C. L. Chang

Instabilities in magnetically insulated gaps with resistive electrode plasmas

Collisional plasma layers exist on the electrode surfaces of magnetically insulated gaps. Coupling of the cathode electron sheath with these plasma layers leads to instabilities. These instabilities are of two types: (i) a destabilized negative energy mode on the electron sheath and (ii) a new low‐frequency resistive mode. The growth rates and physical picture of these modes suggest that they might be extremely dangerous in practice, leading to sporadic breakdown of magnetic insulation.

Electromagnetic stability of high-power ion diodes

The stability of high‐power magnetically insulated ion diodes is investigated. Interactions between the fields, the electron flow, and the ion beam in the diode gap lead to instabilities. These instabilities are (i) low‐frequency (below electron plasma frequency) instabilities that include a two‐stream type instability at ω≊0 and ion transit time instabilities at finite frequency, and (ii) high‐frequency instabilities (also called ‘‘magnetron instabilities’’) at a frequency above the electron plasma frequency. Under certain experimental conditions, one of the ion transit time instabilities is found to be broadbanded and may become absolutely unstable. Analysis based on realistic parameters shows the elimination of this broadband instability at diode operation close to insulation threshold, and implications of this finding are discussed.

Theory of the rippled field magnetron

The rippled field magnetron, a device for the generation of high‐power, short‐wavelength electromagnetic radiation, is studied theoretically. This device features smooth conducting coaxial anode and cathode electrodes, an axial insulating magnetic field, and a periodic azimuthal transverse wiggler magnetic field. The analysis treats the equilibrium in the fluid limit, including self‐fields, and is fully self‐consistent. Unstable coupling and growth of the positive energy (transverse electric TE) and negative energy (transverse magnetic TM) waves is demonstrated.

Stability of magnetically insulated ion diodes

Magnetically insulated ion diodes are examined for instability using analytical and numerical techniques. Two basic sources which drive instability are found: one due to a two‐stream‐type interaction between electrons and ions and the other due to ion transit time effects.

Parametric scaling of the stability of relativistic laminar flow magnetic insulation

The short wavelength limit of the magnetron instability of a relativistic sharp boundary electron sheath is examined. For short wavelengths the mode is localized to the sheath edge. This localization leads to a simple relationship (essentially a Lorentz transformation) between the relativistic and nonrelativistic growth rates. This relationship involves only equilibrium quantities evaluated at the sheath edge and explains previously noted trends that have been observed numerically.

Three-dimensional modeling of AC space charge for large-signal TWT simulation

We describe a new model for calculating the ac space charge in a linear-beam traveling wave tube (TWT) large-signal simulation code when the true three-dimensional (3-D) geometry of the interaction circuit is taken into account. We use the 3-D electromagnetic simulation code CTLSS to characterize the ac space charge fields generated by a set of test currents placed inside the periodic interaction structure. This information, expressed in matrix form, is used by the large-signal simulation codes CHRISTINE-1D and CHRISTINE-3D to compute self-consistently the additional space charge field terms due to the structure in response to the beam evolution during the simulation. We present the formulation, and describe the implementation in both CTLSS and the large-signal codes. We validate the model by comparison with the analytical sheath helix model, and evaluate the importance of including this correction for modeling a number of helix and coupled-cavity TWT devices.

Calculation of DC space-charge fields in a traveling-wave amplifier in the large signal regime

A fully two-dimensional (2-D) dc space charge model has been implemented in a large-signal traveling-wave amplifier code. The simulation algorithm takes an iterative approach by alternately solving the Poisson equation and the beam trajectory equations to converge toward a self-consistent steady-state solution. This approach is similar to that employed in steady-state gun codes. However, it is well known from gun simulations that the iterative algorithm can be slow to converge. We have found the slow convergence is due to a convective numerical instability. To speed up convergence, we implemented and tested stabilization schemes based on mixing one-dimensional and 2-D Poisson potentials during the iteration cycles. These schemes are shown to accelerate convergence considerably. The fully 2-D dc space-charge model permits accurate treatment of the axial dc space-charge field in the computation of the large signal gain and efficiency, taking into account the fast variation of beam parameters along the device axis. Therefore, it can be applied to a mismatched beam with large scalloping motion. The methodology of incorporating dc space charge is general and could be incorporated in other large signal codes.

Kinetic stability theory of space‐charge‐limited flow

The effect of a spread in energy of the emitted beam on the stability of the space‐charge‐limited diode is investigated. It is found that for small thermal spreads the so‐called emittron or transit time instability persists and is correctly described by cold fluid equations. Thermal effects become important when ωT∼e−1/4T, where ω is the mode frequency, T is a typical particle transit time, and eT is the ratio of the thermal energy of the beam to potential energy associated with the applied voltage. For modes with frequencies above this value, phase mixing of the particles causes a dramatic reduction in growth rate, such that other damping mechanisms will be able to stabilize the high‐frequency modes. The analysis presented here applies specifically to transverse electromagnetic (TEM) modes. However, the results can be expected to qualitatively describe other modes as well.

Linear stability of obliquely propagating electromagnetic waves in magnetically insulated gaps

A linear stability analysis for obliquely propagating electromagnetic waves in a magnetically insulated planar anode–cathode gap is presented. Previously published work [Phys. Fluids 24, 1821 (1981)] considered propagation perpendicular and parallel to the insulating magnetic field. Here the effect of propagation at oblique angles to the insulating field is considered. In general, growth rates decrease monotonically when the propagation angle becomes more parallel to B, and this effect is more pronounced for shorter‐wavelength waves for which analytic asymptotic results are obtained.

A complete space-charge model for 3D structures in the CHRISTINE 3D large-signal code

The CHRISTINE 3D code was developed to simulate the large-signal characteristics of slow-wave devices using a fast, parametric model. The model includes a fully three-dimensional representation of both particle motion and electromagnetic fields, treating external fields, the traveling-wave circuit field, and the RF space-charge field separately, but self-consistently. In common with existing parametric large-signal models, the space-charge fields (due to the beam charges) are computed assuming that they exist only within a cylindrical pipe at the inner radius of the circuit structures. In this paper, we develop a method for correcting the space-charge field to take account of the true 3D geometry. The correction terms are pre-computed using the 3D electromagnetic simulation code CTLSS, and the additional fields are included in the non-linear simulation. The corrected model shows a reduction in predicted gain.