The magnetron “threshold voltage” revisited

Abstract

In view of the revival of interest in high-power magnetrons, an important magnetron parameter called the threshold voltage has been rederived for both relativistic and nonrelativistic cases using a novel and simplified approach. The main purpose of the paper is to investigate the physical significance of the threshold voltage and to show that, contrary to a long established opinion, no restriction on the amplitude of oscillations is required. In fact, the name itself is a misnomer, since in practice the threshold voltage is an approximate dc anode voltage at which the tube operates when delivering full power. It is this feature which, in our opinion, makes the threshold voltage so important and useful in practice. A set of numerical computations confirms our analysis and also reveals a form of Lorenz’s “butterfly effect” associated with the perceived start of oscillations.

Application of metamaterials in spatial harmonic magnetrons

“…Since -atApm determines the RF component of the magnetic field which its effect is negligible in comparison with the effect of the RF electric field [4], this term is neglected and therefore Pe is simplified to (4) According to (4), the synchronous harmonic of the cp directed electric field (ECPm) plays the most important role in the interaction process. The analysis of [5] also confirms this result. In SHMs, due to the localization of the synchronous harmonic (m=-l also called first backward harmonic) of the <p directed electric field to the region near the anode surface, an effective interaction of the electrons and the electric field occurs only in this area, therefore (4) can be further simplified to Pe = eQ,mraEIfI-1 (ra,cp) (5) E<p_l (ra' qJ) is proportional to the amplitude of the first backward harmonic of E<p denoted by A-I' Therefore…”

“…The analysis of [5] also confirms this result. In SHMs, due to the localization of the synchronous harmonic (m=-l also called first backward harmonic) of the <p directed electric field to the region near the anode surface, an effective interaction of the electrons and the electric field occurs only in this area, therefore (4) can be further simplified to Pe = eQ,mraEIfI-1 (ra,cp) (5) E<p_l (ra' qJ) is proportional to the amplitude of the first backward harmonic of E<p denoted by A-I' Therefore…”

Three-Dimensional Particle-in-Cell Simulation of 10-Vane Strapped Magnetron Oscillator

“…The Buneman-Hartree voltage is written as . Here, is the radius of anode, is the radius of cathode, is the angular velocity, and is the cyclotron angular velocity [20]. The calculated operating point is marked at the beam voltage of 4.3 kV and the external axial magnetic field of 0.19 T as shown in Fig.…”

70% Efficient Relativistic Magnetron With Axial Extraction of Radiation Through a Horn Antenna

“…The relation (14) is for a planar magnetron; however, as noted in [28], the characteristics of cylindrical magnetrons with r a /r c < 2.273 differ very little from the planar characteristics, and the difference can be ignored for most practical purposes.…”