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     

A slow wave free-electron laser in a longitudinal wiggler field

Linearized Vlasov-Maxwell equations are solved to obtain the growth rate of free electron laser instability from a tenuous relativistic electron beam propagating in a partially dielectric loaded waveguide immersed in combined axial and longitudinal wiggler magnetic fields. The instability appears via cyclotron resonance interactions for wave perturbations very close to w-kV_z-w_c=nk ₀V_Z where n is the general harmonic number. For n=0, the gain is similar to a slow wave cyclotron amplifier. For n⩾1, the growth rate is substantially larger than the standard slow wave free electron laser scheme utilizing a transverse wiggler field     

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     

A slow wave free-electron laser

A simple calculation of a free-electron laser in the Compton regime that uses a dielectric-lined waveguide is presented. The introduction of a dielectric lining in a free-electron laser considerably reduces the requirements on beam voltage for generating a given frequency ω₁=k₀c/(1 - v_b η/c), where k₀ is the wiggler wave period η is the effective index of refraction (1<η<√ϵ) and ϵ is the permittivity. The system supports electromagnetic waves whose Poynting flux is largely concentrated in the dielectric; hence the electron beam is required to propagate close to the dielectric lining. The mode structure and dispersion behavior of the guiding system without the beam are discussed. a thin annular beam is introduced, and a perturbation theory is used to obtain the frequency and growth rate of radiation     

Equilibrium lengths of railgun plasma armatures

Recent data have shown that the length of railgun plasma armatures increases with bore size. The mechanisms for plasma growth and mass loss are treated analytically through a simple thermodynamic model in which mass is added through ablation of bore materials and lost through friction. It is assumed that at the bore wall, a thin boundary layer is formed in the plasma in which the velocity is sufficiently slow that the boundary layer is left behind the bulk of the plasma. Using the scaling relations of J.D. Powell and J. Batteh (1983), a functional relationship between the plasma length l_p and bore height h of the form l_p=kh^α, where α≃0.68. Using the model developed in the present work, a linear relationship between l_p and h is derived, but the proportionality factor depends on temperature, plasma conductivity, velocity, and boundary-layer thickness. Predictions of the model are interpreted in the light of available data. The model is shown to predict lengths which are in reasonable agreement with the observed data     

Disproof of Cowling's theorem

T.G. Cowling's theorem (1934) is a general statement that axisymmetric dynamos cannot be constructed in astrophysical bodies. The theorem is based on the assumption that the electrical conductivity is a scalar, σE=J. In a counterargument, the author demonstrates that this statement is not valid for a diffuse plasma. He suggests that, in an astrophysical plasma, collisional processes can violate Cowling's theorem by scattering current into a current-free channel     

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     

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     

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     

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)     

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     

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     

Townsend-type breakdown as a criterion for high-frequency vacuumarc interruption at submillimeter gaps

In vacuum circuit breakers, multiple reignitions give rise to HF current arcing (≈500 A; ≈200 kHz). Due to the small contact distance and the very large current gradient, at every arc-current zero pressures of several tens of millibars can be expected. Very soon thereafter (≈30 ns) this gap is dielectrically stressed by the first component of the restriking voltage (≈10 MHz), originating from parasitic impedances. The combination of the associated high electric field and the relatively high neutral density may cause Townsend-type breakdown, leading to another half-sine of continued arcing. Both dielectric stress and residual neutral density are expressed as a function of di/dt, yielding values of interruptible di/dt as a function of the contact distance with the Townsend breakdown criterion. Comparison with experiments shows fair agreement in the range of di/dt of 100-1000 A/μs and distances of 0.1-0.5 mm for two different circuits     

A Raman regime free-electron laser in a partially dielectric-loadedwaveguide

A partially dielectric-loaded waveguide supports modes with phase velocity ν_ph>c/∈^1/2, where ∈ is the dielectric constant of the lining. The coupling of a fast mode (with ν_ph>c) with a slow mode (with c /∈^1/2<ν_ph<c) via a negative-energy beam mode gives rise to the explosive growth of all the three waves at the expense of the energy of the beam. The slow mode of lower frequency can be launched from an external source and can become an efficient wiggler for the generation of the fast free-electron laser mode     

Railgun armature plasma-current density from deconvolvedB-dot probe signals

It is shown that the spatial distribution of the moving armature current profile in an electromagnetic railgun can be recovered from the recorded signal of a B-dot probe. This approach differs from previous methods in that no a priori assumptions for the functional form of the armature current density are required. From certain simplifying assumptions, a model of the railgun circuit is developed from which the B-dot probe signal can be derived as a convolution of the armature current density with an impulse-response function dependent on the physical parameters of the experimental configuration. Deconvolution of the resulting signal corrupted with measurement noise is performed using a parametric Wiener filter. Simulated and actual numerical examples show that the physical length and overall shape of the armature current profile can be accurately determined using this method. However, the spatial resolution in the deconvolved signal is limited to approximately 1 to 2 cm for practical railgun applications     

Field theory of a traveling wave tube amplifier with a tape helix

A self-consistent relativistic field theory for a helix traveling wave tube (TWT) is presented for a configuration in which a magnetized pencil beam propagates through a tape helix enclosed with a loss-free well. A linear analysis of the interaction is solved subject to the boundary conditions imposed by the beam, helix, and wall. The wave equation for the fields within the electron beam corresponds to the Appleton-Hartree magnetoionic wave modes that are of mixed electrostatic/electromagnetic polarization. Hence, the determinantal dispersion equation that is obtained implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. This dispersion equation includes azimuthal variations and all spatial harmonics of the tape helix. Solutions that correspond to both the extraordinary (X) and ordinary (O ) solutions for the Appleton-Hartree modes are found numerically     

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     

A planar electromagnet microwiggler for free electron lasers

The authors have designed and tested an electromagnet planar microwiggler for use in free electron lasers (FELs), constructed of current conductors wound on ferromagnetic cores. A prototype with a period of 1 cm and a gap of 0.5 cm produced a peak field on axis in excess of 4.6 kG, with a linear B/H characteristic to about 3.2 kG. The field of each half-period of the wiggler is independently tunable by adjusting the current delivered to each, thus allowing for precision tuning and/or wiggler tapering. General scaling laws are employed to predict the performance of a geometrically similar design with a period of 5 mm     

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