Brooke S. Stutzman

Loss of Magnetic Insulation in a Crossed-Field Diode: Ion and Collisional Effects

The effect of ion production through ionizing collisions in a magnetically insulated crossed-field gap is studied by using one-dimensional particle-in-cell software. These results are compared with the predictions from previous efforts that assumed immobile sheets of positive charge at different positions within the gap. Our results with mobile ions created via collisions indicate that the diode can lose magnetic insulation of the electron flow at ion densities lower than that predicted from the immobile ion case. Furthermore, we observe that electron scattering plays a significant role in this gap closure. This loss of insulation depends on the background pressure and leads to time-dependent migration of charge across the gap. We characterize both the time-scale and the degree of current transport for cases relevant to the high-power microwave community.

Conservation of energy analysis of collisional cross-field diffusion

Summary form only given. Cross-field diodes are instrumental in the operation of high-power microwave sources in relativistic magnetrons, magnetically insulated transmission lines for pulsed power systems, and Hull thrusters in space propulsion. These diodes are magnetically insulated in order to prevent electron migration across the gap. In spite of this insulation, many electrons still move towards the anode which leads to pulse shortening and/or excitation of undesired modes. It has previously been shown that the presence of ions in a crossed-field gap increases the electrons excursion toward the anode region. Further work has shown that both electron-electron scattering and ionization of the background species exacerbate this crossed-field migration. In this work, we show that an electron, once scattered or created through an ionizing collision, will move according to the Lorentz force equation and conservation of energy. Using a 1D PIC code we will show that these electrons scattered or created midgap have total energies greater than those injected at the cathode; thus, they are able to penetrate farther into the gap.

Electron excursion in a collisional cross-field diode

The operation of high-power microwave sources in relativistic magnetrons, magnetically insulated transmission lines for pulsed power systems, and Hull thrusters for space propulsion all rely on cross-field diodes. Electron migration from the cathode to the anode should be eliminated due to magnetic insulation, however, many electrons still transit the gap. This leads to the excitation of undesired modes and/or pulse shortening. Previous work has shown that not only does the presence of ions in a crossed-field gap increase the electron excursion toward the anode region1, but electron scattering and ionization of the background species exacerbate this crossed-field migration.2 We have also shown that the farther into the gap the scattering or ionization occurs, the greater the maximum excursion of the scattered or created electron.3 We also showed that above the excitation energy, there was no difference in gap penetration between elastically scattered electrons and those scattered through excitation.4 In this work, we will determine the scattering angles during elastic collisions from a 1D PIC code model of our diode (PDP15) and compare those to the average and median scattering angles calculated for a series of monoenergetic beams with energies comparable to those found in the PDP1 model. We will use these analytically determined scattering angles to predict the energy dependent change in the position of the guiding center during elastic scattering events and compare these data to the changes in guiding center found in our PDP1 data. For both the analytical model and the PDP1 data, we will determine an energy dependent electron diffusion rate from the change in the guiding center position and the collision frequency.

Electron excursion versus scattering mechanism in a cross-field diode

Summary form only given. The operation of high-power microwave sources in relativistic magnetrons, magnetically insulated transmission lines for pulsed power systems, and Hull thrusters for space propulsion all rely on cross-field diodes. Electron migration from the cathode to the anode should be eliminated due to magnetic insulation, however, many electrons still transit the gap. This leads to the excitation of undesired modes and/or pulse shortening. Previous work has shown that not only does the presence of ions in a crossed-field gap increase the electron excursion toward the anode region1, but electron scattering and ionization of the background species exacerbate this crossed-field migration.2 We have also shown that the farther into the gap the scattering or ionization occurs, the greater the maximum excursion of the scattered or created electron.3 In this work, we will break down the scattering problem further by looking at the scattering due to elastic collisions and excitation events separately. We will use a 1D PIC code4 to compare the electron excursions based on scattering mechanism and scattering site. We will further compare the collision type with the expected energy change due to the collision mechanism.

Deconstructing ionization and scattering effects in crossed-field diodes

The presence of plasma has long been suspected to be a major cause of gap closure in high power crossed-field diodes and HPM sources, even under the condition of magnetic insulation. Previous work [1] shows that the presence of fixed ions anywhere in the diode gap increases penetration of the electron hub height into the gap. Further work shows that [2] mobile ions exacerbate this effect causing gap closure on time scales comparable to desired pulse lengths. We use PIC simulations in an attempt to electrostatically decouple some of the basic physics of electron scattering and ionization in order to determine in which pressure regimes a particular hub-height expansion mechanism dominates.

Role of ions in a crossed-field diode II: Monte Carlo collisions

Summary form only given: The effect of ions in a magnetically insulated crossed-field gap is studied using a particle-in-cell simulation with Monte Carlo collisions (MCC). (Code available through the PTSG at UC Berkeley.) These results are compared with the predictions from single particle orbit, shear flow models and previous particle-in-cell simulations in which the ions were modeled as a sheet of charge fixed at different positions within the gap. The results of this experiment indicate that the diode loses insulation much more rapidly than shown in the immobile ion sheet model. The reasons for this increased rate of electron migration toward the anode are that the ions in this simulation are mobile and that the effects of MCC are being taken into account. Thus, ambipolar transport plays a role in the migration as does the fact that ions are being created throughout the gap by collisions. The implications of these findings, as suggested in previous work, are that of pulse shortening in relativistic magnetrons and bipolar flows in pulsed power systems.