For some years the Muon Collaboration - a group of particle and accelerator physicists from the US, Europe and Japan interested in neutrino factories and muon colliders - has been looking at the problems associated with operating high-gradient radiofrequency (RF) cavities at low frequencies (~200 MHz). In addition there has recently been considerable progress in the development of high-frequency, high-gradient cavities for linear colliders. So in order to review the common problems, whilst also aiming to communicate with the materials-science community, the idea of a workshop on high-gradient RF at Argonne National Laboratory began to form. Although we initially expected about 40 participants, almost 90 attended on 7-9 October 2003. The aim of the workshop was to try to identify the effects limiting gradients in a wide variety of different applications, and to connect these with the properties of the materials involved. Although most of the research in achieving high gradients in RF cavities has been in support of linear-collider proposals, similar challenges exist for klystrons and photoinjectors, and, more recently, the low-frequency cavities required for muon cooling.

While much of the discussion at the workshop concerned copper cavities, talks from KEK and DESY outlined the state of the art for superconducting RF. These talks implied that RF cavity surfaces could be made good enough to avoid breakdown processes, but that the procedures involved were expensive and the applicability to normal cavities was not always clear, as breakdown events seem to be produced from clean, smooth surfaces.

In a later session, measurements of direct current (DC) breakdown from Cornell, which resulted in "starbursts" identical to those seen in superconducting RF cavities, were shown. These events seem to connect the phenomena seen in DC, normal conducting and superconducting RF. There were also presentations of new data from Argonne on dielectric acceleration structures, and theoretical discussions on multipactoring in these structures.

Most of the workshop, however, was devoted to summaries of results from groups working on linear-collider development. The CLIC team from CERN reported the results of studies of refractory materials (molybdenum, tungsten), which seem to be able to survive higher fields than the copper usually used, but require much longer to condition (CERN Courier March 2003 p6). They also reported the frequency and temperature dependence of breakdown, showing data indicating that these two parameters do not have a strong effect.

Participants from SLAC and KEK described the efforts being made for the Next Linear Collider (NLC) and Global Linear Collider (GLC) projects, respectively, to develop 11.4 GHz structures (figure 1) that operate stably at 65 MV/m with 400 ns pulses. Although the performance of these structures is approaching that required for a linear collider, the gradient limits are not fully understood. One limitation that has been overcome is thought to originate from pulse heating at the sharp-edged waveguide openings to the coupler cells. Pulse temperature increases above 100 °C appear to cause stress-related fracturing of the copper surface, which leads to breakdown. Rounding these edges to reduce the high peak magnetic fields that enhance the pulse heating has eliminated these events. Other breakdown mechanisms have been more elusive. In general the breakdown rate is seen to depend strongly on surface field for a given structure design, while breakdown-related damage appears to depend on the RF power level, independent of the design. At high power this damage leads to breakdowns on subsequent pulses (so-called "spitfests"), preventing further increases in gradient. For the three generations of structure designs that have been evaluated, this mechanism has limited input power levels to 60-80 MW, while the surface fields at this limit have varied by almost a factor of two (110 MV/m to 195 MV/m). The structure design efforts have therefore focused on reducing the input power for a given gradient, which is difficult due to efficiency and wakefield constraints.

KEK also reported on methods of surface treatment for the new S- and C-band accelerator structures they are building. The relative merits of diamond turning, chemical etching, electropolishing, vacuum baking, hydrogen baking and water rinsing are being systematically studied as part of their programme to upgrade the injector linac. A new method of smoothing, almost to the level of single atoms, was proposed by Epion Corporation. Gas-cluster ion beams (for example argon clusters at kilovolt energies) can produce very smooth surfaces on a variety of materials, with respectable erosion rates and coverage.

The Muon Collaboration reported on recent measurements in Lab G at Fermilab, which showed much new detail on dark-current production, as well as plans for the development of 201 MHz cavities, which are required by the Muon Ionization Cooling Experiment. In addition new data on high gradients in high-pressure cavities was presented by Muons Inc - a small business that was set up to perform R&D for muon cooling. A unique feature of this facility is the ability to produce very high magnetic fields in a variety of geometries.

Talks on modelling breakdown, from SLAC, Cornell and Argonne, looked at the process from a variety of directions. The most complete description of the development of RF breakdown events, which relies on an artificial injection of ions to get the process started, is a model that has been under development at Cornell for some time. Perry Wilson from SLAC summarized the many different mechanisms that have been shown to be involved in breakdown. Plasmas have been seen in many cavities and DC structures, and dark currents are known to be present at some levels in high-gradient cavities. Surface treatments affect the behaviour of the cavities, at least until the by-products of previous breakdown events dominate the surface, and surface heating due to wall currents and perhaps dark currents is known to contribute. In addition the plasma physics of ions, atoms and surfaces in high, rapidly changing electric fields is quite complex.

It seems that while many applications are limited by the same mechanisms, these mechanisms are not well understood. The designs for the SLAC/KEK 11.4 GHz NLC, CERN's 30 GHz CLIC linac and the Muon Collaboration's 805 and 200 MHz cavities seem to be affected by breakdown at operating fields consistent with the production, by field enhancements, of local surface electric fields of 5-10 GV/m. In addition to this mechanism, a separate failure mode connected with the local current density in the walls can occur - the phenomenon known as pulse heating. While breakdown in lower frequency cavities seems to be dominated by the high electric fields, pulse heating is more of a concern at higher frequencies.

There was considerable interest in isolating a "breakdown trigger". In a session on modelling, there seemed to be some agreement that the missing element was a mechanism that would propel large numbers of atoms and ions into the volume of the cavity, to mix with the field-emitted electrons that are known to be there already.

Work at Argonne over the past year has been aimed at identifying the breakdown trigger(s). Detailed measurements on dark currents at Fermilab have shown local fields of around 10 GV/m at emitters. Such fields can produce tensile stresses close to the tensile strength of copper, where fragments could break off and fly into the cavity. Also, some preliminary but very photogenic modelling of field evaporation (figure 2), seems to show that large fluxes of single atoms, ions and clusters could be injected into the cavity volume at the appropriate electric field and temperature. The effects of grain boundaries and defects also seem to be important (figure 3). At the high current densities present in high-frequency cavities, the resistivity of defects would produce very high local ohmic heating densities (and electric fields) in the surface of the material.

The surfaces that exist in cavities are complex, both structurally and chemically, and not completely understood, so continued effort will be required to progress further. Although the priorities are not entirely clear, it seems as if a variety of material-science measurements could begin to provide useful information on how some of the proposed trigger mechanisms for breakdown might actually work. There was some talk about the measurements that should be made and who might be involved in them. There was also discussion of the scope of current experimental and theoretical programmes that are aimed at improving cavity performance.

While a complete description or explanation of breakdown remains to be found, the workshop began to show how processes at surfaces and surface properties could influence the phenomenon. Ultimately, the relevant question is how much control is it possible to have over breakdown, and the answer will require some aggressive multidisciplinary research and development.

Further reading

Talks from the workshop are available at www.hep.anl.gov/RF.