A hydrodynamic model of vacuum arc plasmas

The properties of plasmas expanding from cathode spots of vacuum arcs are calculated with a one-dimensional two-fluid model. The system of simplified hydrodynamic equations can be solved under stationary conditions using asymptotic power series. Although necessarily only an approximation, such analytical solutions prove to be advantageous compared with numerical integrations. All the plasma parameters are functions of (I/r)^2/5 (current, I: distance, r). The three forces accelerating the ions to high kinetic energies are quantitatively calculable: the electric field, the ion pressure gradient, and the electron-ion friction. The potential is decreasing towards the anode, and the residence of the plasma is negative. The ion temperature reaches only about 35% of the electron temperature. Although only asymptotic, the solution is suited to describe the arc plasma in a sufficient manner all over the expansion region     

Generation of stable mixed-compact-toroid rings by inducing plasmacurrents in strong E rings

In the RECE-Christa device, hybrid-type compact toroid rings are generated by inducing large toroidal plasma currents I_p in strong electron rings using a thin induction coil positioned along the ring axis. Starting from field-reversal values δ_p =50-120% of the original pure fast-electron ring, the induced plasma current I_p raises δ to a maximum value of up to 240% with I_p contributing more than 50% of the total ring current. The generated hybrid compact toroid configurations appear gross-stable during the full I_p pulse length (half-amplitude width about 100 μs)     

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     

The short vacuum arc. I. Experimental investigations

High-current vacuum arcs drawn between commercial radial-magnetic field, chromium-copper contacts were studied by high-speed photography. The aim of the investigation was to study phenomena of relevance to high-current interruption, such as arc constriction and arc motion. The arcs were drawn at contact opening speeds typical of commercial devices, are duration being 10 ms or less. The arcs were `short' for much of their lifetime, and strong electrode-discharge coupling could be expected. Such arcs are also of principal interest. Arc behavior was found to be strongly influenced by the gap length d and the arc current I. No diffuse mode was observed at d less the d_min≈4 mm and at instantaneous currents I above I_max±25 kA. The diffuse discharge mode was assumed more readily when d was large. At d below 2 mm, the arcs could not be moved by a magnetic field. Increasing both I and d resulted in an increase of the probability and duration of arc motion and of the arc path length. Arc speed was often irregular, showing that arc motion is also affected by parameters other than the purely electrodynamic ones     

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     

The use of bubbles for plasma liners in ICF experiments

The production of thin, axially symmetric bubbles between electrodes in a plasma-focus discharge chamber at pressures below 1 torr is described. A theory of their use as plasma lines (PLs) is given. A mechanism of imploding such liners using a plasma-focus snowplow (SP) for the accumulation of magnetic energy is described. The transfer of the discharge current I from the SP to the PL should result in a substantial amplification of the dI/dt as seen by the PL, resulting in very high density of the latter. Possible applications of such dense plasma liners in ICF are mentioned     

The type and extent of non-LTE in argon arcs at 0.1-10 bar

A 30-A, 3-mm-diameter, wall-stabilized argon arc with 1% hydrogen is examined spectrometrically at pressures of 0.1-10 bar. Values of T_g, and T_exa diverge as pressure decreases below 5 bar (n_e⩽1×10¹⁷ cm^-3) at r=0. T_exβ is 20-40% larger than the other temperatures. The results are dependent on the transition probability scale used     

Multimode simulations without particles in the quasi-opticalgyrotron

A set of coupled nonlinear differential equations, involving the slow amplitude and phase variation for each mode, is used to simulate the multimode dynamics in the quasi-optical gyrotron. The interaction among various modes is mediated by coupling coefficients of known analytic dependence on the normalized current I, the interaction length μ, and the frequency detunings Δ_i corresponding to the competing frequencies ω_i. The equations include all the possible resonant combinations of up to four different frequencies, ω_i-ω_j+ω _k-ω_l≃0, among a set of N participating modes, keeping terms up to fifth order in the wave amplitudes. The formalism is quite general and can be used to study mode competition, the existence of a final steady state and its stability, and its accessibility from given initial conditions. It is shown that when μ/β_⊥≫1, μ can be eliminated as an independent parameter. The control space is then reduced to a new normalized current I and the desynchronism parameters ν_i=Δ_iμ for the interacting frequencies. Numerical simulations for cold beams of various cross sections demonstrate that ν_i is the most important parameter for the system behavior. Overmoding is not determined by the frequency separation δω among the cavity modes per se, but by the separation among the corresponding desynchronism parameters     

