1. Soft and hard mode switching in gyrotrons
Gregory S. Nusinovich, Oleksandr V. Sinitsyn and Thomas M. Antonsen, Jr.
IREAP, University of Maryland, College Park, MD, USA
IRMMW-THz 2007, Cardiff, UK
September 3-7, 2007

2. Motivation
High-power microwave oscillators can operate in one of many modes with close frequencies – How to switch such a device from operation in one mode to another?
There is a strong interest in developing frequency step-tunable gyrotrons for suppression of NTM modes in tokamaks and stellarators – Mode switching can be used in such gyrotrons

3. Free-running two-mode oscillator
Introduction: how difficult is to switch an oscillator from one mode to another?
Weak and strong coupling between modes
[W. E. Lamb, Jr., “Theory of optical masers”, Phys. Rev. vol. 134, A1429 (1964)]
Free-running two-mode oscillator
K>1 – strong coupling
Single-mode oscillations are stable
K<1 –weak coupling
Two-mode oscillations
are stable
K is the coupling coefficient
which shows to what extent
excitation of one mode affects
another mode

4. Apply an external source for the switching.
Introduction: how difficult is to switch an oscillator from one mode to another?
We want to switch an oscillator from one mode to another. Hence, we need a device with strong mode coupling.
Apply an external source for the switching.
Required switching amplitude is proportional to k-1!

5. Conclusion from Introduction
When an oscillator operates in the parameter region corresponding to strong coupling, but near the border between regions of strong and weak mode coupling, such oscillator can be easily switched from one mode to another with the use of low-power driver.
The case when device can be switched by a low-power driver can be called soft switching in contrast to the case when switching requires a high-power driver – hard switching.
k>1, but lk-1l<<1

6. Gyrotron with azimuthally corrugated resonator wall
In conventional gyrotrons with ideally symmetric resonators and e-beams the coupling coefficient for modes with close frequencies is equal to 2 (as in radio oscillators studied by B. van der Pol). So, in such devices only hard switching is possible.
Coupling coefficients close to 1.0 can be realized in gyrotrons with azimuthally corrugated resonator walls. These are the devices where soft switching can be realized.

7. Gyrotron with azimuthally corrugated resonator wall
Number of corrugations should be equal to twice the azimuthal index of the operating modes. Then, the modes co- and counter-rotating with electrons will form standing wave patterns. Such sine and cosine modes have different frequencies. (Nusinovich, 1974)

8. Gyrotron with azimuthally corrugated resonator wall
Coupling between standing modes in a gyrotron with azimuthally corrugated resonator depends on the ratio of electron coupling to the co- and counter- rotating waves (Nusinovich, 1974)
- Weak coupling
Otherwise – strong coupling

9. Gyrotron with azimuthally corrugated resonator wall
Example: fundamental harmonic (s=1) gyrotron operating at the TE22,6 mode
It makes sense to position the beam in the near-caustic region

10. Gyrotron with azimuthally corrugated resonator wall
Some estimates:
Switching time for GHz gyrotrons with Q-factors about 1,000 is less than 100 ns
Power required for switching a MW-class gyrotron (90 kV, 40 A e-beam with alpha of 1.3, Q=1,600, TE22,6-mode, cavity length = 6 wavelengths) with k=1.1 is about 1 kW only!
Conclusion: One can use a 1 kW, short-pulse driver for manipulating a MW-level CW radiation

11. Possible application – NTM stabilization
The most efficient stabilization of neoclassical tearing modes (NTMs) in large tokamaks and stellarators (such as ITER or W7X) can be done with the use of gyrotrons operating in a modulated regime (AC stabilization).
Modulated regime means modulation of gyrotron radiation frequency with the frequency corresponding to the rotational frequency of magnetic islands (about 10 kHz).
In our case it means that a gyrotron should be switched from the first mode to the second and then back with the frequency about 10 kHz.

12. Possible application – NTM stabilization
FADIS (Fast Directional Switch) is proposed by W. Kasparek and M. Petelin for AC stabilization of NTMs.
This device combines a small frequency-shift keying
of the gyrotron and a narrow-band frequency diplexer,
which directs an input wave beam to one of two output
channels.
At present, the gyrotron for FADIS is assumed to operate
In a given mode and modulation of gyrotron frequency
should be provided by deviation of the mod-anode voltage.
To resolve the frequency modulation by a diplexer, this
modulation should be large enough. However, significant
variations in the mod-anode voltage spoil gyrotron
efficiency.
Gyrotron with azimuthally corrugated wall can improve the frequency resolution

13. Efficiency of gyrotrons with standing waves
There is no free lunch –interaction efficiency in gyrotrons with standing waves is lower than in conventional ones.
In conventional gyrotrons the amplitude of rotating waves is the same for all beamlets.
In gyrotrons with azimuthally standing waves, electron beamlets having different azimuthal coordinates of guiding centers interact with RF fields of different amplitude.
It follows from the analytical theory (Luchinin and Nusinovich, 1984) that gyrotrons operating near the boundary between regions of strong and weak mode coupling should have interaction efficiency equal to ¾ of the efficiency of conventional gyrotrons.
This reduction, however, can be smaller than in gyrotrons with periodically varying mod-anode voltage.

14. Conclusions
It is shown that oscillators operating near the boundary between regions of strong and weak mode coupling can be switched from one mode to another with the use of low-power drivers.
It is shown that such regimes can be realized in gyrotrons with azimuthally corrugated walls of resonators.
It is shown that such gyrotrons can be used for NTM stabilization in large tokamaks and stellarators.

15. General comment: how mode coupling can be weakened for realizing soft switching?
In gas lasers (W. E. Lamb), the coupling between modes weakens due to velocity spread causing inhomogeneous Doppler broadening of the amplification band –only two velocity fractions contribute to coherent radiation in two modes – low efficiency.
In microwave sources driven by electron beams, the coupling can be weakened due to spatial separation of interaction regions for two modes: (a) Cosine and sine standing modes in our case is just one example,
(b) Similar situation can take place in any multiple-beam device.
(c) Any small-orbit gyrotron can be treated as a multiple-beam device.
(d) When the beam geometry matches the transverse distribution of modes, the efficiency can be almost as high as in ideal gyrotron.
(e) However, we don’t need weak (k<1) coupling, we want just to weaken the coupling. So, the modes should be coupled to certain degree due to the fact that some electrons will interact with the fields of both modes.
Some efficiency degradation is inevitable!

16. Acknowledgments
This work was supported by the Office of Fusion Energy of the U.S. Department of Energy.
Authors are indebted to M. Petelin and J. Lohr for fruitful discussions.