Rapid kinematic bunching and parametric instability in a crossed-field gap with a periodic magnetic field

Abstract

Single particle orbit considerations show that the cycloidal orbits of electrons in a gap with crossed electric and magnetic fields lead to rapid spoke formation if the external magnetic field has a periodic variation. This spoke formation is primarily a result of kinematic bunching, which is independent of the radio frequency electric field and of the space charge field. A parametric instability in the orbits, which brings a fraction of the electrons from the cathode to the anode region, is discovered. These results are examined in light of the recent rapid startup, low noise magnetron experiments and simulations that employed periodic, azimuthal perturbations in the axial magnetic field.

Relativistic Magnetron Priming Experiments and Theory

“…[9,11 ] By first studying the nonreiativistic, thermionic magnetron, we discover a parametric instability in the electron orbits which provide instantaneous creation of the electron spokes, even before the rf mode is excited. [12] This is a very important discovery, because even in the MAGIC simulations, startup is a major issue.…”

Increased efficiency and faster turn-on in magnetrons using the transparent cathode

“…This realization of magnetic priming differs from that described in [13], where magnetic priming is implemented through the azimuthal perturbation of the externally applied axial magnetic field H 0z with permanent magnets, mounted externally around the magnetron. Here the periodic, azimuthal magnetic field, leads to a periodic total tangential magnetic field H(θ) = H 0z 2 + H θ 2 (θ) that gives the same kinematic effect on motion of the electron hub with azimuthal drift velocity € v eθ = c E 0 H 0z H 2 as in [13] ( € E 0 is the dc electric field of the applied voltage and c is the speed of light).…”

“…Here the periodic, azimuthal magnetic field, leads to a periodic total tangential magnetic field H(θ) = H 0z 2 + H θ 2 (θ) that gives the same kinematic effect on motion of the electron hub with azimuthal drift velocity € v eθ = c E 0 H 0z H 2 as in [13] ( € E 0 is the dc electric field of the applied voltage and c is the speed of light). Thirdly, due to the concentration of the dc electric field on the emitters this electric field is also a periodic perturbation.…”

Magnetic Priming of a Relativistic Magnetron

“…This technique introduces systematic azimuthal variations in the axial magnetic field of the magnetron. Following the experimental discovery of magnetic priming, simulation and analytical work by Neculaes et al [49] showed that cycloidal orbits of electrons in a gap with crossed electric and magnetic fields, such as a magnetron, lead to rapid spoke formation if the external magnetic field has periodic variations. This rapid spoke formation is due in part to kinematic bunching caused by a parametric instability in the electron orbits in the periodically perturbed magnetic field [50].…”