Excitation of slow EM waves in a waveguide having a thin, annularplasma sheet

A thin, annular plasma sheet in a waveguide slows down the phase velocity of electromagnetic modes in a plasma density window for frequencies below the electron cyclotron frequency via Cerenkov interaction. At lower densities, the plasma is not effective enough to reduce the phase velocity of the EM wave below c. At higher densities the plasma expels the radiation field, leading to enhancement of phase velocity. The lowest mode having azimuthal number l=0 is most unstable. The radial mode having amplitude maximum at r=a, viz the plasma boundary, has the largest growth rate     

Interrupting capacity of vacuum interrupters depending on thefrequency of current

Results of arc reignition voltages during current interruption of frequencies from 5.9 to 60 kHz by a short vacuum gap are presented. Measured arc reignition voltages depend on current amplitude and frequency, the values of preliminary arc current at the moment of switching on the HF current, and the discharge mode in the preceding current semiwave. Threshold amplitudes of the first semiwave of currents l_m1l and I_m1h as a function of frequency are determined. I_m1l and I_m1h divide current into three ranges to which different kinds of arc reignition voltage distribution correspond. Particularly large dispersion of reignition voltages takes place in the current range from I_m1l to I_m1h. The threshold current I_m1h is inversely proportional to frequency in the range from about 10 to 60 kHz, which is in agreement with the elaborated mathematical model     

Some interruption criteria for short high-frequency vacuum arcs

If the contacts of a vacuum interrupter open shortly before a current zero, the transient recovery voltage (TRV) can cause a reignition and reestablish the arc. When the current in a diffuse vacuum arc passes through zero, there is a distinct pause before the TRV builds up (approximately 40 ns for copper). During this pause the gap carries conduction current only with an ion component which depends on dI /dt, varying between 3 A for dI/dt=60 A/μs and 60 A for dI/dt=1235 A/μs. The ion current subsequently decays in tens or hundreds of nanoseconds. It can be distinguished from the displacement current at this time by varying dV/dt, keeping the other parameters constant. Among the interruption criteria for short high-frequency vacuum arcs, dI /dt prior to current zero and initial dV/dt are the most important. High values of dI/dt are more likely to precipitate reignitions, but breakdowns can occur after lower dI/dt's if the gap has been subjected to a high current for a relatively long time (>100 μs)     

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     

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     

Computation of the electric and magnetic fields induced in a plasmacreated by ionization lasting a finite interval of time

S.C. Wilks et al. (1988) showed that when an infinite expanse of gas, carrying a linearly polarized electromagnetic wave, is instantly ionized, the initial wave is frequency upshifted. This phenomenon of frequency upconversion through flash ionization gives rise to steady-state transmitted and reflected electromagnetic waves and to a time-independent magnetic field. The case in which the final state of ionization is achieved not instantly but in a finite turn-on time, 0⩽t⩽t 0, which is followed by the steady state, is studied. It is shown that the electric field is obtained from the one-dimensional Helmholtz equation, d²F(t)/dt² +ω₀²g(t)F( t)=0, if electrons are born at rest when they are created during ionization. As a result, the instantaneous frequency of the upshifted radiation is ω(t)=√g(t). The electric field can be solved exactly for specific choices of g(t). It is solved using WKB approximations for arbitrary g(t). The magnetic field is then found by integrating Faraday's law. It is found that the steady-state electric field amplitude depends on the steady-state value o f g(t) but does not depend on the ionization time t₀. Conversely, the static magnetic field amplitude decreases with increasing turn-on time     

Plasma motion in a filtered cathodic vacuum arc

A model is proposed for the flow of a plasma originating from a cathodic vacuum arc into a curvilinear magnetic field. The model gives good agreement with measurements obtained from a filtered cathodic-arc thin film deposition system. The important parameters involved in the motion of a vacuum arc plasma beam through a magnetic filter are examined. The analysis is based on the use of the guiding center approximation to describe the motion of the charged particles produced in the plasma where the thermal energy is negligible compared to the mass flow energy. Electron-ion collision effects are included within the framework of the drift model. It is shown that under the limiting condition of a collision frequency which is much higher than the cyclotron frequency of the electron, the motion of the plasma ions around the bend becomes independent of the magnetic field, with the number of ions traversing the filter significantly reduced. However, in the collisionless plasma case (cyclotron frequency higher than the collision frequency), the model predicts a square-law relationship between ion-saturation current and magnetic field , I_p ∞B²     

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     

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     

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