# Design Criteria for High-Gradient Radio-Frequency Linacs
## 3 RF Breakdown
### Material Studies
#### 3.6.1 Hard Metals  
After I realized that there is a correlation between the peak pulse surface heating and the breakdown rate [31], a twofold program was initiated, one dedicated to the study of pulse heating damage [54] and the other one to study the breakdown performance of hard, non-heat-treated copper alloys [74], including CuZr, CuCr, CuAg, and copper of high 6N and 7N purity. To do this, we built a vacuum vessel in which we could high-power test cavities constructed of bolted-together cells. One such structure is shown during its assembly in Figure 6. Of all these experiments, cavities built from hard copper and hard copper-silver showed the largest improvement, and cavities made out of hard CuAg have the best performance outmatched only by cryogenic cooper.  
I show the results of the high-power test of a hard copper cavity in Figure 7a. A hard copper cavity with a beam aperture radius of 2.75 mm had an order of magnitude lower rf breakdown rate at a gradient of 175 MV/m than a cavity of the same shape joined by means of high-temperature brazing.  
Figure 5: Breakdown probability plots for three SW cavities with different \(P_{max}/Max(H^{2})\)[79]. The cavities are fed with a shaped rf pulse with 200 ns flat top and \(\sim\)170 ns charging time. Breakdown rate is vs. (**a**) accelerating gradient; (**b**) pulse heating; (**c**) pulse heating multiplied by \(P_{max}/Max(H^{2})\). Aperture radius is 3.75 mm and \(a/\lambda=0.143\) for all three structures.  
Figure 6: RF breakdown tests of hard copper structures [74;79]: vacuum can with the clamped structure during assembly.  
I used the same bolted-together setup to conduct experiments with cavities made of hard CuAg alloys. Compared to both soft copper cavities and even hard copper cavities, the CuAg structures demonstrated lower rf breakdown rates and faster processing. As shown in Figure 7b, a hard CuAg cavity had a breakdown rate below \(10^{-3}\) per pulse per meter at a gradient of 200 MV/m [80]. I note that there is overwhelming experimental evidence that a particular cell clamping method has a decisive effect on high-power test results. It is often overlooked that metal-to-metal contact alone produces poor results [81].  
One method to build an accelerating cavity without exposing it to high temperatures is electroforming, where metal is deposited on a precision-machined aluminum mandrel using an electrochemical process. Then the mandrel is removed by chemical etching. Experimental data obtained from high-power testing of electroplated and electroformed cavities were published in [82; 83]. In a recent experiment, a nickel cavity was electroformed, while the surface exposed to rf fields was plated with a thin layer of gold. The measured rf breakdown rates for these cavities were the same or higher than those for soft copper cavities. Although electroformed cavities have not outperformed soft copper ones, this fabrication method has great potential for the economic mass production of precision components of the accelerating structures.  
Simultaneously with these experiments, cell-joining technologies are being developed and tested that allow the fabrication of practical accelerating structures without high-temperature brazing or diffusion bonding [84; 85; 86; 87; 88; 89; 32; 82; 84; 85; 82; 86; 87; 88; 89].