Investigation of the diocotron instability of an infinitely wide sheet electron beam by using the macroscopic cold-fluid model theory

This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting walls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low-frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency ω_c to a wider usage range, which is restricted to be much larger than the plasma frequency ω_p in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold λ_b, which is greatly dependent on the parameter ω_c/ω_p. The larger ω_c/ω_p is, the smaller λ_b will be needed. Moreover, the system parameters, including the wave number k_x of the perturbations and the relativistic mass factor γ_b, will also influence the growth rate of diocotron instability obviously.     

Study of the influence of the injection section on the stability of a high-current relativistic electron beam propagating through the gaseous medium of a plasmochemical reactor

Results are presented from experimental study of the influence of the injection section on the stability of a high-current relativistic electron beam (REB) propagating through the gaseous medium of a plasmochemical reactor (PR). An REB with the electron energy E _e =1 MeV, beam current I _b =10–22 kA, and pulse duration t=60 ns was generated by the Tonus accelerator and, then, injected into a 0.1-m-diameter PR filled with air. The PR consisted of two sections with lengths L ₁= 0.3–1.0 m and L ₂=1.1–2.5 m; the total length of the system was no longer than 3.5 m. The first section was filled with air at a pressure of P ₁=0.8–1.5 torr, and the pressure in the second section was varied within the range P ₂=0.1–760 torr. The current I _b of an REB passed through both sections of the PR was measured with the help of a sectioned vacuum Faraday cup. The transportation efficiency of the beam was determined as the ratio I _b /I _inj, where I _inj is the beam current measured at the point of injection into the PR. It is shown that, for the optimal dimensions of the first PR section, it has a stabilizing action on the REB with a current density of up to 3 kA/cm², which makes it possible to increase the effective length of the second (working) PR section, which is filled with a gas at various pressures, to L ₂=(25–35)L _bet, where L _bet is the beam betatron length.     

Interaction of a modulated electron beam with a magnetoactive plasma

Experimental results concerning the interaction of a modulated electron beam with a magnetoactive plasma in the whistler frequency range are reported. It was shown experimentally that when a beam is injected into the plasma, waves can be generated by two possible mechanisms: Cherenkov emission of whistlers by the modulated beam, and transition radiation from the beam injection point. In the case of weak beam currents (N _b/N ₀)≪⁻⁴) the Cherenkov resonance radiation is more than an order of magnitude stronger than the transition radiation; the Cherenkov emission efficiency decreases at high beam currents. The transformation of the distribution function of the beam is investigated for the case of weak beam currents. It is shown that in the case of the Cherenkov interaction with whistlers the beam is retarded and the beam distribution function becomes wider and acquires a plateau region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 378–382 (25 March 1998)     

Analysis of the effects of plasmas and beam slippage in optical klystron FEL devices

We examine here the effects of plasmas and beam slippage on the gain of an optical klystron (OK) free electron laser (FEL) device under the influence of a weak guiding magnetic field and background plasma. The beam energy spread decreases with background plasma density nop and increases with beam plasma density nob. The maximum gain (Gmax) scales proportional to . The beam slippage phase Δψ scales directly to five power of relativistic factor γ₀ and one half power to nob.     

On the pumping of plasma lasers by a high-frequency-modulated electron beam

The possibility of effective pumping of plasma lasers by a high-frequency-modulated electron beam, i.e. an electron beam in the form of a periodic train of electron bunches, is discussed. It is shown that if such parameters of the medium as the relaxation times of the electron temperature ρ_Te and the electron density ρ_Ne are in agreement with the pulse width ρ_p and the interval between pulses, 1/?_m, this will facilitate effective laser pumping and amplitude modulation of the laser radiation. Existing microwave tubes, such as a traveling-wave tube and a klystron, provide the required parameters of a periodic train of current pulses (electron bunches) over a wide range of pulse widths ρ_p and pumping current amplitudes.     

A planar relativistic electron beam in a plasma channel bounded by conducting walls

The force interaction of a relativistic electron beam with a plasma in a channel bounded by planegeometry highly conducting walls is studied. The steady-state interaction regime, ω=ku, is analyzed using the model of a cold collisional electron plasma. The formulas for the transverse component of the force acting on the beam electrons are derived for an arbitrary deviation of the beam from the symmetry plane of the channel.     

Non‐linear interaction of a q‐Gaussian laser beam in a plasma channel created by the ignitor‐heater technique

This paper presents a theoretical investigation of the propagation characteristics of a q‐Gaussian laser beam propagating through a plasma channel created by the ignitor‐heater technique. The ignitor beam creates the plasma by tunnel‐ionization of air. The heater beam heats the plasma electrons and establishes a parabolic channel. The third beam (q‐Gaussian beam) is guided in the plasma channel under the combined effects of density non‐uniformity and non‐uniform ohmic heating of the plasma channel. Numerical solutions of the non‐linear Schrodinger wave equation (NSWE) for the fields of laser beams are obtained with the help of the moment theory approach. Particular emphasis is placed on the dynamical variations of the spot size of the laser beams and the longitudinal phase shift of the guided beam with the distance of propagation.     

