Diocotron stability properties of relativistic non-neutral electron flow in a planar magnetron are investigated within the framework of the cold-fluid-Maxwell equations. The eigenvalue equation for the extraordinary-mode waves in a relativistic velocity-sheared electron layer is obtained, and is solved in the massless, guiding-center approximation. Approximating the electromagnetic field in the anode resonator by the lowest-order mode, the dispersion relation for the diocotron instability is obtained. Although the tenuous beam approximation is assumed, the eigenvalue equation and corresponding dispersion relation are both fully electromagnetic, and valid for relativistic electron flow. The dispersion relation is numerically investigated for a broad range of system parameters. From numerical calculations of the dispersion relation, it is shown that the typical growth rate of the diocotron instability indicates a strong instability. The early evolution of the diocotron instability as an important precursor to the evolution of the full magnetron oscillation is discussed.

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The diocotron instability of a general relativistic electron beam is studied using a macroscopic, cold fluid model. In contrast with the previous treatments where the theoretical analyses are carried out for a teneous electron beam in a strong magnetic field, i.e., plasma frequency << cyclotron frequency, the restriction on the magnitude of the beam density and guiding magnetic field is removed in deriving the general eigenvalue equation. In the limit of long axial wavelengths, a dispersion relation is extracted for a special case of a sharp boundary density profile. The stability properties for various rotating beams are investigated for a broad range of beam parameters. The results show that the kink mode can be unstable as the plasma frequency approaches the cyclotron frequency. Introducti onConsiderable reserch effort has been focussed recently on the development of high-current powerful relativistic electron beams. The beams with high current become very attractive because it provides some nice features as far as the beam propagation on the plasma media. Historically high current beams generated from accelerators are annular and guided by a strong magnetic field. The applied magnetic field provides radial confinement of the electrons. The diocotron instability has been studiedl previously in the parameter regime where the plasma frequency is much smaller than the cyclotron frequency (wpb << Wc). Because the cost and physical limitation for the strength of the magnetic field, the criteria of wpb << wc can be easily broken down if the beam density continues to increase. Consequently, a somewhat more general type of treatment of the instability is needed. In other words, this paper examines the general theory of the diocotron instability of a relativistic electron beam, especially in the regime where the plasma frequency is comparable or even larger than the cyclotron frequency. EquilibriumLet us consider a cylindrically symmetrical relativistic annular electron beam propagating parallel to a strong axial magnetic field in a conducting tube. The inner and outer radii of the electron beam are denoted by R1 and R2 respectively. Rc is the radius of the conducting wall. The analysis of dynamic properties is based on a maroscopic cold fluid model in which the electron flow is assumed to be laminar. The positive ions are assumed forming a stationary background (mii + ) which gives a partial fractional neutralization F. The balance forces in the radial direction give the angular velocity of an electron fluid element Wb(r) -2 l -[1 2w2b(i1 y2F ) 2 2 ( wc R2 1/2 1 -7)] r Where the electron density profile is assumed to be a rectangle function in the radial direction and the angular velocity of an electron fluid element is in a slow rotational equilibrium. It is necessary for the confinement of the annular electron beam that w 2 2 pCb i'pb > 2 2 --7) Stability Analysis In the linear stability analysis, the first-order perturbed quantities can be Fourier-decomposed according to 5&t(r,e,t) = 61(r) exp [i(ZB -wt)]where the ...

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A general treatment of ion resonance instability for a non-neutral plasma column is performed using a macroscopic cold-fluid-Maxwell model. The azimuthal motion of the plasma components has an important influence on the behaviour of the instability. When the electrons are in slow rotational equilibrium, the instability occurs in both slow and fast ion rotational equilibrium. However, there is stability when the electrons are in fast rotational equilibrium except that the l = 1 mode becomes unstable and independent of plasma rotation. The kink (l = 1) mode only occurs when the plasma column boundary exceeds a certain threshold value that depends on the ratio of the plasma frequency to the cyclotron frequency.