Dispersion relation and growth rate of a relativistic electron beam propagating through a Langmuir wave wiggler

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
H. Zirak ◽  
S. Jafari
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Wave Equations ◽  
Axial Magnetic Field ◽  
Equations Of Motion ◽  
Langmuir Wave ◽  
Electron Trajectories ◽  
Runge Kutta Method ◽  
Guide Magnetic Field

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge–Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

Zur Rayleigh-Taylor-Instabilität eines rotierenden Wasserstofflichtbogens im axialen Magnetfeld

1970 ◽  
Vol 25 (2) ◽  
pp. 273-282 ◽  
Author(s):  
H. F. Döbele
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Heat Conduction ◽  
Dispersion Relation ◽  
Electrical Conduction ◽  
Growth Rates ◽  
Plasma Column ◽  
Qualitative Agreement ◽  
Axial Magnetic Field ◽  
Rayleigh Taylor Instability

Abstract The Rayleigh-Taylor instability of a rotating hydrogen arc in an axial magnetic field is investigated with allowance for electrical conduction, heat conduction and viscosity. The r-depending part of the perturbation was assumed to be in the form of a half-period of a standing wave. The corresponding dispersion relation is derived in the WKB-approximation and is solved numerically. In contrast with the case without dissipation, the frequencies and growth rates of the different modes depend on the parameters of the unperturbed plasma column. The calculation shows, in qualitative agreement with the experiment, that with increasing magnetic field the highest growth rate passes successively to the next higher mode.

Self-consistent and complete field theory of relativistic travelling wave tube amplifier with plasma loaded tape helix

2012 ◽  
Vol 90 (12) ◽  
pp. 1237-1257 ◽  
Author(s):  
S. Saviz
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Beam Energy ◽  
Axial Magnetic Field ◽  
Travelling Wave ◽  
Wave Tube ◽  
Constant Growth Rate ◽  
Energy Beam

The dispersion relation was derived for electromagnetic wave propagation through a plasma-loaded helix travelling wave tube (TWT). The analysis is based on field theory for a configuration in which a magnetized pencil-type beam propagates through cold plasma in the helix enclosed with a loss-free wall. The obtained dispersion relation implicitly includes azimuthal variations and all spatial harmonics of the tape helix. The characteristics of the growth rate were studied numerically. The results show that the phase velocity increases with increasing plasma density and axial magnetic field. By numerical computation, the dispersion characteristic of plasma-loaded helix TWT analyzed in different cases of various plasma densities, beam energy, beam density, and axial guide magnetic field. The results show that the presence of plasma significantly increases the growth rate and bandwidth. The enhancement in beam energy and density cause an increase in growth rate and frequency. The growth rate increases with increasing axial field until is reaches a maximum; further increases in the axial guide field lead to a relatively constant growth rate.

Dispersion relation and growth rate in a free-electron laser with a background plasma

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
T. Mohsenpour ◽  
B. Maraghechi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Plasma Density ◽  
Free Electron ◽  
Free Electron Laser ◽  
Axial Magnetic Field ◽  
Background Plasma ◽  
Positive Energy ◽  
Induced Velocity

The method of perturbation has been applied to derive a general dispersion relation for a free-electron laser (FEL) with background plasma and helical wiggler in the presence of an axial magnetic field. This dispersion relation is solved numerically to find unstable interactions among all of the wave modes. Numerical calculations show that new coupling between the left wave and positive-energy space-charge of electron beam are found when wiggler induced velocity is large. This coupling does not change with increasing the plasma density. The growth rate of FEL is changed with increasing the plasma density and the normalized axial magnetic field.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Contact Discontinuity ◽  
Homogeneous Magnetic Field ◽  
Taylor Instability ◽  
Wide Range ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field ◽  
Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

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