High gradient experiments with $X$-band cryogenic copper accelerating cavities

Vacuum radio-frequency (rf) breakdown is one of the major factors that limit operating accelerating gradients in rf particle accelerators. The occurrence of rf breakdowns was shown to be probabilistic, and can be characterized by a breakdown rate. Experiments with hard copper cavities showed that harder materials can reach larger accelerating gradients for the same breakdown rate. We study the effect of cavity material on rf breakdowns with short $X$-band standing wave accelerating structures. Here we report results from tests of a structure at cryogenic temperatures. At gradients greater than $150\mathrm{MV}/\mathrm{m}$ we observed a degradation in the intrinsic cavity quality factor, $Q_0$. This decrease in $Q_0$ is consistent with rf power being absorbed by field emission currents, and is accounted for in the determination of accelerating gradients. The structure was conditioned up to an accelerating gradient of $250\mathrm{MV}/\mathrm{m}$ at 45 K with $10^8$ rf pulses and a breakdown rate of $2\times {10}^{-4}/\mathrm{pulse}/\mathrm{m}$. For this breakdown rate, the cryogenic structure has the largest reported accelerating gradient. This improved performance over room temperatures structures supports the hypothesis that breakdown rate can be reduced by immobilizing crystal defects and decreasing thermally induced stresses.

Figure 1

Electric and magnetic fields for the cryogenic cavity. The fields are scaled to 3.46 MW dissipated in the cavity walls. $\mathrm{T}=45\mathrm{K}$ and $Q_0=30$, 263. (a) shows the surface electric fields, with a maximum $507\mathrm{MV}/\mathrm{m}$. (b) shows the surface magnetic fields, with a maximum $736\mathrm{kA}/\mathrm{m}$.

Figure 2

Electric and magnetic fields along the surface for the $X$-band cryogenic cavity, scaled to $250\mathrm{MV}/\mathrm{m}$ accelerating gradient in the middle cell.

Figure 3

(a) Solid model of the cryostat and (b) zoom in on Cryo-Cu-SLAC-#2 in same model. (1) Cold head of cryocooler; (2) current monitor; (3) brazed metal foil; (4) Cryo-Cu-SLAC-#2; (5) rf flange; (6) thermal shield; (7) Cu-plated stainless steel waveguide; (8) rf input.

Figure 4

Schematic diagram of the experimental setup: (1) Cryo-Cu-SLAC-#2; (2) ${\mathrm{TM}}_{01}$ mode launcher; (3) current monitors for field emission currents; (4) high power directional couplers; (5) waveguide 3 dB hybrid; (6) high power loads; (7) SLAC XL-5 X-band klystron; (8) variable attenuator; (9) booster traveling wave tube; (10) mixer for klystron signal shaping; (11) signal generator; (12) arbitrary function generator; (13) fast digitizer; (14) peak power meter; (15) probes of peak power meter; (16) mixer for data acquisition; (17) low pass filters; (18) signal generator for data acquisition; (19) cryostat envelope. Not numbered: cross guide directional couplers that couple signal between low pass filter (17) and probes (15) and (16) and low power rf loads which are connected to high power directional couplers (4) and cross guide directional couplers.

Figure 5

Photo of experimental setup: (1) WR90 waveguide towards the klystron; (2) pulse tube cooler; (3) helium lines; (4) WR90 directional couplers; (5) vacuum chamber of the cryostat; (6) ${\mathrm{TM}}_{01}$ mode launcher.

Figure 6

Measured and reconstructed rf and current monitor signals for an example rf pulse. The measured current will be a small percentage of the field emitted current inside the cavity, which we estimated to be on the order of .1–1% [70]. Measured signals are in purple and red. Results of the nonlinear model are in blue and results from a linear model are in green. $t_1$ and $t_2$ are defined as the section where the input rf power is decreased to a lower power level and the gradient is flat, which for this pulse is 150 ns long.

Figure 7

(a): Measured $|\mathrm{S}11|$ vs frequency and (b): measured on-axis electric fields for Cryo-Cu-SLAC-#2 both at room temperature.

Figure 8

Measured $Q_0$ versus temperature for the three modes of Cryo-Cu-SLAC-#2, and the design value for the $\pi$ mode.

Figure 9

The processing history for Cryo-Cu-SLAC-#2. (a): Black is the input flat steady-state power (average between $t_1$ and $t_2$ as defined in Fig. 6) and purple is the temperature. (b): Purple is the number of accumulated breakdowns. Black and red points are the calculated average gradient (average between $t_1$ to $t_2$). Red indicates the time period where BDR was measued and a zoom-in is shown in Fig. 10.

Figure 10

Purple is the accumulated breakdowns and black the calculated average accelerating gradient (average over $t_1$ to $t_2$) from the nonlinear model. This is a zoom in of Fig. 9 for the time period where the BDR was measured.

Figure 11

Breakdown rate vs gradient:(a): first, trigger rf breakdowns; (b): all rf breakdowns. For the breakdown probability $\sim {10}^{-4}/\mathrm{pulse}/\mathrm{m}$ cryogenic structure clearly outperforms record data from hard CuAg [36].