rf breakdown measurements in electron beam driven 200 GHz copper and copper-silver accelerating structures

This paper explores the physics of vacuum rf breakdowns in subterahertz high-gradient traveling-wave accelerating structures. We present the experimental results of rf tests of 200 GHz metallic accelerating structures, made of copper and copper-silver. These experiments were carried out at the Facility for Advanced Accelerator Experimental Tests (FACET) at the SLAC National Accelerator Laboratory. The rf fields were excited by the FACET ultrarelativistic electron beam. The traveling-wave structure is an open geometry, 10 cm long, composed of two halves separated by a gap. The rf frequency of the fundamental accelerating mode depends on the gap size and can be changed from 160 to 235 GHz. When the beam travels off axis, a deflecting field is induced in addition to the longitudinal field. We measure the deflecting forces by observing the displacement of the electron bunch and use this measurement to verify the expected accelerating gradient. Furthermore, we present the first quantitative measurement of rf breakdown rates in 200 GHz metallic accelerating structures. The breakdown rate of the copper structure is ${10}^{-2}$ per pulse, with a peak surface electric field of $500\mathrm{MV}/\mathrm{m}$ and a rf pulse length of 0.3 ns, which at a relatively large gap of 1.5 mm, or one wavelength, corresponds to an accelerating gradient of $56\mathrm{MV}/\mathrm{m}$. For the same breakdown rate, the copper-silver structure has a peak electric field of $320\mathrm{MV}/\mathrm{m}$ at a pulse length of 0.5 ns. For a gap of 1.1 mm, or 0.74 wavelengths, this corresponds to an accelerating gradient of $50\mathrm{MV}/\mathrm{m}$.

Figure 1

Solid model of the output section of the 200 GHz traveling-wave accelerating structure (a), picture of one-half of the Cu-Ag structure (b), and picture of the output section of the structure (c).

Figure 2

Geometry of one-quarter of the vacuum part of the regular cell (a) and of the rf power coupler of the structure (b).

Figure 3

Coupler reflection (a) and power transmission (b) as a function of the gap aperture, calculated with the coupler matched at the 0.3 mm gap.

Figure 4

Output rf power signals generated by a 3.2 nC bunch of $50\mu \mathrm{m}$, without coupler reflections (a) and taking into account the coupler reflection (b). The pulse rf durations depends on the group velocity, structure length, and attenuation.

Figure 5

Plot of the synchronous frequency (a), group velocity (b), accelerating and peak electric field of the fundamental mode (without considering the coupler reflections) (c), pulse length (d), peak power traveling along the cells and power exiting from the waveguides considering the coupler reflection (e), and pulse energy with and without considering the coupler reflection (f). The electron beam is in the central axis; by opening the gap, the field is reduced because the interaction decays. The bunch charge is 3.2 nC, and ${\sigma }_z=50\mu \mathrm{m}$.

Figure 6

Temperature variation in a cell, generated by a 3.2 nC bunch of $50\mu \mathrm{m}$, without taking into account the coupler reflections (a) and surface peak magnetic field as a function of the time (b).

Figure 7

Derivation of equivalent pulse lengths for $\mathrm{gap}=0.9\mathrm{mm}$, a field generated by a 3.2 nC bunch of $50\mu \mathrm{m}$ (without taking into account the coupler reflections). (a) The blue plot is the power pulse generated by the electron beam in the regular cell of the structure. The corresponding pulsed surface heating is the magenta plot, that reaches 67 K of peak pulsed heating. The black pulse is the equivalent square pulse “in temperature,” with pulse length ${\tau }_T$, which produces the same peak pulsed heating as the beam-generated rf pulse. Note that ${\tau }_T$ is calculated under the constraint that the blue and black rf pulses have the same max power (at $t=0$). The red plot is the pulsed heating generated by the square pulse. (b) The blue plot is the power pulse generated by the electron beam in the regular cell of the structure. The black pulse is the equivalent square pulse “in energy,” with pulse length ${\tau }_W$, which has the same pulse energy and same max power (at $t=0$) as the blue. The red plot is used to illustrate the power decay time ${\tau }_D$: it is the ordinate intercept of a line tangent at $t=0$ to the beam-excited power.

Figure 8

Longitudinal decelerating wakefield (blue curve), electron bunch shape (red curve), of the 235 GHz structure, for 0.3 mm gap (a), for 0.5 mm gap (b), for 0.7 mm gap (c), for 0.9 mm gap (d), for 1.1 mm gap (e), and for 1.3 mm gap (f), calculated using the HFSS+Mathematica method [68].

Figure 9

Integrated loss factors for the TW structure, with ${\sigma }_z=50\mu \mathrm{m}$, for all the analyzed gaps, with the electron beam on axis.

Figure 10

Loss factor (a),(b) and kick factor (c),(d) as a function of the horizontal beam-structure displacement, for different gaps. The fields are generated by a ${\sigma }_z=50\mu \mathrm{m}$ bunch in a 10 cm long structure.

