Part III. Waveguides & Amplifiers





Negative Group Velocity in Waveguides from Perfectly Conducting Subwavelength Corrugations.

We are motivated by the numerical experiments carried out in [S.C. Yurt, A. Elfragani, M.I. Fuks, K. Ilyenko, and E. Schamiloglu, IEEE Trans Plasma Sci., 44 (2016), pp. 1280--1286] which s how correguated wave guides exibiting backwards wave propagation for sufficientlydeep corrugations. Together with A. Polizzi, and L. Thakur we apply an asymptotic analysis that shows that corrugated waveguides can be represented as cylindrical waveguides with a smooth metamaterial surface for subwavelength corrugtions. Here the metamaterial delivers an effective anisotropic surface impedance and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation, and we provide a systematic investigation of the effect of corrugation geometry on wave dispersion, group velocity, and power flow. This research has appeared in SIAM J. Appl. Math. 77:4 (2017) pp.1269--1291.


This work is supported by NSF Grant DMS-1211066 and Air Force Research Office through award FA9950-12-1-0489

Slow Wave Amplifiers from Subwavelength Beam Wave Interaction Structures.

From an operational viewpoint, a traveling wave tube amplifier can be thought of as a cylindrical dielectrically loaded waveguide with an electron beam running through its center. The electron motion is parallel to the waveguide and confined by a strong uniform magnetic field applied along the beam. The beam is surrounded by a dielectric jacket separated from the beam by vacuum. When the dielectric constant is larger than unity, it is possible to get amplification from the traveling wave tube (TWT), see (Schacter, 2011), (Schachter, Nation, and Kerslick, 1990), Unfortunately, most dielectric materials are insufficient for high power applications and break down after a few operational cycles. On the other hand, (Shiffler et al., 2010) propose sub-wavelength all-metal interaction structures that effectively act as a dielectric medium with dielectric constant greater than unity. This provides the opportunity for design of TWTs with metal beam-wave interaction structures.

In this project, togeather with A. Polizzi, we investigate the influence of metal interaction structures on the anisotropy of the effective dielectric tensor and the tune-ability of gain, bandwidth, and frequency of operation for short TWT amplifiers. Along the way, it is shown that effective dielectric properties arise naturally and in a systematic way by applying a two-scale asymptotic expansion for the solution of Maxwell's equations describing the beam-wave interaction inside the TWT.

We numerically calculate amplifier gain as a function of the geometry of metallic interaction structures. Here we consider cercular TWTs contining periodic ring like interaction structures with constant cross-section. The analysis is carried out for operational frequencies in the range of $7$ to $15$ GHz range. Our amplifier is $15$cm long by $1.82$cm in radius and driven by a 1-KA beam current. We show that the range of amplifier operation increases as the filling fraction decreases, while both gain and bandwidth remain relatively constant. It is found that more longitudinally eccentric geometries yield a higher gain. This project is published in Journal of Applied Physics 116, 144504 (2014); doi: 10.1063/1.4897235


This work is supported by NSF Grant DMS-1211066 and Air Force Research Office through award FA9950-12-1-0489

References

  1. R. Lipton, A. Polizzi, and Lokendra Thakur. Novel metamaterial surfaces from perfectly conducting subwavelength corrugation. SIAM Journal on Applied Mathematics, 77, Issue 4, 2017, pp. 1269-1291. .
  2. S.C. Yurt, A. Elfragani, M.I. Fuks, K. Ilyenko, and E. Schamiloglu, IEEE Trans Plasma Sci., 44 (2016), pp. 1280--1286.
  3. R. Lipton and A. Polizzi, Tuning gain and bandwidth of traveling wave tubes using metamaterial beam-wave interaction structures. Journal of Applied Physics 116, 144504 (2014); doi: 10.1063/1.4897235
  4. L.Schachter,Beam-WaveInteractioninPeriodicandQuasi-Periodic Structures (Particle Acceleration and Detection), 2nd ed. (Springer, Berlin, 2011).
  5. L. Schachter, J. A. Nation, and G. Kerslick, J. Appl. Phys. 68, 5874 (1990)
  6. D. Shiffler, J. Luginsland, D. French, and J. Watrous, IEEE Trans. Plasma Sci. 38, 1462 (2010).