broader region of magnetic guide field strength. Trivelpiece-Gould modes (T-G modes) are observed with frequencies up to the background plasma frequency in a plasma-filled BWO. Mode competition between the T-G modes and the X-band Tm₀₁ mode prevailed when the background plasma density was below 6×10¹¹ cm^-3 . At a critical background plasma density of ≃8×10¹¹ cm^-3 power enhancement appeared in both X-band and the T-G modes. Power enhancement of the S-band in this mode collaboration region reached up to 8 dB. Electric fields measured by the Stark-effect method were as high as 34 kV/cm while the BWO power level was 80 MW. These electric fields lasted throughout the high-power microwave pulse     

Acoustic double layers in multispecies plasma

Particle simulation in a one-dimensional bounded system is used to examine the formation of acoustic double layers in the presence of two ion species. Double-layer formation depends critically on the details of the distribution functions of the supporting ion populations, and their relative drifts with respect to the electrons. The effect of having two ion components, an H⁺ and an O⁺ beam, on double-layer evolution from ion acoustic turbulence driven by an electron drift relative to the H⁺ beam of ≈0.5u _e, where uu_e is the electron thermal speed, is examined. The ratio of ion drifts is taken to be consistent with acceleration by a quasi-static auroral potential drop (i.e. V _H/V_O=√M_O/ M_H=4.0). Acoustic double layers form in either ion species on the time scale τ≈100ω_ps^-1, where ω_ps is the ion plasma frequency for species `s' and s=H or O, and for drifts relative to the electrons lower than that required for double layer formation in simulations of single ion component plasma     

Initial stage of discharge current growth in a triggered vacuum gap

The dynamics of light emission accompanying the initial stage of electric discharge in a substantially undervoltaged vacuum gap was studied with a knock-down model using high-speed photorecording. Voltage across the gap was maintained within the range of 0.5-5 kV, which corresponded to the minimum operating voltage of vacuum-triggered gaps. It was found that front layers of a plasma cloud near a cathode, formed by a firing pulse, scattered at a speed of (5-8)×10⁶ cm/s. During firing, a channel directed to the opposite electrode was formed from the plasma cloud near the cathode. It was found that the average switch-on delay time of the triggered vacuum gap is ~d(1+h/d) I_f^-α, where d is the interelectrode gap length, h is the trigger assembly penetration height, and I_f is the firing current     

Validity conditions for complete and partial local thermodynamicequilibrium of nonhydrogenic level systems and their application tocopper vapor arcs in vacuum

Validity conditions for complete and partial local thermodynamic equilibrium (CLTE and PLTE) of homogeneous, time-dependent, and optically thin plasmas are derived. For Cu I, electron densities of n_e⩾(5×10²²-5×10²³ ) m^-3 are required for the establishment of CLTE. For Cu I and Cu II, n_e⩾(5×10²¹-5×10²¹ -5×10²²) m^-3 is necessary for PLTE (for electron temperatures of 1-2 eV). Application to low-current copper vapor arcs in vacuum shows that CLTE can be expected for r<200-600 μm (r=distance from the cathode spot). A further limitation follows for temperatures of 2 eV or higher if diffusion effects are taken into consideration. Consequently, the use of the LTE formulas in plasma spectroscopy of low-current vacuum arcs is very limited     

X-ray laser research at the LULI (Palaiseau)

The X-ray laser program at Palaiseau is based on the recombination scheme in lithiumlike ions, which requires a moderate pump power and seems to be promising for the purpose of scaling to shorter wavelengths. In aluminum plasmas, peak gain values of 2-2.5 cm^-1 have been obtained at a wavelength of 105.7 Å corresponding to the 3d -5f transition, 6 ns after the top of a 2 ns laser pulse. The same transition in sulfur is emitted at 65.2 Å and has shown a gain of 1 cm^-1 in a preliminary time-integrated experiment. Simulations using a collisional-radiative model as the postprocessor of a hydrodynamic numerical code predict amplifications for the 3d-4f, 3d-5f, and 4d-5f transitions. A new experiment, in progress at the present time, has been designed to enhance the gain-length product up to 10-15 at 105.7 Å. The recently extended facilities of the LULI make it possible to produce a 6-cm-long plasma column, keeping the flux density at the same level as in the previous experiments     

Soft X-ray recombination laser research at the Institute of LaserEngineering

Soft X-ray laser experiments recently carried out using the Gekko MII glass laser facility at the Institute of Laser Engineering, Osaka University, are described. Hydrogenic and lithiumlike lasing schemes in recombining plasmas were investigated using foil targets exploded with line-focused 532 nm laser radiation of approximately 100 J energy. In a preliminary study, time-integrated emissions of Balmer-α transitions in C⁸⁺ and O⁷⁺ and 5-3 transitions in Al¹⁰⁺ were found to increase nonlinearly with increasing target length, yielding gain coefficients of G=0.9 to 2.3 cm ^-1. In a subsequent, more refined study, which included time-resolved measurements, the authors obtained a gain of G=2 cm^-1 and a gain-length product GL=3 for the Balmer-α transition in F⁸⁺ at 80.9 Å     

