Influence of Electron Velocity Spreads on the Operation of a 263 Ghz Gyro-Twa with a Helically Corrugated Interaction Circuit

Gyrotron traveling wave amplifiers (gyro-TWAs) are widely utilized for broadband, high-power applications such as dynamic nuclear polarization (DNP), Earth-orbit radar, and communications. These vacuum electron devices operate by transferring a portion of the electron beam's perpendicular energy to an electromagnetic wave. For this to occur, the phase velocity of the electromagnetic wave has to be similar to the axial velocity of the electron. Traditionally, the interaction between the electron beam and the wave occurs in an ordinary cylindrical waveguide. This configuration restricts the achievable bandwidth to just a few percent. To overcome this limitation and enhance bandwidth, alternative interaction circuits are used. One such design is the helically corrugated interaction region <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${ }^{1}$</tex> (HCIR), which incorporates helical corrugations along the wave propagation direction. The radius of the HCIR is described by the equation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r(\theta, z)=r_{0}+r_{1} \cos \left(m_{\mathrm{B}} \theta+2 \pi z / d\right)$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r_{0}$</tex> is the mean radius, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r_{1}$</tex> the corrugation depth, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex> the axial corrugation period. The parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m_{\mathrm{B}}$</tex> defines the number of azimuthal perturbations and is set to 3 in this case to enable coupling between the oppositely rotating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{TE}_{-11}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{TE}_{21}$</tex> circular waveguide modes. Non-idealities, like manufacturing tolerances, inhomogeneities of electric and magnetic fields close to the emitter, and foremost, the surface roughness of the electron emitter itself, result in a non-ideal electron beam. Instead of uniform axial and transversal velocities of all electrons, the individual electrons in the beam possess Gaussian-distributed velocities, which can be quantified by standard deviation, so-called velocity spreads.