Time-dependent Behaviour of Gas Ejected from an Accelerating Structure after a Discharge

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A discharge or RF-breakdown event in a CLIC acceleration structure causes the localized release of gas molecules in- sideathinconductionlimitedsystemwithdistributedpump- ing. We discuss the transient behavior of such a system in the molecularflow regime that allows an analytical solution with the helpof Greensfunctions. Theydescribethe tempo- ralevolutionofthegasdensityandthegasflowejectedfrom the ends of thin pipes of finite length. Distributed pumping, for example through the HOM damping slits is taken into account. INTRODUCTION AND MODEL We calculate the temporal evolution of the gas density following a spontaneous injection of a known amount of gas in a thin pipe with or without distributed pumping. Ex- amples of such systems are radio-frequency structures for linear accelerators that experience a discharge due to high power levels. Below we show that the pressure distribution inside the pipe as well as the amount of gas ejected from the end of the pipe as a function of time can be calculated analytically. This allows to estimate the behavior of such a system without computer simulations and might be use- ful in debugging numerical codes or calibrating hardware such as pumps. We assume that only a reasonably small amount of gas is desorbed at each particular event such that we can assume to operate in the molecular flow regime un- der isothermal conditions. In this case there is no interac- tion among gas molecules and that the interactions with the walls of the vacuum vessel can be described by diffuse scat- tering. Under these conditions the time dependent pressure profile P(z; t) along a conduction limited pipe of length l with 0< z< l obeys the following partial differential equa- tion (1) v ∂