Multiple harmonic frequencies resonant cavity design and half-scale prototype measurements for a fast kicker

Quarter wavelength resonator (QWR) based deflecting cavities with the capability of supporting multiple odd-harmonic modes have been developed for an ultrafast periodic kicker system in the proposed Jefferson Lab Electron Ion Collider (JLEIC, formerly MEIC). Previous work on the kicking pulse synthesis and the transverse beam dynamics tracking simulations show that a flat-top kicking pulse can be generated with minimal emittance growth during injection and circulation of the cooling electron bunches. This flat-top kicking pulse can be obtained when a DC component and 10 harmonic modes with appropriate amplitude and phase are combined together. To support 10 such harmonic modes, four QWR cavities are used with 5, 3, 1, and 1 modes, respectively. In the multiple-mode cavities, several slightly tapered segments of the inner conductor are introduced to tune the higher order deflecting modes to be harmonic, and stub tuners are used to fine tune each frequency to compensate for potential errors. In this paper, we summarize the electromagnetic design of the five-mode cavity, including the geometry optimization to get high transverse shunt impedance, the frequency tuning and sensitivity analysis, and the single loop coupler design for coupling to all of the harmonic modes. In particular we report on the design and fabrication of a half-scale copper prototype of this proof-of-principle five-odd-mode cavity, as well as the rf bench measurements. Finally, we demonstrate mode superposition in this cavity experimentally, which illustrates the kicking pulse generation concept.

Figure 1

The scheme of the ERL-based electron circulator cooler ring in the proposed JLEIC and the design concept of an ultrafast kicker with multiple harmonic modes generated by a group of QWRs.

Figure 2

Deflecting QWR cavity model of the fundamental mode (47.63 MHz) with the left view section showing the magnetic field distribution (left) and the front view section for the electric field distribution (right).

Figure 3

Field distribution of the fundamental mode (47.63 MHz, left) and the highest mode (428.67 MHz, right) in the five-odd-mode cavity along the beam axis of the deflecting QWR. The magnetic field is multiplied by the free space impedance (${\eta }_0=120\pi$) to give a fair comparison of the respective contribution of the electric and magnetic field to the transverse kick. All these electromagnetic fields are normalized to 1 J stored energy.

Figure 4

Optimization of the shunt impedance of the fundamental mode for different gaps g when b is 157 mm.

Figure 5

Transit time factor (left) and the required compensated power (right) change with the particle velocity.

Figure 6

The cavity schematic model (top) and the equivalent circuit of this capacitor loaded QWR cavity (bottom).

Figure 7

Normalized required tuning amount (for tapers and stub tuners) verses cavity length, the curve inflection is due to the tuning range going to other direction from the target frequency.

Figure 8

Tuner position simulation for the 5 harmonics modes cavity with a cylinder trail stub radius $R=20\mathrm{mm}$, insertion height $H=10\mathrm{mm}$, perturbation moving along the outer conductor wall in the axial direction.

Figure 9

Taper points chosen on the inner conductor.

Figure 10

Frequency convergence with taper simulation iteration number.

Figure 11

A prototype cavity with five manual stub tuners for tuning five harmonic frequencies.

Figure 12

Coupling strength for each mode at different locations along the cavity wall. Coupler loop size and orientation are fixed in this simulation.

Figure 13

Prototype cavity made of copper.

Figure 14

Tuning process to achieve the target frequencies by solving the tuning matrix equation and adjusting the stub tuners three times in the measurement.

Figure 15

The transmission coefficient between the input coupler port and the pickup port (left), and the reflection coefficient at the input coupler port (right) as a function of frequency.

Figure 16

On-axis field magnitude square of the different components of the electric field $E_x$ (top left), $E_z$ (top right) and the magnetic field $H_y$ (bottom). The magnetic field is multiplied by the free space impedance (${\eta }_0=120\pi$) to give a fair comparison of the respective contribution of the electric and magnetic field to the transverse kick. All these electromagnetic fields are normalized to 1 J stored energy.

Figure 17

Complete bead pull measurement setup.

Figure 18

Perturbing objects employed in the measurement with their dimensions measured by caliper. (Left: Teflon. Right: Brass).

Figure 19

Pillbox cavity used for calibration of the perturbing beads.

Figure 20

Result of the measurement with the dielectric (top) and the metallic (bottom) bead, and the comparison with simulation result.

Figure 21

Schematic drawing (top) and bench set up (bottom) for the mode combination experiment.

Figure 22

The result of the odd harmonic modes combined one by one viewed on the oscilloscope display. Here the fifth mode is in the reverse phase to make the final kicking pulse more flat. The final working pulse is a flat-top kicking pulse which is the combination of a DC component and 10 continues harmonic modes separated in four cavities, here we just use five odd harmonic modes in the first cavity for a demonstration purpose.

Figure 23

Comparison of the combined kick pulse from the oscilloscope display image capture with the simulation.