Radiophysics and Quantum Electronics, Vol. 50, No. 2, 2007 INFLUENCE OF AN EXTERNAL MAGNETIC FIELD ON THE THRESHOLD OF MULTIPACTOR ONSET ON A DIELECTRIC SURFACE N. K. Vdovicheva, A. G. Sazontov, and V. A. Sazontov ∗ UDC 537.521.7+621.385.6 In this paper, we propose a theoretical model of the initial stage of development of a one-sided secondary-emission (multipactor) discharge on a dielectric surface. Consideration is based on a statistical method supported by an exact analytical solution for the transit-time distribution function of secondary electrons. The general integral equation allowing us to determine the stationary emission-phase distribution functions and the threshold of multiplicator onset in the presence of an external magnetic field is formulated. It is shown that the presence of an external magnetic field can significantly change the conditions of multipactor onset. It is found that the discharge-zone boundaries calculated within the framework of a statistical model are in qualitative agreement with the results obtained by the Monte-Carlo method. 1. INTRODUCTION In the last decade, significant attention has been paid to the problem of appearance of a multipactor discharge on the dielectric surface. First, it is related to the necessity of solving an important practical problem of the microwave radiation output from the vacuum gap of a microwave device or the radiation input from the atmosphere to the corresponding gap. The fact is that a radio-transparent window made of dielectric material is the key element of the output and input systems. Specific vacuum discharge due to the processes of the secondary electron emission, which is developed on the window surface, destructs the window (see, e.g., [1–4]) and eventually is a significant cause impeding the creation of high-power microwave sources. Theoretically, analysis of such a discharge is reduced to a study of dynamics of the electrons under the combined action of an alternating electric field parallel to the dielectric surface and a static electric field normal to the dielectric surface (the latter returns electrons to the initial emitting plane). In this respect, we note that the conditions of multipactor onset on the dielectric surface were studied mainly numerically by the Monte-Carlo method [5–9], except for work [10] presenting an analytical solution of the problem, which allows one to determine the regions of existence of the multipactor discharge in the absence of an external magnetic field. It seems important to generalize the results obtained in [10] to the case where an external magnetic field is present. The latter is necessary for developing the system of input of the high-power radiation to the magnetic confinement plasma device. In this paper, we develop a statistical theory of the initial stage of development of a one-sided multipactor discharge on the dielectric surface. Such a theory permits one to calculate systematically the discharge threshold in the presence of an external magnetic field. To interpret the obtained results (where possible), approximate analytical estimates of the discharge boundaries are presented. * vladimir.sazontov@gmail.com Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 2, pp. 118–133, February 2007. Original article submitted July 3, 2006; accepted December 8, 2006. 108 0033-8443/07/5002-0108 c  2007 Springer Science+Business Media, Inc.