Periodic Permanent Magnet Stack Research Articles

Nonlinear time-domain analysis of coupled-cavity traveling-wave tubes

A time-dependent nonlinear analysis of a coupled-cavity traveling-wave tube (CCTWT) is presented. The coupled-cavity structure is modeled by a set of equivalent circuit equations where the equations for currents and voltages are coupled to the nearest neighbor cavities. Input and output coupler models as well as sever cavities are included in the formulation. The electron dynamics are treated using the three-dimensional Lorentz force equations although the RF field representation is an analytic model based on cylindrically symmetric geometry. The magnetic focusing fields are also cylindrically symmetric and can be either a solenoid or a periodic permanent magnet stack. The space-charge fields are found by mapping charge to a two-dimensional grid (r, z) and solving Poisson's equation by a finite difference grid formulation. The circuit and Lorentz force equations are integrated in time in a self-consistent manner. The formulation is capable of treating multiple drive frequencies and the associated intermodulation products as well as oscillations and backward wave instabilities. Hence, the model can be used to perform stability analyses. Furthermore, the cavity parameters can be varied to model dynamic velocity tapering for efficiency enhancement. The simulation is applied to the analysis of a sample C-Band CCTWT, and comparisons with measured performance of a Ka-Band CCTWT at Communications and Power Industries, Palo Alto, CA, are made.

Effect of geometric azimuthal asymmetries of PPM stack on electron beam characteristics [TWTs

A three-dimensional (3-D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions, allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3-D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.

Time-dependent simulation of helix traveling wave tubes

A time-dependent nonlinear analysis of a helix traveling wave tube (TWT) is presented for a configuration where an electron beam propagates through a three-dimensional tape helix surrounded by a conducting wall. The effects of dielectric- and vane-loading are included as is efficiency enhancement by tapering the helix pitch and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric-loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane-loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of waves in a vacuum tape helix. The propagation of each wave as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in z and t. The field equations are solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Collective effects are included by both a finite-difference grid formulation of Poisson’s equation and an analysis based upon a modal superposition of solutions of the Helmholtz equation. The time-dependent simulation is compared with a steady-state simulation for a model corresponding to a TWT built at Northrop–Grumman Corporation.

Nonlinear theory of collective effects in helix traveling wave tubes

A time-dependent collective nonlinear analysis of a helix traveling wave tube including fluctuating (ac) space-charge effects is presented for a configuration where an electron beam propagates through a sheath helix surrounded by a conducting wall. The effects of dielectric and vane loading of the helix are included, as is efficiency enhancement by tapering the helix pitch, and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of azimuthally symmetric waves in a vacuum sheath helix. The propagation of each wave in vacuo, as well as the interaction of each wave with the electron beam, is included by allowing the amplitudes of the waves to vary in z and t. The dynamical equation for the field is solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Collective effects from the fluctuating rf beam space-charge waves are also included in the analysis by means of a superposition of solutions of the Helmholtz equation. The simulation is compared with a linear theory of the interaction, and an example is described corresponding to a tube built at Northrop–Grumman Corp.

Lightweight permanent magnet stack for traveling-wave tubes

A prototype of an iron-free periodic permanent magnet stack was designed and built to serve as the electron beam focusing element in a traveling-wave tube. The stack is composed entirely of permanent magnet material and hence has no iron pole pieces that are subject to saturation. For the bore dimensions and period of interest, this design affords an order of magnitude size and weight reduction below conventional structures for field amplitudes in the technologically interesting 4 to 5 kOe range. A comparison with other novel and conventional structures is made with regard to attainable field amplitude, mass, bulk, and general practicality. The measured field of the prototype agrees with the theoretical values to within a few percent.