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)     

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     

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     

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     

Ion current collected at various distances and argon backgroundpressures in a copper vacuum arc

The ion current collected by a probe biased at the cathode potential and located behind an annular anode of a vacuum arc is measured as a function of distance to the cathode and background argon pressure. The arc is formed between a circular Cu cathode and an annular anode. Arc current is 170 A, and the arc duration is 0.9 s. The arc is ignited by momentary contact of a movable W trigger rod (held at anode potential) with the cathode. Arc voltage, arc current, and ion current are measured using an analog data acquisition card and a personal computer. Arc voltage and arc current values are stable during the arc and their normalized standard deviation is less than 0.07. Ion current is noisy and fluctuates during the arc with a normalized standard deviation that varies from 0.5 at p<0.1 torr up to more than 1.5 at p>1 torr     

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     

Electrical characteristics of pulsed glow discharges

The i-v characteristics, energy partitioning, and time evolution of the discharge current and reduced field (E/N) for a nitrogen discharge are simulated using a self-consistent calculation of the electron energy distribution function and the vibrational level populations. The model includes diffusion losses and takes account of the external circuit parameters. The results discussed are for pressures of 1-100 torr, discharge currents in the range of 10^-3-5.0 A, and a reduced field (E/N) in the range of 150-250 Td. For a typical discharge in a tube of 2-cm diam. and a current of a few amperes, the results show that the energy stored in the vibrational manifold saturates a few milliseconds after the initiation of the discharge     

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     

A revised theoretical model of vacuum arc spot plasmas

The quasi-stationary hemispherical expansion of the cathodic plasma in vacuum arcs can be modeled with hydrodynamic two-fluid equations. In any case, the state of the plasma is determined by the only variable (I/r)^2/5 (with current I , distance r). In order to avoid some deficiencies of the model (as published) and to investigate more carefully the dependence of the plasma parameters on the arc current, the known analytic solution to the problem is improved by taking into consideration the variability of the Coulomb logarithm and the dependence of the boundary conditions on I. These effects are treated separately. Examples are used to illustrate the new results, with particular emphasis on ion acceleration. The influence of the above factors turns out to be rather unimportant. Quantitatively, they cause some shifts, but no qualitative change of the basic behavior of the plasma is seen     

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     

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     

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     

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     

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     

Finite conductivity and the interchange instability in railgun arcs

A first-order perturbation expansion of the MHD (magnetohydrodynamic) equation is used to describe the onset of the interchange instability due to the high accelerations in railgun plasma-arc armatures. J.D. Powell (1986) considered the problem of perturbing an initial isothermal equilibrium with appropriate distributed current and density profiles, treating the perturbation equations with infinite conductivity. Here, the authors model the arc the same way, but they include the effects of finite conductivity σ. A fourth-order mode equation is derived and solved numerically. The authors find continuous spectra of unstable modes for a nonzero plasma acceleration g, whose growth rates are mostly greater than √kg, depending on the values of k and σ. The resistivity always raises growth rates higher than Powell's especially for large k and large resistivity. The resulting growth rates in typical railgun situations are large enough to permit full development of the instability     

Recombination lasing in heliumlike silicon: a possible path to thewater window

A major goal of current X-ray laser research is the achievement of gain in the 23.3-43.7 Å wavelength region, known as the `water window'. Silicon is the lowest atomic number element for which all the heliumlike 3-2 transitions lie in this region. The authors examine the fundamental kinetics of recombination lasing in this species, and conclude that the Si XIII 1s3d¹D ₂-1s2p¹P₁ line at 39.1 Å is an attractive candidate for recombination-pumped lasing. Attainment of gain in this line is somewhat more energetically favorable than for the hydrogenic Al XIII 3-2 transitions, but radiative trapping may be somewhat more troublesome than for H-like Al     

Theory of the cathode sheath in a vacuum arc

A previous theory of the plasma sheath transition starting from the charge exchange model for ion collisions is extended to account for ionization and recombination. It is applied to the quasi-neutral boundary layer (presheath) in front of the cathode sheath of a vacuum arc. An essential potential and density difference between the sheath edge and cathodic plasma ball is found. This difference is accounted for in a unified theory of the arc cathode based on G. Ecker's (1971) existence diagram method, which indicates possible areas of arc operation in the T_cj plane, where T_c is the spot temperature and j is the current density. A numerical evaluation for Cu gives the results which are qualitatively similar to Ecker's theory. The existence areas are quantitatively enlarged and shifted to lower current densities     

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     

Research into pulsed power-driven recombination lasers

Time-resolved measurements of XUV emissions from recombining Ne and Al plasmas are reported. The DNA/PITHON pulsed-power generator was used to produce hot, dense aluminum and neon plasmas in a Z-pinch configuration. The Al Xl, 4f-3d and 4 d-3p lines at 154.4 and 150.4 Å were observed to be anomalously bright compared to the Al Xl, 4d-2p line. This anomaly, which might be suggestive of recombination lasing, may also be explained by opacity, whereby the optically thick 4→2 lines are reduced in apparent intensity with respect to the 4→3 lines. The Ne X 4-3 line was observed to be spatially localized on axis where emissions from the Ne X 3-2 line were sharply reduced in intensity. On axis, the anomalous brightness of the Ne X 4-3 line suggests a strong inversion