Local analysis of extraordinary-mode stability properties for relativistic non-neutral electron flow in a planar diode

1987 ◽  
Vol 37 (1) ◽  
pp. 63-79
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Dispersion Relation ◽  
Cyclotron Frequency ◽  
Electron Flow ◽  
Electron Cyclotron ◽  
Local Analysis ◽  
Planar Diode ◽  
Stability Properties ◽  
Local Dispersion ◽  
Electron Cyclotron Frequency ◽  
Wide Range

The extraordinary-mode eigenvalue equation is used to investigate the local stability properties of relativistic, non-neutral electron flow in a planar diode. The local stability analysis assumes gentle equilibrium gradients and short perturbation wavelengths. The lowest-order local dispersion relation is derived assuming that localized solutions for the eigenfunction exist, and stability properties are investigated numerically over a wide range of System parameters for perturbations with frequency small in comparison with the electron cyclotron frequency. It is found that the local dispersion relation supports three solutions in this frequency regime. One of the solutions corresponds to a stable diocotron mode driven by the local density gradient. The other two branches are found to exhibit instability over a wide range of electron density. These modes are electromagnetic in nature and require relativistic electron flow with velocity shear in order for instability to exist. Moreover, the growth rate of the unstable electromagnetic mode can be substantial (a few per cent of the electron cyclotron frequency).

scholarly journals Kinetic stability properties of relativistic nonneutral electron flow for low-frequency extraordinary-mode perturbations

1989 ◽  
Vol 7 (1) ◽  
pp. 85-109 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Dispersion Relation ◽  
Layer Thickness ◽  
Electron Energy ◽  
Electron Flow ◽  
Low Frequency ◽  
Outer Edge ◽  
Stability Properties ◽  
System Parameters ◽  
Wide Range ◽  
Electron Layer

The kinetic stability properties of relativistic nonneutral electron flow in planar diode geometry are examined for extraordinary-mode perturbations about the self-consistent Vlasov equilibrium . Here, the cathode is located at x = 0; the anode is located at x = d the outer edge of the electron layer is located at is the equilibrium flow velocity in the x-direction; n^b is the electron density at the cathode (x = 0); and is the axial magnetic field, with const. in the vacuum region (xb < x ≤ d). The extraordinary-mode eigenvalue equation, derived in a companion paper for low-frequency, long-wavelength perturbations, is solved exactly. This leads to a formal dispersion relation, which can be used to determine the complex eigenfrequency ω over a wide range of system parameters and wavenumber k in the y-direction. The formal dispersion relation is further simplified for and , assuming low-frequency perturbations about a tenuous electron layer with and . Here, , and , where denotes the average equilibrium orbit, and [γ(x) − 1]mc2 is the average kinematic energy of an electron fluid element. The resulting approximate dispersion relation is solved numerically over a wide range of system parameters to determine the detailed dependence of stability properties on electromagnetic effects, layer thickness, and electron energy, as measured by , and γb − 1, respectively. Here, γb = γ(xb) denotes the electron energy at the outer edge of the electron layer. As a general remark, it is found that increasing the electron energy (γb − 1), increasing the strength of electromagnetic effects , and/or decreasing the layer thickness (xb/d) all have a stabilizing influence.

scholarly journals Radial variation of whistler-mode chorus: first results from the STAFF/DWP instrument on board the Double Star TC-1 spacecraft

2005 ◽  
Vol 23 (8) ◽  
pp. 2937-2942 ◽  
Author(s):  
O. Santolík ◽  
E. Macúšová ◽  
K. H. Yearby ◽  
N. Cornilleau-Wehrlin ◽  
H. StC. K. Alleyne
Keyword(s):  
Cyclotron Frequency ◽  
Power Spectra ◽  
Double Star ◽  
Electron Cyclotron ◽  
Radial Variation ◽  
Whistler Mode ◽  
Electron Cyclotron Frequency ◽  
The Earth ◽  
First Results ◽  
Initial Results

Abstract. We use the first measurements of the STAFF/DWP instrument on the Double Star TC-1 spacecraft to investigate whistler-mode chorus. We present initial results of a systematic study on radial variation of dawn chorus. The chorus events show an increased intensity at L parameter above 6. This is important for the possible explanation of intensifications of chorus, which were previously observed closer to the Earth at higher latitudes. Our results also indicate that the upper band of chorus at frequencies above one-half of the electron cyclotron frequency disappears for L above 8. The lower band of chorus is observed at frequencies below 0.4 of the electron cyclotron frequency up to L of 11-12. The maxima of the chorus power spectra are found at slightly lower frequencies compared to previous studies. We do not observe any distinct evolution of the position of the chorus frequency band as a function of L. More data of the TC-1 spacecraft are needed to verify these initial results and to increase the MLT coverage.

Electromagnetic cyclotron-loss-cone instability associated with weakly relativistic electrons

1982 ◽  
Vol 28 (3) ◽  
pp. 503-525 ◽  
Author(s):  
H. K. Wong ◽  
C. S. Wu ◽  
F. J. Ke ◽  
R. S. Schneider ◽  
L. F. Ziebell
Keyword(s):  
Cyclotron Frequency ◽  
Maximum Growth ◽  
Basic Mechanism ◽  
Electron Cyclotron ◽  
Relativistic Electrons ◽  
Electron Component ◽  
Loss Cone ◽  
Electron Cyclotron Frequency ◽  
Cone Type ◽  
Consistent Manner

The amplification of fast extraordinary mode waves with frequencies very close to the electron cyclotron frequency is investigated for a plasma which consists of a weakly relativistic electron component with a loss-cone type distribution and a cold background electron component. The basic mechanism of the amplification is attributed to a relativistic cyclotron resonance between the wave and the energetic electrons. The method employed in the present analysis enables us to solve the dispersion relation in a self-consistent manner for arbitrary ratio of the densities of the energetic and background electrons. It is found that the maximum growth rates occur at certain values of ω2pe/Ω2e and the angular dependence of the growth rate is sensitive to the ratios ω2pe/Ω2e and ne/nb. Here ωpe and Ωe are the electron plasma frequency and the electron cyclotron frequency, respectively, and ne and nb denote the number densities of the energetic and background electrons, respectively.

Transport model of plasma heating at the second harmonic of the electron-cyclotron frequency

2021 ◽  
Author(s):  
Yurii N Dnestrovskij ◽  
Alexander V Danilov ◽  
Alexey Dnestrovskiy ◽  
Sergey E. Lysenko ◽  
Alexander V Melnikov ◽  
...  
Keyword(s):  
Cyclotron Frequency ◽  
Transport Model ◽  
Second Harmonic ◽  
Plasma Heating ◽  
Electron Cyclotron ◽  
Electron Cyclotron Frequency
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