The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Chaos in High-Power High-Frequency Gyrotrons

Markus Airila

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 6th of February, 2004, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-6917-1)   [1955 KB]
Dissertation is also available in print (ISBN 951-22-6916-3)


Gyrotron interaction is a complex nonlinear dynamical process, which may turn chaotic in certain circumstances. The emergence of chaos renders dynamical systems unpredictable and causes bandwidth broadening of signals. Such effects would jeopardize the prospect of advanced gyrotrons in fusion. Therefore, it is important to be aware of the possibility of chaos in gyrotrons.

There are three different chaos scenarios closely related to the development of high-power gyrotrons: First, the onset of chaos in electron trajectories would lead to difficulties in the design and efficient operation of depressed potential collectors, which are used for efficiency enhancement. Second, the radio-frequency signal could turn chaotic, decreasing the output power and the spectral purity of the output signal. As a result, mode conversion, transmission, and absorption efficiencies would be reduced. Third, spatio-temporal chaos in the resonator field structure can set a limit for the use of large-diameter interaction cavities and high-order TE modes (large azimuthal index) allowing higher generated power.

In this thesis, the issues above are addressed with numerical modeling. It is found that chaos in electron residual energies is practically absent in the parameter region corresponding to high efficiency. Accordingly, depressed collectors are a feasible solution also in advanced high-power gyrotrons. A new method is presented for straightforward numerical solution of the one-dimensional self-consistent time-dependent gyrotron equations, and the method is generalized to two dimensions. In 1D, a chart of gyrotron oscillations is calculated. It is shown that the regions of stationary oscillations, automodulation, and chaos have a complicated topology in the plane of generalized gyrotron variables. The threshold current for chaotic oscillations exceeds typical operating currents by a factor of ten. However, reflection of the output signal may significantly lower the threshold. 2D computations indicate that stationary single-mode operation of gyrotrons would be impossible if the azimuthal index is about 46 or larger, which is rather close to the presently used values. Moreover, electron beam misalignment can lower this critical value. Above the critical value, less favorable modes suppress the operating mode.

This thesis consists of an overview and of the following 7 publications:

  1. Airila M. I., Dumbrajs O., Reinfelds A. and Teychenné D., 2000. Traces of stochasticity in electron trajectories in gyrotron resonators. International Journal of Infrared and Millimeter Waves 21, number 11, pages 1759-1776. © 2000 Kluwer Academic Publishers. By permission.
  2. Airila M. I. and Dumbrajs O., 2001. Generalized gyrotron theory with inclusion of adiabatic electron trapping in the presence of a depressed collector. Physics of Plasmas 8, number 4, pages 1358-1362. © 2001 American Institute of Physics. By permission.
  3. Airila M. I., Dumbrajs O., Reinfelds A. and Strautiņš U., 2001. Nonstationary oscillations in gyrotrons. Physics of Plasmas 8, number 10, pages 4608-4612. © 2001 American Institute of Physics. By permission.
  4. Airila M. I. and Kåll P., 2004. Effect of reflections on nonstationary gyrotron oscillations. IEEE Transactions on Microwave Theory and Techniques 52, number 2, to appear. © 2004 IEEE. By permission.
  5. Airila M. I., Dumbrajs O., Kåll P. and Piosczyk B., 2003. Influence of reflections on the operation of the 2 MW, CW 170 GHz coaxial cavity gyrotron for ITER. Nuclear Fusion 43, number 11, pages 1454-1457. © 2003 International Atomic Energy Agency (IAEA). By permission.
  6. Airila M. I. and Dumbrajs O., 2002. Spatio-temporal chaos in the transverse section of gyrotron resonators. IEEE Transactions on Plasma Science 30, number 3, pages 846-850. © 2002 IEEE. By permission.
  7. Airila M. I., 2003. Degradation of operation mode purity in a gyrotron with an off-axis electron beam. Physics of Plasmas 10, number 1, pages 296-299. © 2003 American Institute of Physics. By permission.

Keywords: depressed collector, spatio-temporal chaos, microwave reflections, electron beam misalignment, modeling

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© 2004 Helsinki University of Technology

Last update 2011-05-26