ABSTRACT
The remarkable history of gyrotrons begins in the distant 1964 [1] when the breakthrough ideas in relativistic electronics [2] and the visionary research of outstanding scientists in Gorky, USSR (now Nizhny Novgorod, Russia) [3], had led to the invention, construction, and experimental demonstration of the first gyrotron. Soon afterward, they gave rise to a new family of fast-wave vacuum tubes that includes amplifiers and oscillators such as Gyro-BWO, CARM (Cyclotron Autoresonance Maser), Gyro-TWT, Gyro-Klystron, etc. An excellent introduction to the physics of gyrotrons can be found in the monographs [4–6]. Their operation is based on the mechanism known as electron cyclotron maser instability which takes place when a synchronization condition for a resonance interaction between a hollow helical electron beam and a high-frequency field of a resonant cavity is fulfilled. The electrons of the beam gyrate in a strong magnetic field B with a cyclotron frequency https://www.w3.org/1998/Math/MathML"> Ω c = eB γ m 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> e and m0 being the charge and rest mass of an electron, γ is the relativistic Lorentz factor given by https://www.w3.org/1998/Math/MathML"> γ= ( 1− v ⊥ 2 + v z 2 c 2 ) −1/2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_420_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , where v⊥, vz , are the transverse and axial velocities of an electron, respectively, and c is the speed of light in vacuum. Due to the relativistic dependence of the cyclotron frequency, an initially uniform electron beam undergoes azimuthal bunching, since during the beam-wave interaction the accelerated electrons (with increased γ) rotate slowly and vice versa, the decelerated (with decreased γ) rotate faster. At a proper beam-wave synchronization, given by the following equations, the formed bunches slip to the deaccelerating phase of the high-frequency electromagnetic field where they radiate (transfer their energy associated with the transverse motion) through bremsstrahlung: https://www.w3.org/1998/Math/MathML"> ω=s Ω c + v z k z , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> ω 2 = c 2 ( k ⊥ 2 + k z 2 ), https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_3_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where ω is the circular frequency of the electromagnetic wave, s is the harmonic number of the cyclotron resonance, kz and k⊥ = https://www.w3.org/1998/Math/MathML"> v mp R cav https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_420_2_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> are the axial and the transverse wavenumber, respectively. Here Rcav is the cavity radius and νmp is the eigenvalue of the operating TEmp mode (p-th zero of the equation https://www.w3.org/1998/Math/MathML"> J m ′ (v)=0, J m ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003459675/fafc68b8-95ef-4abf-93d4-ddf80cebf367/content/math16_420_3_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> being a Bessel function of the first kind of order m). Therefore, the gyrotron operates at the intersection point of the beam line (16.2) and the dispersion curve (16.3) of the working mode. The gyrotron operation is characterized by a small Doppler shift (second term of (16.2)) and thus the frequency of radiation is close to the cyclotron frequency or its harmonics (ω ≈ sΩc). As already mentioned, since only the energy of the electrons associated with their transverse motion is available for the beam-wave interaction, the velocity ratio (pitch factor) g = v⊥ /vz must be greater than unity (typically 1.2–1.5). Such beams are being formed initially by a magnetron injection gun (MIG) and then in the rest of the electron-optical system (EOS) are “pumped” increasing the pitch factor in an adiabatically increasing magnetic field that reaches its maximum in the flat top region inside the cavity resonator.