Monte Carlo simulation of electron swarms in nitrogen in uniformE×B fields

The motion of electrons in nitrogen in uniform E× B fields is simulated using the Monte Carlo technique for 240⩽E/N⩽600 Td (1 Td=1×10^-17 V cm²) and 0⩽B/N⩽0.45×10^-17 T cm³ . The electron-molecule collision cross sections adopted are the same cross sections as those used previously for the numerical solution of the Boltzmann equation. The swarm parameters obtained from the Monte Carlo simulation are compared with the Boltzmann solution and with the experimental data available in the literature. In relation to E×B fields, it is concluded that the Monte Carlo approach provides an independent method of substantiating the validity of the equivalent electric-field approach     

A two-component model for the electron distribution function in ahigh-current pseudospark or back-lighted thyratron

Temperature, energy, and densities of two electron distribution function components, including an isotropic bulk part and an anisotropic beam, are analyzed for a hydrogen pseudospark and/or back-lighted thyratron switch plasma with a peak electron density of 1-3×10¹⁵ cm^-3 and peak current density of ≈10⁴ A/cm². Estimates of a very small cathode-fall width during the conduction phase and high electric field strengths lead to the injection of an electron beam with energies ⩾100 eV and density of 10¹³-10¹⁴ cm^-3 into a Maxwellian bulk plasma. Collisional and radiative processes of monoenergetic beam electrons, bulk plasma electrons and ions, and atomic hydrogen are modeled by a set of rate equations, and line intensity ratios are compared with measurements. Under these high-current conditions, for an initial density n_H2=10¹⁶ cm^-3 and electron temperature of 0.8-1 eV, the estimated beam density is ≈10¹³ -10¹⁴ cm^-3. These results suggest the possibility of producing in a simple way a very high-density electron beam     

Computer simulation of a carbon-deposition plasma in CH4

A transport and reaction model of a low-pressure, high-frequency (13.56 MHz) CH₄ plasma used for diamondlike carbon (a-C:H) deposition was developed. The model includes reactions among four molecular species (CH₄, C₂ H₆, C₂H₄, and H₂), five radicals and atom (CH₃, CH₂, CH, C₂H₅, and H), and four ions (CH₄⁺ , CH₃⁺, CH₅⁺, and C ₂H₅⁺). It also accounts for the influence of the sticking coefficient of species at the walls. Calculated values of the dissociation degree for several flow rates are in good agreement with experimental measurements made by quadrupole mass spectroscopy. A simple surface-model based on the hydrogen coverage of surface and ion flux and energy at the substrate surface was established. This model permitted the calculation of the deposition rate on the powered electrode as a function of the power applied to this electrode. Good agreement between experimental and calculated growth rates was obtained when CH₃, C₂H₅, and CH₂ were assumed to participate in film formation, and when hydrogen removal by ion bombardment with variable energy as a function of the power was included in the model     

Spectroscopic investigation of a low current arc in pure fluorine

A pure fluorine 10-A DC arc has been operated in an Al₂O₃ tube of 18 mm diameter at atmospheric pressure. This arc was used to perform radially resolved spectroscopic end-on measurements in the visible and UV-spectral regions. An excitation temperature of 7800 K on the arc axis was determined from the intensity of atomic fluorine lines, and an ion density of 1.7×10 ²¹ m^-3 was determined from the half-width of the contamination line H_β. A Boltzmann plot of the affinity continuum in the UV-spectral region yields two groups of electrons. A group of hot electrons is characterized by a temperature that agrees with the excitation temperature, and a group of cold electrons has a temperature in accordance to the gas temperature of 4000 K. The absolute intensity of the affinity continuum gives and electron density of 1.3×10²⁰ m^-3 on the arc axis, which is lower than the density of both positive and negative ions in the discharge. From the difference between the electron and gas temperature, an elastic collision cross section between the electrons and F-atoms of 2×10^-20 m² is determined     

Temperature dependence of intensities and widths of N2-broadened lines in the 15 μm CO2 band from tunable laser measurements

Intensities and nitrogen-broadened widths of several low-J lines in the Q-branch of the 15 μm band of CO₂ have been determined over the temperature range 200–300 K. Measurements were made with a tunable infra-red diode laser spectrometer having a spectral resolution 10^-4 cm^-1. Measured intensities are uniformly about 7% lower than available calculations which were based on previous measurements of band intensity. Measured line widths are higher than available calculations and generally followed the relation

b_L⁰(T)=b_L⁰(T₀)(T₀|T)ⁿ

with n = 0.74 (standard deviation 0.08).