Figure 11

Schematic of the experimental FACET section.

Figure 12

Schematic of the experimental setup (a): signal to scope (1), interferometer (2), vacuum chamber (3), electron beam (4), laser alignment mirror (5), phosphor screen (6), right reflected rf horn (7), left forward rf horn (8), vacuum feedthrough (9), rf window (10), output rf beam (11), pyrodetector (12), and video camera for beam-structure alignment and rf breakdown diagnostic (13). The accelerating structure was assembled on remotely controlled motorized stages, with the arc-detector cables connected (b). The accelerating structure was installed in the vacuum chamber (c).

Figure 13

Oscilloscope signals with no breakdowns (a), a breakdown that generated a positive signal (b), and a breakdown that generated a negative signal (c).

Figure 14

Timeline of the experiments with the 200 GHz traveling-wave accelerating structures, copper structure with 3.2 nC of bunch charge and ${\sigma }_z=50\mu \mathrm{m}$ (a),(b) and copper-silver structure with 1.6 nC of bunch charge and ${\sigma }_z=25\mu \mathrm{m}$ (c). The green plot is the reference pyrodetector signal, the blue is the gap, and the red is the integrated number of breakdowns, recorded with the arc detector. Bell-shaped curves of the pyrodetector signal are generated during the scans of the beam over the cavities, and flat parts are the time intervals when we performed frequency measurements and collection of breakdowns.

Figure 15

Predicted (blue curve) and measured with the interferometer pyrodetector (red) pulse energy in a function of the horizontal position of a 3.2 nC electron beam, for the copper structure with $\mathrm{gap}=1.3\mathrm{mm}$ (a) and $\mathrm{gap}=1.5\mathrm{mm}$ (b).

Figure 16

Predicted (blue curve) and measured (red) peak pulse energy in a function of the gap, copper structure with a 3.2 nC electron beam (a) and copper-silver structure with a 1.6 nC electron beam (b).

Figure 17

Measurement of beam deflection in a horizontal scan with $\mathrm{gap}=1.1\mathrm{mm}$, a longitudinal bunch length ${\sigma }_z$ of $50\mu \mathrm{m}$, and a charge of 3.2 nC (red plot). The blue plot is the simulation.

Figure 18

Current monitor signal recorded by placing the electron beam in the central axis of the copper structure (a) and histogram of the distribution of the current monitor voltages (b), with 1.3 mm gap, 3.2 nC of bunch charge, and ${\sigma }_z=50\mu \mathrm{m}$.

Figure 19

Constant gradient breakdown rate measurements, obtained by placing the electron beam in the central axis of the copper structure, with 3.2 nC of bunch charge and ${\sigma }_z=50\mu \mathrm{m}$, as a function of the peak electric field (a), as a function of the accelerating gradient (b), and as a function of the peak pulsed heating (c). The repetition rate varied from 1 to 15 Hz.

Figure 20

Breakdown rate measurements, achieved during a horizontal scan of the copper structure with a 1.5 mm gap, with 3.2 nC of bunch charge and ${\sigma }_z=50\mu \mathrm{m}$, plots of the pyrodetector signal and of the arc detector, showing that the arc probability increases with the gradient (a), the histogram of the distribution of the current monitor voltages (b), the breakdown rate as a function of the peak electric field (c), and as a function of the peak pulsed heating (d).

Figure 21

Schematic of the interferometer, including the following components: 45° beam splitter (a), 90° beam splitter (b), front surface mirror on a translation stage (c), detector focusing mirror (d), and reference detector focusing mirror (e).

Figure 22

Example of a frequency measurement carried out with the interferometer, where the blue curve is the interferometer pyrodetector signal as a function of the motor position, and the red curve is a sinusoidal fitting.

Figure 23

SEM picture of breakdowns generated during the experiment involving the 235 GHz copper structure, driven by a bunch charge of 3.2 nC and $50\mu \mathrm{m}$ length. Input part of the structure: Little damage sign, from the input coupler to cell 152 (a). Output end of the structure: Damage concentrated at output irises, the bottom part has more sputter, and all the heavy damage occurs in cells 154–167 (b); iris between cells 159 and 160, heavy damage (c); bottom cell 166, areas adjacent to heavy surface melting are covered with sputtered material (d).

Figure 24

Constant gradient breakdown rate measurements, obtained by placing the electron beam in the central axis of the copper-silver structure, with 1.6 nC of bunch charge and ${\sigma }_z=25\mu \mathrm{m}$, as a function of the peak electric field (a), as a function of the accelerating gradient (b), and as a function of the peak pulsed heating (c). The repetition rate was 29 Hz.

Figure 25

SEM picture of breakdowns generated during the experiment involving the 235 GHz copper-silver structure, driven by a bunch charge of 1.6 nC and $25\mu \mathrm{m}$ length. Input part of the structure: Little damage sign, from the input coupler to cell 149 (a). Output end of the structure: First areas of heavy arcing and surface melting occur after cell 155 (b); iris between cells 155 and 156, damage and surface melting (c).