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     

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     

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     

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     

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     

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     

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 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     

A model of the cathode spot glow discharge for a cathode withinclusions of low work function material

A model that describes the self-maintained glow discharge for a composite cathode in which cathode spots are formed on low work function material inclusions is presented. Based on this model, expressions are obtained for the radius of the spot, the cathode voltage, and the spot current as functions of Pd (where P is the gas pressure and d is the thickness of the cathode layer), the parameters of the inclusions, and the basic material matrix are obtained. Numerical results for the case of a glow discharge in 75 torr neon gas with a copper cathode matrix and inclusions of LaB₆ are presented. The average radii of inclusions were 0.05 and 0.015 mm. Conditions under which the glow discharge migrates from the inclusions and begins to spread onto the surface of the basic matrix are obtained. The transition of the glow discharge into a contracted state, depending on the structure of the composite material, is also considered     

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)     

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     

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     

Propagation in a warm collisional magnetoplasma enclosed in aconducting cylinder

A study is presented of the propagation of electron plasma waves in a warm collisional plasma filling a conducting cylinder and magnetized strongly in the axial direction, the plasma parameters being taken to be such that the electron-ion collision is the dominant damping process. The attenuation and phase constants are derived in suitably normalized form by using the electrodynamic method. The dispersion and attenuation characteristics for propagation in the lowest order mode in a hydrogen plasma are obtained for various values of the normalized plasma radius αω_pe/c, the electron temperature and electron density being held constant, and the characteristics are compared with those given by the usual quasi-static approximation, which is found to be valid only if αω_pe /c≲1, where α is the plasma radius, ω _pe is the plasma frequency, and c is the velocity of light in free space. The effect of the plasma frequency on the characteristics is investigated     

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     

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     

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     

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     

The role of dust particles with large gyroradii in the `2/3'fall-down process

The authors consider the Alfven-Arrhenius fall-down process and propose a mechanism whereby the Rosseland electric field (the field needed to maintain quasineutrality) may be responsible for the capture and confinement of large-gyroradius dust particles within a plasma shell stratified along the direction of the magnetic-field lines. For these particles, the effect of the magnetic force is rather weak, and they move with a constant z component of the angular momentum in a one-dimensional equivalent potential (gravitational plus centrifugal). This has a maximum at the equator and a minimum at the `2/3' points, i.e. the points where the field-aligned components of the gravitational and centrifugal forces balance. It is shown that under suitable initial conditions these are points of maximum dust density and minimum plasma density. The plasma-planetisemal transition is therefore expected to take place at the `2/3' points in accordance with the Alfven-Arrhenius mechanism. It is also shown that the fraction of infalling dust particles that can accrete onto the equatorial plane by the Alfven-Arrhenius and Rosseland mechanisms is rather small (~(L/ R_e)≪1), L being the thickness of the plasma shell, and R_e, a characteristic length scale of the field line