472 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 3, JUNE 2000 Microwave Magnetic Field Effects on High-Power Microwave Window Breakdown David Hemmert, Andreas A. Neuber, Member, IEEE, James Dickens, Member, IEEE, Hermann Krompholz, Senior Member, IEEE, L. L. Hatfield, Member, IEEE, and Magne Kristiansen, Life Fellow, IEEE Abstract—Microwave window breakdown in vacuum is investi- gated for an idealized geometry, where a dielectric slab is located in the center of a rectangular waveguide with its normal parallel to the microwave direction of propagation. An S-band resonant ring with a frequency of 2.85 GHz and a power of 60 MW is used. With field enhancement tips at the edges of the dielectric slab, the threshold power for breakdown is observed to be dependent on the direction of the microwaves; i.e., it is approximately 20% higher for the downstream side of the slab than it is for the upstream side. Simple trajectory calculations of secondary electrons in an RF field show a significant forward motion of electrons parallel to the direc- tion of microwave propagation. Electrons participating in a satu- rated secondary avalanche on the upstream side are driven into the surface, and electrons on the downstream side are driven off the surface, because of the influence of the microwave magnetic field. In agreement with the standard model of dielectric surface flashover for dc conditions (saturated avalanche and electron-in- duced outgassing), the corresponding change in the surface charge density is expected to be proportional to the applied breakdown threshold electric field parallel to the surface. Index Terms—Dielectric breakdown, electron emission, mag- netic field effects, magnetic insulation, microwave devices. I. INTRODUCTION D IELECTRIC breakdown on high-power microwave (HPM) interfaces represents a critical limit for the operation of HPM devices. Theoretical aspects of initiation mechanisms for dielectric breakdown involving RF electric fields and external magnetic fields center around the multi- pactor and have been summarized in [1] and [2]. Previous experimental studies using high-speed diagnostics of the break- down phenomena [3], [4] revealed similarities to dc-flashover, i.e., a sequence of field emission of electrons, saturated sec- ondary electron surface avalanche [5], and electron-induced outgassing [6]. Additionally, previous experimental studies on dc (or unipolar) flashover found that an externally applied magnetic field can alter the electric field strength at breakdown [7]. Experimental investigations of the X-ray emission in HPM dielectric breakdown point to the importance of high-energy (several kiloelectronvolts) electrons initiating breakdown [4]. For these electrons, the force from the microwave magnetic field plays a major role in determining the electron trajectories Manuscript received September 3, 1999; revised December 16, 1999. This work was supported by the High Energy Microwave Device MURI Program, funded by the Director of Defense Research and Engineering and managed by the Air Force Office of Scientific Research. The authors are with the Department of Electrical Engineering and Physics, Texas Tech University, Pulsed Power Laboratory, Lubbock, TX 79409 USA (e-mail: dhemmert@ppl.ee.ttu.edu). Publisher Item Identifier S 0093-3813(00)05370-4. Fig. 1. Schematic of a planar dielectric normal to the direction of the microwaves with a positive charge buildup on the upstram surface of the dielectric/microwave interface. The RF electric and magnetic fields of the microwaves are indicated in addition to the dc electric field resulting from the dieletric surface charge [3]. and the build-up of the saturated avalanche. The experimental manifestation of this magnetic field influence is evident in the differences between “upstream” breakdown (propagation direc- tion of the microwaves into the surface) and “downstream”-case (propagation direction away from the surface). II. MODELING OF MAGNETIC FIELD EFFECTS Results of trajectory calculations, including the effects of the microwave magnetic field have been presented in [3] and are briefly summarized here. A basic planar geometry is considered for the following discussion. Fig. 1 shows the schematic for a planar dielectric normal to the microwave power flow. A posi- tive surface charge on the dielectric surface is included, resulting in an electric field, , near the surface. The following calcu- lations used a microwave electric field amplitude of 30 kV/cm (equivalent power density of W cm ), and a secondary crossover energy (energy at which the secondary emission co- efficient is unity) of 29.7 eV. Fig. 2 shows the -displacement ( is the principal direction of the microwave electric field, TE -mode), the impact energy, and the return time of individual secondary electrons with dif- ferent emission phases. Here, a constant electric field above the surface in -direction was assumed, and its magnitude was de- termined by the requirement that the phase-averaged impact en- ergy was 29.7 eV. More refined calculations use a distributed electron density above the surface, which was determined by multiple iterations in a self-consistent way. Fig. 3 shows the corresponding -dis- placements, return-times, and impact energies for this case. The 0093–3813/00$10.00 © 2000 IEEE