Erratum to: Electromigration occurences and its effects on metallic surfaces submitted to high electromagnetic field: A novel approach to breakdown in accelerators

We regret to inform you that the: Electromigration occurences and its effects on metallic surfaces submitted to high electromagnetic field: A novel approach to breakdown in accelerators which is found in the issue 665C (pp 54–69) is an incorrect version. The correct version is the following: The application of a high electrical field on metallic surfaces leads to the well described phenomena of breakdown. In the classical scenario, explosive electron emission (EEE), breakdown (BD) originates from an emitting site (surface protrusion): the current at the apex vaporizes the emitting tip and the emitting current triggers a plasma in the vapor close to the surface. The plasma in turn melts the emitting site and makes it (hopefully) disappear. The conditioning process consists of “burning” the emitting sites one after another and numerous observations exhibit surfaces covered with molten craters that more or less overlap. In the case of radiofrequency (RF) applied fields, the effects of fatigue are also considered due to the cyclic nature of the applied stress. Nevertheless when dealing with RF cavities for accelerators, where higher fields are now sought, one can legitimately wonder if other physical phenomena should also be taken into account. In particular, we believe that electromigration, especially at surfaces or grain boundaries cannot be neglected anymore at high field (i.e. 50–100 MV/m). Many publications in the domain of liquid metal emission sources show that very stable and strong emission sources, either ions or electrons, build up on metallic surfaces submitted to electrical fields through a mechanism that is slightly different from the usual localized breakdown evoked in accelerators. This mechanism involves the combination of electromigration and collective motion of surface atoms. In the case of emission source, this effect is sought after and has been extensively studied, whereas in our case it is very detrimental to the possibility of reaching high fields. The recent results obtained on 30 GHz Compact Linear Collider (CLIC) accelerating structures, altogether with the data exposed hereafter have led us to propose a complementary scenario, which could explain early melting of large areas of the surface. In this paper we will concentrate on the early stages of breakdown, before plasma apparition. We will not discuss the plasma spot formation at the surface as we consider it to be the next step into the formation of the vacuum arc. We have gathered from the literature several examples of the physical phenomena involved on metallic surfaces submitted to very high fields. Definition of well-known concepts and terms used in other research fields will be introduced, like electrosprays, capillary waves, etc. while some others have been left aside; not because they were irrelevant but because they would have requested extensive development, which in turn would make this paper heavier. Because these concepts are, in a given community, well known a lot can be found using your favorite search engine and such without having to download the extensive bibliography cited in this paper. In the introduction ( Section 1 ), we describe some of the damage that has been observed in CLIC accelerating structures, which led us to suspect that electromigration is involved. We will present an alternative possible scenario for explosive breakdown (BD), which can result into the melting of extended area. In Section 2 we will present RF simulations, which show that pulse heating cannot be accountable for the observed melting. In Section 3 we will describe what electromigration is and how it can lead to the appearance of nanotip and/or surface pre-melting. We will give several example of the occurrence of electromigration in several different experimental situations and we will try to evaluate some figures of merit. In particular we will show that electromigration is liable to occur at room temperature at fields close to 100 MV/m. We will also discuss other surface mechanisms that could also interfere with the breakdown mechanism. A general discussion will be given in Section 4 and the conclusion in Section 5 . We hope to provide a new angle of observation that could help the accelerators community to better understand, and possibly overcome, the observed experimental limitation. Although it is very difficult to provide an evaluation of the relative weight of each phenomenon: electromigration, material type, surface state, plasma formation, we strongly think that the electromigration role needs to be explored.