Streaming Electron Beam Research Articles

Weibel instability for a streaming electron, counterstreaming e-e, and e-p plasmas with intrinsic temperature anisotropy

The existence of Weibel instability for a streaming electron, counterstreaming electron-electron (e-e), and electron-positron (e-p) plasmas with intrinsic temperature anisotropy is investigated. The temperature anisotropy is included in the directions perpendicular and parallel to the streaming direction. It is shown that the beam mean speed changes the instability mode, for a streaming electron beam, from the classic Weibel to the Weibel-like mode. The analytical and numerical solutions approved that Weibel-like modes are excited for both counterstreaming e-e and e-p plasmas. The growth rates of the instabilities in e-e and e-p plasmas are compared. The growth rate is larger for e-p plasmas if the thermal anisotropy is small and the opposite is true for large thermal anisotropies. The analytical and numerical solutions are in good agreement only in the small parallel temperature and wave number limits, when the instability growth rate increases linearly with normalized wave number kc∕ωp.

Stabilization of beam-weibel instability by equilibrium density ripples

In this paper, we present an approach to achieve suppression/complete stabilization of the transverse electromagnetic beam Weibel instability in counter streaming electron beams by modifying the background plasma with an equilibrium density ripple, shorter than the skin depth; this weakening is more pronounced when thermal effects are included. On the basis of a linear two stream fluid model, it is shown that the growth rate of transverse electromagnetic instabilities can be reduced to zero value provided certain threshold values for ripple parameters are exceeded. We point out the relevance of the work to recent experimental investigations on sustained (long length) collimation of fast electron beams and integral beam transport for laser induced fast ignition schemes, where beam divergence is suppressed with the assistance of carbon nano-tubes.

Electromagnetic sub‐bands in an axisymmetric doubly rippled wall metallic slow wave structure

Slow wave structure (SWS) is the vital component of slow wave type high-power microwave (HPM) devices where the kinetic energy of an axially streaming electron beam is resonantly extracted to produce microwave radiation. The frequency of the generated microwave predominantly depends on the beam energy and the dispersion characteristics of the SWS. Many types of SWSs have been investigated and implemented in real experiments. Among them, cylindrical metallic structures with sinusoidally rippled inner wall have gained popularity in backward wave oscillators. To enhance the efficiency of the devices, prolonged and stable interaction of the EM wave with electron beam is important. One of the possible techniques to improve the performance of the devices could be the use of non-uniform SWS. In this study, a doubly rippled inner wall SWS is considered. The radius of the structure is varied sinusoidally with two periods. Using linear theory, the dispersion relation of the EM wave inside the structure in the absence of electron beam has been analysed numerically. It has been observed that a single band of the conventional sinusoidally rippled SWS is decomposed into several sub-bands depending on the ratio of the length of two periods. Some of the sub-bands are so flat that the frequency of the microwave radiation can be made insensitive to the beam energy fluctuation.

How really transverse is the filamentation instability?

It is generally considered that the linear filamentation instability encountered when two counter streaming electron beams interpenetrate is purely transverse. Exact and approximated results are derived in the relativistic fluid approximation showing that within some parameter range, filamentation can be indeed almost longitudinal with cos(k,Ê)≲1−3.1∕γb, where γb is the relativistic factor of the beam. Temperature effects are then evaluated through relativistic kinetic theory and yield even fewer transverse filamentation modes. In the cold case, the transverse approximation overestimates the growth rate by a factor ∝γb.

Use of EBIS in the string mode of operation on the Nuclotron facility in JINR

The reflex mode of EBIS operation in certain conditions (a special construction of electron gun and electron reflector, a precise axial symmetry of solenoid with a strong magnetic field, a sufficient injected electron current at a certain energy which provide a sufficient density of accumulated electrons in EBIS drift space) leads to formation of the so-called electron string state of a pure one component electron plasma. It was shown experimentally, that electron strings are stable in a broad range of operational conditions to be used for production of highly charged ions in electron string ion sources (ESIS) similarly to streaming electron beams in EBIS. The EBIS “Krion-2” in the string mode of operation, by means of which electron string formation was first observed and majority of experimental information on its features has been obtained, was recently used as the source of highly charged ions on the Nuclotron accelerator facility. During two runs in June 2002 and June 2003 N6+, N7+, Ar16+ and Fe24+ ions of 300, 350, 200, and 150 μA pulse current, respectively, produced by this source were accelerated to relativistic energies and used in several experiments. During the runs the source situated on the high voltage platform of the LINAC preinjector worked mostly in an automatic mode of operation and showed high stability and reliability.