Calculation of parameters of krypton plasma excited by electron beam with additional heating by high-frequency electric field

The electron energy-distribution functions, the rates of plasmochemical reactions, and the densities of various plasma components have been calculated for a microwave discharge (f = 1000 MHz, P = 100–700 mW) in krypton plasma (p = 0.5 atm) excited by an electron beam with an energy of 12 keV. It has been found that the heating by a microwave field shifts the peak of the electron energy-distribution function (EEDF) from 0.5 to 2 eV, which leads to higher rates of reactions with excitation thresholds lying near the EEDF peak. As a result, the population of excited levels increases by two to three times.     

Electeostatic equilibrium of a modulated electron beam in a magnetoactive plasma

The two-dimensional (axisymmetric) equilibrium of a modulated electron beam (sequence of bunches) in a magnetoactive plasma under resonance conditions, when the frequency of modulation of the beam _M is close to (less than) the plasma frequency _p, is studied. The field of the collective electrostatic wave, focusing the bunches, is compensated by the thermal repulsion of the beam electrons. Based on the solutions obtained, it is established that the external magnetic field has a twofold effect on the equilibrium beam: first, to a weakening of the radial component of the focusing field because of the appearance of anisotropy in the dielectric permittivity tensor of the plasma and, second, an additional radial focusing of the bunches when they are rotated by the Lorentz force. The regions of the beam and plasma parameters in which one or another of the indicated effects predominates are determined and the conditions for the predominance of magnetic over electrostatic focusing are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–8, March, 1985.The author thanks V. B. Krasovitskii for proposing the subject and for constant interest in this work.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Peculiarities of filamentation of sharply focused ultrashort laser pulses in air

Peculiarities of the self-focusing and filamentation of high-power femtosecond laser pulses in air have been experimentally and theoretically studied under conditions of broad variation of the beam focusing parameter. The influence of the numerical aperture (NA) of the initial radiation focusing on the main characteristics of laser-induced plasma columns (characteristic transverse size, length, and concentration of free electrons) is considered. It is established that, for a rigid (NA > 0.05) initial laser beam focusing, the transverse size of the plasma channel ceases to decrease at a level of R _pl ≈ 2–4 μm as a result of strong refraction of radiation on the plasma formed at the focal waist, which prevents further contraction of the laser beam due to its focusing and self-focusing.     

Power Reflection,Transmission and Absorption Coefficients for a Moving Plasma Slab

Expressions for power reflection (R), transmission (T) and absorption (A) coefficients for p-polarized wave for a warm, collisional, magnetized and moving plasma slab (with sharp boundaries and thickness d₀) are investigated. The effects of plasma slab velocity (β=v/c), electron density (ωp/ω)² and plasma temperature (K_BT) on reflection (R), transmission (T) and absorption (A) coefficients are discussed numerically. It is observed that for the value β=?0.6, reflection coefficient (R) becomes more than unity, whereas absorption coefficient (A) becomes quite negligible while transmission coefficient (T) shows oscillatory behaviour. The variation with plasma frequency (ω_p/ω)² shows that at lower plasma frequency (ω_p/ω)²=0.2 transmission (T) and absorption (A) coefficients are minimum while reflection coefficient (R) is maximum.     

The energy of thermal electrons in electron beam created helium discharges

We have measured the electron energy of the thermal group of electrons in both longitudinal and transverse electron beam created helium glow discharges. The measurement technique employs the ratio of intensities of spectral lines in the 2s³S?np³P He I series. Values of kT_e between 0.07 and 0.11 eV were obtained. These energies are typical of the beam-generated electric field free plasmas. The competitive loss of helium ions by recombination and by charge transfer in a He?Hg electron beam created plasma is calculated. The results are applied to the Hg⁺ laser pumping scheme using a electron beam created He?Hg plasma.     

Hot microplasma in the channel of a solid target induced by a sequence of femtosecond laser pulses

The dynamics of the hard X-ray yield is studied as a function of the laser-shot number, and the maximum temperature of the hot electron plasma component in the channel formed by a sequence of tightly focused near-IR femtosecond laser pulses (τ = 110 fs, λ = 1.24 μm, and I = 10¹⁵–10¹⁶ W/cm²) in air at various pressures (P = 0.01–760.00 Torr) is analyzed. The dependence of the depth of the channel in which the hard X rays are generated with the highest efficiency on the air pressure and the laser focusing is obtained. The electron concentration in air plasma in the laser beam waist is estimated using the spectral shift of the second harmonic radiation that is back reflected from the target channel.     

Device for Producing and Investigating an Electron Beam Plasma Discharge

A survey on the properties and applications of the beam plasma discharge is given. A device for the experimental investigation of this discharge is described in which a magnetically guided (H = 0.05?0.1 T), ribbonlike electron beam (eU = 0.5–5 KeV, I = 10^?3?1 A) passes through a working chamber (p = 0.1–10 Pa; l = 10 cm, ø = 22 cm). The beam plasma discharge is sustained by collective beam plasma interaction. First results concerning the wall current and the ignition of the discharge as dependent on beam parameters are presented.     

