Numerical Investigation of Gyro-Multiplier Schemes

David A. Constable#, Ilya V. Bandurkin+, Wenlong He#, Adrian W. Cross#, Andrei V. Savilov+, Alan D.R. Phelps#, Vladimir L. Bratman+ & Kevin Ronald#

# SUPA, Department of Physics, University of Strathclyde, Glasgow, United Kingdom. + Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, Russia.

david.a.constable@strath.ac.uk

Abstract: Numerical simulations using the PiC code Magic 3-D have investigated two distinct gyro-multiplier schemes. Subsequent results have predicted the operation of a single cavity device operating at the 2nd and 4th harmonics, at frequencies of 37.5 GHz and 75 GHz, respectively. As a result, this device is currently under experimental investigation. Additionally, a sectioned cavity device has shown promising output, delivering 4th harmonic output at ~1.36 THz. Results of both schemes will be presented.

Keywords: Gyrotron; harmonic; frequency multiplication; gyro-multiplier; gyro-device.

Introduction The gyrotron has proven itself a capable vacuum electronic device, providing high power, coherent radiation within the millimeter band [1,2], through the cyclotron resonance maser (CRM) instability [3]. However, with increasing demand for output at THz frequencies, scaling of conventional gyrotrons has proven difficult, due to their dependence on magnetic field strength, Bz.

An attractive possibility for high frequency gyrotrons is the use of frequency multiplication. Such gyro-multiplier [4,5] schemes involve the generation of high-harmonic, high frequency (HF) radiation through the direct excitation of a low-harmonic, low frequency (LF) resonance. In order to provide optimum generation of the HF signal, it is imperative that the frequencies of the two signals are of an integer ratio. As a result, the requirements on the magnetic field strength are relaxed. In addition, the electron beam current only has to be sufficient to start the LF signal, further reducing the ancillary requirements of the system.

Two such gyro-multiplier schemes are currently the subject of investigation using the PiC code, Magic 3-D. The first scheme, operating using a single cavity setup, excites the 2nd and 4th harmonics, at frequencies of 37.5 GHz and 75 GHz, respectively. This so-called co-harmonic generation, is facilitated by an azimuthal corrugation of the walls of the interaction region. The second system features a sectioned cavity scheme, with resonances at the 1st and 4th harmonics, operating at frequencies of 340 GHz and 1.36 THz, respectively.

Co-harmonic cavity gyro-multiplier The co-harmonic cavity features a sinusoidal corrugation around its azimuth, as shown in Figure 1. The radius of the

cavity, r(φ), is dictated by (1), where r0 is the mean radius of 8.0 mm, and l0 is the corrugation depth of 0.7 mm. Such a corrugation introduces a change in effective radius for the electromagnetic modes generated at the 2nd and 4th harmonics. Separation of the two radiation signals was planned through tapering to a section of waveguide which is cut-off to the LF signal. The electron beam used is of voltage 60 kV, ~5 A, and is confined with a 0.7 T magnetic field. Initial numerical simulations [6] attempted to predict the behavior of an experiment [7], using a Magic 3-D model employing a cylindrical co-ordinate scheme. The simulations predicted a leakage of the 2nd harmonic, which in turn, dominated the output radiation. This was also evident in the initial experimental investigation; however, it has been shown that by extending the length of the cut-off taper, the degree of mode conversion can be reduced by an order of magnitude [8]. More recent endeavors have focused on using a Cartesian mesh to investigate the system, due to the difficulties presented by the numerical singularity of a cylindrically meshed geometry [9].

0 0 sin 8r r l (1)

Figure 1. Representation of the co-harmonic cavity.

The results from the simulations show significantly improved performance. Figure 2, below, shows the time evolution of the x component of the electric field and an FFT of the signal, recorded at the output for both the original output taper and the extended variant. Output of the 2nd and 4th harmonics, at frequencies of 37.46 GHz and 74.92 GHz, respectively, is displayed, demonstrating the desired integer divisibility of the frequency of the signals. The extension of the output taper leads to the amplitude of the output signal decreasing by a factor of 5. In turn this has the effect of considerably improving the ratio of the relative magnitudes of the two output signals. Further experiments are under construction, which will attempt to

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confirm the improved rejection shown by the extended output taper.

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Figure 2. X component of the electric field and its FFT, recorded at the output, for a) the original 6 mm taper, and b) the extended 40 mm taper.

Sectioned cavity gyro-multiplier The sectioned cavity scheme investigated is shown in Figure 3. In such a scheme, the first and third cavities are tuned to operate at the fundamental harmonic, at a frequency of ~340 GHz, while the second cavity operates at the 4th harmonic, at ~1360 GHz. The second cavity differs in radius from the first cavity by ~30 microns, with the first and third cavities providing modulation of the electron beam, in order to generate the HF signal. The electron beam used is of voltage 80 kV, 0.7 A, and is confined by a ~14.1 T magnetic field. Unlike the co-harmonic scheme, a cylindrical co-ordinate system is employed.

Figure 3. Geometry of the sectioned cavity system. The simulations show that while the first four harmonics of the electron cyclotron frequency are generated, their amplitude is incredibly sensitive to the strength of the applied magnetic field, Bz. Figure 4 shows FFTs of the radial component of the output electric field, showing the divisibility of the frequencies of the 1st and 4th harmonics at ~341.5 GHz and ~1.366 THz, respectively. Currently, refinements to the cavity are currently ongoing to improve the relative magnitude of the 4th harmonic signal.

Figure 4. Radial component of the electric field recorded at the output for the 1st and 4th harmonics.

Acknowledgements Thanks are extended to the UK Engineering and Physical Sciences Research Council (EPSRC), the UK Faraday Partnership, the UK Royal Society, and the Russian Foundation for Basic Research.

References 1.V.A. Flyagin, A.V. Gaponov, M.I. Petelin, and V.K. Yulpatov, "The gyrotron", IEEE Transactions on Microwave Theory and Techniques, MTT-25(6), pp. 514-21, (1977).

2. V.A. Flyagin and G.S. Nusinovich, "Gyrotron oscillators", Proc. of the IEEE, 76(6), pp. 644-656, (1988).

3. P. Sprangle and A.T. Drobot, "Linear and self-consistent nonlinear theory of the electron cyclotron maser instability", IEEE Transactions on Microwave Theory and Techniques, MTT-25(6), pp. 528-544, (1977).

4. I.V. Bandurkin, V.L. Bratman, G.G. Denisov, et al., "Single-cavity Gyromultipliers", Terahertz Sci. Techno., 1(3), pp. 169-188, (2008).

5. I.V. Bandurkin and S.V. Mishakin, "Gyromultiplier with sectioned cavity", Phys. Plasmas, 17(11), 110706, (2010).

6. D.A. Constable, K. Ronald, A.D.R. Phelps, et al., "A co-harmonic gyro-oscillator with a novel interaction cavity", 2009 IEEE International Vacuum Electronics Conference Rome, Italy, (2009).

7. I.V. Bandurkin, V.L. Bratman, A.V. Savilov, S.V. Samsonov, and A.B. Volkov, "Experimental study of a fourth-harmonic gyromultiplier", Phys. Plasmas, 16(7), 073101, (2009).

8. D.A. Constable, K. Ronald, W. He, et al., “Recent progress on a co-harmonic gyrotron”, 2011 IEEE International Vacuum Electronics Conference, Bangalore, India, (2011).

9. D.A. Constable, K. Ronald, W.He, et al., “Numerical simulations of a co-harmonic gyrotron”, J. Phys. D., 46(6), 065105, (2012).

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