High power breakdown testing of a photonic band-gap accelerator structure with elliptical rods

An improved single-cell photonic band-gap (PBG) structure with an inner row of elliptical rods (PBG-E) was tested with high power at a 60 Hz repetition rate at X-band (11.424 GHz), achieving a gradient of $128\mathrm{MV}/\mathrm{m}$ at a breakdown probability of $3.6\times {10}^{-3}$ per pulse per meter at a pulse length of 150 ns. The tested standing-wave structure was a single high-gradient cell with an inner row of elliptical rods and an outer row of round rods; the elliptical rods reduce the peak surface magnetic field by 20% and reduce the temperature rise of the rods during the pulse by several tens of degrees, while maintaining good damping and suppression of high order modes. When compared with a single-cell standing-wave undamped disk-loaded waveguide structure with the same iris geometry under test at the same conditions, the PBG-E structure yielded the same breakdown rate within measurement error. The PBG-E structure showed a greatly reduced breakdown rate compared with earlier tests of a PBG structure with round rods, presumably due to the reduced magnetic fields at the elliptical rods vs the fields at the round rods, as well as use of an improved testing methodology. A post-testing autopsy of the PBG-E structure showed some damage on the surfaces exposed to the highest surface magnetic and electric fields. Despite these changes in surface appearance, no significant change in the breakdown rate was observed in testing. These results demonstrate that PBG structures, when designed with reduced surface magnetic fields and operated to avoid extremely high pulsed heating, can operate at breakdown probabilities comparable to undamped disk-loaded waveguide structures and are thus viable for high-gradient accelerator applications.

Figure 1

Expanded three-quarter view of solid model of elliptical-rod PBG structure, showing two coupling cells and central PBG cell. Power is coupled in from the left.

Figure 2

Elliptical-rod PBG lattice showing lattice spacing $\beta$, rod radius (minor radius for elliptical rods) $\alpha$, and major radius $\delta$.

Figure 3

Axisymmetric views of the vacuum space of the PBG-E structure showing the fixed parameters (a), and tuning parameters (b), for the elliptical-rod PBG structure.

Figure 4

Normalized electric field profile on axis in PBG-E structure; the field amplitude in each coupling cell is approximately half that in the PBG cell.

Figure 5

Calculated reflection as a function of frequency for the PBG-E structure.

Figure 6

Electric (a) and magnetic (b) field amplitudes looking at a radial cut of the structure through an inner rod. At an accelerating gradient of $100\mathrm{MV}/\mathrm{m}$ the peak surface electric field amplitude is $207\mathrm{MV}/\mathrm{m}$ at the iris surfaces. At the same gradient the peak surface magnetic field occurs on the inner surface of the inner rod, and reaches a value of $713\mathrm{kA}/\mathrm{m}$.

Figure 7

Electric (a) and magnetic (b) field amplitudes looking at a top-down view of the structure. The peak surface electric field of $207\mathrm{MV}/\mathrm{m}$ for a $100\mathrm{MV}/\mathrm{m}$ accelerating gradient is seen on axis. The peak surface magnetic field of $713\mathrm{kA}/\mathrm{m}$ for an accelerating gradient of $100\mathrm{MV}/\mathrm{m}$ is confined to the center of the inner surface of the innermost rod.

Figure 8

$S_{11}$ of PBG-E structure, showing resonances for, in order of increasing frequency, the 0 mode, the $\pi /2$ mode, and the $\pi$ mode.

Figure 9

$\pi$ mode field profile

Figure 10

Calculated peak surface temperature rise due to pulsed heating in the PBG-R structure. Note the excursions to over 200 K early in the testing.

Figure 11

A sample set of scope traces showing a normal shot. This is a 150 ns shot at approximately $125\mathrm{MV}/\mathrm{m}$ gradient. The measured incident rf signal is shown in blue, and the measured reflected rf signal is shown in yellow. The forward and reverse current monitor signals are shown in red and green, respectively.

Figure 12

A sample set of scope traces showing a breakdown shot, as indicated by the peaks in the current monitor signals, and an increase in reflected rf signal. This is a 150 ns shot at approximately $125\mathrm{MV}/\mathrm{m}$ gradient. The measured incident power is shown in blue, and the measured reflected power is shown in yellow. The forward and reverse current monitor signals are shown in red and green, respectively. Note that the currents generated by the breakdowns saturate the current monitors.

Figure 13

Sample traces from the peak power meter for a 150 ns pulse at a gradient of $126\mathrm{MV}/\mathrm{m}$. The incident and reflected power measured by the peak power meter are shown in black and blue, respectively. The calculated reflected power and power coupled into the structure are shown in green and red, respectively.

Figure 14

Sample traces from the peak power meter for a 150 ns pulse at a gradient of $126\mathrm{MV}/\mathrm{m}$. The incident power measured by the peak power meter is shown in black. The calculated gradient is shown in orange, and the calculated peak surface temperature rise is shown in purple.

Figure 15

Accumulated breakdowns and gradient during the majority of testing.

Figure 16

Calculated peak surface temperature rise due to pulsed heating in the PBG-E structure.

Figure 17

Breakdown probability per pulse per meter of structure vs gradient at 150 ns pulse length for the PBG-R, PBG-E, and a conventional disk-loaded waveguide structure with the same iris geometry (DLWG). The two data sets for the PBG-E represent the beginning and end of testing.

Figure 18

Breakdown probability per pulse per meter of structure vs gradient for PBG-E at pulse lengths of 150 and 600 ns.

Figure 19

Breakdown probability per pulse per meter of structure vs peak surface temperature rise for PBG-E at pulse lengths of 150 and 600 ns.

Figure 20

Breakdown probability per pulse per meter of structure vs peak surface temperature rise for PBG-E, PBG-R, and DLWG structures at a pulse length of 150 ns.

Figure 21

SEM micrograph of damage on the iris on the input side of the PBG cell. The view shows a close-up view of the iris looking perpendicular to the axis of the structure, so that the curvature of the iris cannot be readily seen. The high-field side of this iris is to the right of the image.

Figure 22

SEM micrograph looking directly at high-field side of an inner rod. Grain boundaries are easily visible, and surface roughness does increase at these boundaries.

Figure 23

Detail micrograph of the high-field side of the inner rod of the PBG-E, showing grain boundaries even at the highest-field region. The PBG-E shows significantly less damage than the PBG-R structure.