Decomposition of methylene chloride by electron beam and pulsed corona processing

Experiments on the plasma-assisted decomposition of dilute concentrations of methylene chloride in atmospheric-pressure N₂ and dry air streams by electron beam and pulsed corona processing are presented. This paper presents the first experimental evidence showing that the decomposition of methylene chloride in a non-thermal plasma at ambient gas temperature proceeds via reaction with nitrogen atoms. The decompositions is more efficient with energy deposition in electron beam generated plasmas because of the higher rate for electron-impact dissociation of N₂. In dry air mixture, the decomposition of methylene chloride is degraded substantially because the nitrogen atoms are consumed in the production of nitrogen oxides. At higher gas temperatures (300°C), the decomposition of methylene chloride in dry air is shown to proceed via reaction with oxygen atoms. The main products of methylene chloride decomposition in dry air mixtures are CO, CO₂, HCl, and probably Cl₂.     

Nonlinear interaction of a modulated beam with plasma

Nonlinear evolution of h. f. instabilities excited by a premodulated electron beam in a magnetized plasma is investigated both theoretically and experimentally. Only the erenkov type of excitation (k_¦|v_b) of the upper branch of the electron plasma oscillations has been observed. The dynamics of excitation of the quasistationary fundamental wave (having the frequency of modulation) has been determined numerically. The wave absorption has been included into the theoretical model through an effective collision frequency. Numerical results agree well with the measured evolution of the amplitude and of the phase velocity of the fundamental wave along the system, as well as with the beam distribution functions. The observed bunching of beam electrons and characteristic features of plasma electrons heating are also reported. Broadening of the frequency spectrum and the occurrence of satellite waves with lower phase velocities have been observed downstream. Physical mechanism of spantaneous excitation of these satellites is suggested and their role in the process of the beam relaxation is discussed. More detailed studies of the nonlinearly excited waves have been performed by modulating the beam at two frequencies.It is a pleasure for us to thank Dr .Körbel who has kindly performed the numerical calculations.     

Measurements of L-shell X-ray emission lines of neonlike europium on an electron beam ion trap

We report a measurement of the two X-ray transitions that proceed from the and (1s²2s_1/22p⁶3p_1/2)_{J = 1} upper levels to the (1s²2s²2p⁶)_{J = 0} ground level in neonlike Eu⁵³⁺ (Z = 63), that is,  near the previously documented avoided crossing of the two upper levels at Z = 68. The measurement was carried out using the calorimeter spectrometer on the Livermore EBIT-I electron beam ion trap. It affirms the trends set by the neighboring neonlike ions both in terms of the relative intensity of the two lines and in terms of the magnitude of disagreement with theoretical energy level predictions.     

Radiation Efficiency and Kinetic Calculations for the Positive Column in Hg/Ar Mixtures II. Impact of Tube Radius and Current Density

In a preceding part of the paper, based on experimental methods and on a corresponding kinetic model, especially the impact of the effective life times of the 6³P₁ and 6¹P₁ Hg resonance levels on the main properties of the low pressure Hg-–Ar positive column has been studied. In the presented second part these investigations, which have been performed under the aspect of their application in fluorescent lamps, will be continued. They are related to the effects of tube radius and discharge current density. New fluorescent lamps have reduced tube radii from R = 18 to 13 mm and compact lamps down to R = 5 mm. Thus it is of interest to study the electron distribution function and main macroscopic properties of such low pressure discharge plasmas, where the latter properties are obtained by adequate energy space averaging. At first, results are reported and discussed which are related to the dependence of main plasma parameters on the Hg partial pressure when reducing the discharge tube radius for constant discharge current i and argon pressure pAr. Starting from the electron distribution function the particle and energy budget will be studied in detail, especially of course the change of the ultraviolet radiation output from both Hg resonance levels 6³P₁ and 6¹P₁ and, in addition, of visible radiation. Then, to understand the effect of the discharge current density, as a representative example two cases with different values of R, i and PAr but with equal current density have been investigated and discussed. Altogether the investigations made will shed light upon the complex relations in the mentioned mixture plasma and give hints to select suitable parameter values which can be useful to improve light sources.     

Ultra-low temperature study of the even-denominator FQHE state

We present experimental data showing unambiguously an even-denominator fractional quantum Hall effect (FQHE) state at . At a bath temperature T_b=8 mK, we observe a Hall plateau quantized to a value of 2h/5e² with an uncertainty smaller than 2 parts in 10⁶ and a vanishing R_xx (R_xx=1.7±1.7 Ω). The thermal activation energy gaps Δ at Landau level filling factors , and are 0.11, 0.10, and 0.055 K, respectively. Adding a disorder broadening (typically 2 K) to these values, we deduce that all three FQHE states have probably very similar energy gaps. The electron heating experiment shows that the 2D electrons are efficiently cooled to the bath temperature for T_b8 mK. We also explore the density dependence of the activation gap at . Preliminary results at T_b25 mK show that the state is very sensitive to disorder.