Abstract
We develop an analytical model for the vacuum electric breakdown rate dependence on an external electric field, observed in test components for the compact linear collider concept. The model is based on a thermodynamic consideration of the effect of an external electric field on the formation enthalpy of defects. Although strictly speaking only valid for electric fields, the model also reproduces very well the breakdown rate of a wide range of radio-frequency breakdown experimental data. We further show that the fitting parameter in the model can be interpreted to be the relaxation volume of dislocation loops in materials. The values obtained for the volume are consistent with dislocation loops with radii of a few tens of nanometers.
Highlights
The development of high-gradient radio-frequency linear collider accelerating structures is strongly limited by vacuum microwave breakdown [1,2,3,4,5,6,7,8,9]
We develop a physically motivated model for the breakdown rate observed in dc conditions
In terms of using electric field, it is important to note that breakdown rate data is frequently provided as a function of the accelerating gradient Eacc rather than the surface electric field E used in the model
Summary
The development of high-gradient radio-frequency (rf) linear collider accelerating structures is strongly limited by vacuum microwave breakdown [1,2,3,4,5,6,7,8,9]. The concept ‘‘vacuum microwave breakdown’’ means in this context that the high electromagnetic field causes first electron and ion emission to the vacuum, building up a plasma that makes the vacuum conductive This is known as vacuum arcing [10]. The breakdowns have been observed in components fabricated from a wide range of metals, such as Al, Ti, Cu, and Mo. Vacuum electric breakdown is often studied under static or slowly varying electric fields in so-called ‘‘direct current’’ (dc) setups [16,17,18,19]. Grudiev et al [8] have shown that the observed breakdown rate in rf structures can be fitted well by power law functions of the form RBD 1⁄4 aEx, where E is the accelerating gradient. Our model reproduces a wide range of literature data organized as RBDðEaccÞ with the comparable quality of the fit as using the power law in [8], under both dc and rf conditions
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