The effect of pinch dynamics on the x-ray emission from self-magnetically pinched diodes

The charged-particle dynamics in self-magnetically pinched diodes are examined with the particle-in-cell code LSP. It is shown that the self-electric and magnetic fields determine the electron angles of incidence on the target which, in turn, determine the angular distribution of the emitted X-rays. At low voltages and currents, the self-magnetic field is negligible and the electron flow is space-charge limited (SCL). Electrons trajectories follow electric field lines and are laminar during this phase. Furthermore, during the SCL phase electrons strike the anode over a relatively large area with an average angle-of-incidence that decreases from about 30° to about S° as the current increases and the self-magnetic field begins to compress and straighten the electron orbits as they strike the anode target. As the voltage and current increase, electron orbits begin to cross and the electron flow moves into a weakly-pinched (WP) regime where a portion of the beam is no longer laminar. In the WP regime, the electron orbit crossings cause the average angle of incidence to rapidly increase from S° to 40° as the beam begins to become more concentrated on an increasingly smaller area of the anode. As the voltage and current increase further, the electron flow moves into the magnetically-limited (ML) regime where the beam is strongly pinched into a small area of the anode target and the electron orbits are non-laminar across the entire beam. The electron flow in the ML regime is unstable and is accompanied by high-frequency, large-amplitude oscillations in the diode voltage and current. As a result of the instability, the electron energy distribution on the anode target in the ML regime changes from a mono-energetic distribution at the applied voltage that is characteristic of the SCL and WP regimes to a distribution that is peaked slightly lower than the applied voltage with a 25 % FWHM energy spread. In addition, the turbulent mixing of the electron orbits causes the average electron angle-of-incidence on the anode target to abruptly drop from 40° to 30° at the onset of the instability. The electron orbits and angular distribution on the anode target remain relatively unchanged as the diode voltage and current increase well into the ML regime.