Cherenkov and Slow Cyclotron Instability in Periodically Corrugated Cylindrical Waveguide with Low Magnetic Field Region

Cherenkov and slow cyclotron instabilities driven by an axially injected electron beam in periodically corrugated cylindrical waveguide are studied by using a new version of self-consistent linear theory considering three dimensional beam perturbations. For the bounded microwave systems, the self-consistent boundary conditions require all field components and the normal modes in the beam are hybrid of transverse magnetic (TM) and transverse electric (TE) modes, even in the axisymmetric case. The slow cyclotron instability as well as Cherenkov instability can be driven by the axially streaming electron beam without any initial perpendicular velocity. In the low magnetic field region, the charge caused by the radial displacement of the beam plays an important role in the beam interaction with the electromagnetic mode. The radial displacement become large by decreasing the magnetic field and the slow cyclotron instability becomes strong and compete with the Cherenkov instability. For the axisymmetric case, the Cherenkov instability is dominant and suppresses the slow cyclotron instability, On the other hand, the slow cyclotron instability becomes dominant and suppresses the Cherenkov instability, for the nonaxisymmetric mode with the left-hand circular polarization

Slow Wave Electron Cyclotron Maser Utilizing Periodically Corrugated Waveguide

Slow wave electron cyclotron maser composed of a periodically corrugated waveguide and an axially streaming electron beam is considered. This slow wave electron cyclotron maser can be driven by the electron beam with predominant axial velocity and is distinct from the conventional fast wave electron cyclotron maser, in which an electron beam having an initial perpendicular velocity to magnetic field is required. Normal modes in the cylindrical slow wave system with magnetized electron beam are analyzed by a linear fluid model, taking into account of three dimensional beam perturbations and boundary conditions self-consistently. The axially streaming electron beam is able to interact with periodic electromagnetic normal modes at an anomalous Doppler cyclotron resonance, resulting in slow wave electron cyclotron maser instability. When the frequency of the slow wave electron cyclotron maser instability coincides with that of conventional Cherenkov instability, two instabilities can be combined favorably to generate microwave radiation.

Interaction of Axially Streaming Electron Beam with Axisymmetric TM Mode in a Periodical Slow Wave Structure with Finite Magnetic Field

Interaction between an axially streaming electron beam and an axisymmetric TM mode in a periodically corrugated waveguide is analyzed using a linear fluid model. Effect of the perpendicular perturbation of the beam by a finite magnetic field is considered. There are two mechanisms of Cherenkov interaction between a beam and a TM mode. One is the conventional mechanism attributed to a longitudinal perturbation. The other is attributed to the vertical perturbation of the beam surface and is dominant in the low magnetic field region. The slow cyclotron mode on an axially streaming beam is able to interact with an axisymmetric TM mode only if beam surface modulation is taken into account. The Cherenkov and cyclotron interactions degenerate for zero magnetic fields. This interaction has higher growth rate compared to the conventional Cherenkov interaction in the region of high current and weakly relativistic energy.

New observations of ion beams in the plasma sheet boundary layer

The Wind perigee passes covered tail distances from 6–24 RE. By use of bulk quantities and the parent distributions, we have found new features in the PSBL that had been missed previously. The PSBL consists of a unidirectional earthward streaming ion beam at the edge and another unidirectional beam inside this edge streaming in the tailward direction. Bidirectional beams are observed with higher densities, further inside the PSBL. The plasma in the region supporting the tailward streaming beams consists of the beam distribution plus an isotropic component, whereas the earthward streaming beams consists mainly of the beam distribution. These distributions yield fast flows (>400 km/s) in the earthward direction and slower flows (≈ 150 km/s) in the tailward direction. Both regions support counter streaming electron beams superposed on an isotropic component. These new findings are substantially different from previous observations and the interpretation of fast flows and ion beams in terms of a neutral line model needs to be reexamined.

Stabilization of counter streaming electron beam instability

Instability at half the electron cyclotron frequency that arises in a system of symmetrical counter streaming electron beams is stabilized by the injection of third beam.

Effects of Low Frequency Plasma Waves on Counter-Streaming Electron Beam Instability

Experimental investigations are made of a high frequency wave at one half the electron cyclotron frequency fee/2 excited by counter streaming electron beams in a magnetoplasma. It is found that the time averaged amplitude of the high frequency wave is decreased by modulating the beam externally at a certain lower frequency. The result is explained qualitatively by considering that the low frequency wave causes a periodic change in the growth rate of the high frequency wave.

Water-bag stability theory for planar bounded plasmas with counter-streaming injection. Part 1. The neutralized diode

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.

Plasma instability in a collisional and thermal magnetoplasma

The interaction of electromagnetic waves and a streaming electron beam is considered in a cold collisional, and warm magnetoplasma. A dispersion relation for such a beam-plasma system is obtained with the help of a kinetic equation. An expression is obtained for the growth rate. The effect of collisions and temperature on the growth rate of electromagnetic and electrostatic instability is investigated. It is shown that both collisional and thermal effects in the plasma decrease the growth rate.