Stabilization of gyrotron frequency by reflection from nonresonant and resonant loads

Abstract

It is known that the gyrotron radiation frequency may be unstable because of supply voltage fluctuations [1]. At the same time, some applications, such as plasma diagnostics, high resolution spectroscopy, and (possibly in the future) formation of a complex of coherently emitting gyrotrons in large setups for con trolled fusion, call for frequency stabilized radiation sources. In this study, we propose a method of gyrotron frequency stabilization by a wave reflected from a dis tant load. The influence of delayed reflections on the operation of active oscillators, including gyrotrons, has been investigated by many researchers (see, for example, [2][3][4][5][6][7][8]). However, specific schemes of gyrotron frequency stabilization by a reflected wave have not been discussed, because the reflected wave in a gyrotron with a conventional output quasi optical transducer returns to the operating space as a counter rotation mode, which weakly interacts with an elec tron beam [9]. Recently, a new type of output quasi optical transducers converting a wave arrived from the output channel (reflection or external signal) into the operating mode has been developed at the Institute of Applied Physics, Russian Academy of Sciences [10]. One might expect these transducers to make it possible to stabilize the gyrotron radiation frequency.In this Letter, we show that the wave reflected from a load, both resonant and nonresonant, can capture and stabilize the gyrotron radiation frequency if the difference in frequencies of the reflected and freely emitted (in the absence of reflections) waves does not exceed a value on the order of |R|ω 0 /Q (Q is the dif fraction Q factor and |R| is the magnitude of the reflec tance) [5]. This value is an analog of the capture band (or locking band) width when a specified external monochromatic force is exerted on the active oscilla tor [4].The self consistent equations of gyrotron, into which the wave arrives from the output waveguide after being reflected from the load, within the approxima tion of fixed longitudinal field structure and small reflectance, can be written as [2,3,9] (1)The electric field of the operating TE mode in the interaction space can be written as E = Re(E s (r ⊥ )G(z, t)), where ω 0 is the reference frequency; the gyrotron cavity is a cylindrical segment with a mean radius r 0 close to the critical one; E s (r ⊥ ) = -i[∇ ⊥ ψ, z 0 ]/k describes the transverse structure coinciding with the transverse structure of one of the cavity modes; k = ω 0 /c; ψ = J m (kr)e -imϕ ; r and ϕ are the radial and azi muthal coordinates, respectively; a(t) = |a(t)|e iφ(t) is the slowly varying in time dimen sionless complex field amplitude; f(z) = exp(-3(zz 0 ) 2 / ) is the longitudinal field structure (it is assumed that |f(0)| = |f(2z 0 )| = |f max |/e 3 ); a τ is the field amplitude at instant t -τ; τ is the delay time; ω r is the real part of the cold cavity frequency; R = |R|e iα is the complex coefficient of reflection from the load; p = (p x + ip y ) / ( β ⊥0 m e cγ 0 ) is the dimension le...

Experimental Demonstration of Gyrotron Frequency Stabilization by Resonant Reflection

“…Dependence of the reflection coefficient (amplitude-wise) on the frequency for the resonant reflector is R = R 0 /(1 + i ξ ) [30], where ξ = 2Q res ( f rad − f res )/ f res , f rad -gyrotron radiation frequency. Using the theory of the gyrotron with resonant reflections, developed in [13], [28], one can obtain the relationship between magnetic field B and the gyrotron radiation frequency:…”

“…Therefore, their spectral characteristics are of great interest to the community, and the gyrotron frequency tuning and stabilization are actively investigated. A number of studies considered active frequency manipulation by variation of the electron beam parameters [1]- [5], as well as phase locking by the external signal [6]- [8] and changing the spectral characteristics of the radiation (spectrum control), in particular, frequency stabilization by the wave reflected from the nonresonant load (theoretically [9]- [13] and experimentally [14]- [19]). Each of the methods has its advantages and limitations.…”

“…This method is well known and is used in numerous applications, such as the feeding of microtron and linear accelerators by magnetrons [20]- [22] in microwave electronics or stabilization of laser frequency [23]- [27]. The theory of gyrotron frequency stabilization by the external high-resonant load was developed in [13], [28], [29]. This Letter presents experimental results and simulation of frequency stabilization of gyrotron by the signal reflected from the resonant (high-Q) load.…”

Optimization of Laser Frequency Stabilization via Self-Injection Locking to WGM Microresonator

“…Using this notation we perform a full parametric optimization of the stabilization coefficient. Figure 3(a) shows the results of the numerical optimization for zero phase ψ = 0 and optimal frequency detuning (8). It can be seen that the critical coupling is optimal for the short lasermicroresonator distance (κ 0 τ s < 0.1) and for the large backscattering β ≥ 1.…”

“…Self-injection locking phenomenon is one of profound effects observed in oscillatory circuits. For many years this effect has been used in Radio-Physics, Radio-Engineering and Microwave Electronics with the goal to improve the spectral purity of the devices [1][2][3][4][5][6][7][8][9][10][11]. It also has been widely applied for stabilization of laser sources enabling various practical applications, including high resolution spectroscopy and high-precision metrology.…”