Electromagnetic design of the transition section between modules of a wakefield accelerator

The electromagnetic design of a transition section consisting of couplers for extracting the 180-GHz ${\mathrm{TM}}_{01}$ accelerating mode and 190-GHz ${\mathrm{HE}}_{11}$ dipole mode of a cylindrical corrugated waveguide used as a collinear wakefield accelerator is presented. Extraction of the high power accelerating mode reduces the power dissipation in the corrugated accelerating structure and allows the much weaker ${\mathrm{HE}}_{11}$ mode to be isolated and used to monitor the stability of the 10-nC electron drive bunch. The final design demonstrates wide bandwidth and high coupling efficiency of two couplers. The design was also optimized to have the surface electric and magnetic fields that do not exceed those in the corrugated waveguide. Finally, coupling between the drive electron bunch and the ${\mathrm{HE}}_{11}$ dipole mode in the corrugated waveguide is considered and the utility of the ${\mathrm{TE}}_{11}$ coupler for detecting the electron beam oscillations in the wakefield accelerator is demonstrated using a few representative examples of oscillations below and above a threshold of the beam breakup instability.

Figure 1

Vacuum space of transition section couplers connected to a short section of the CWG accelerating structure.

Figure 2

Vacuum space of the ${\mathrm{TM}}_{01}$ and ${\mathrm{TE}}_{11}$ couplers in the transition section.

Figure 3

Vacuum space of a quarter section of the coupler cross, showing the two PMC symmetry planes used to eliminate higher modes in the overmoded cylindrical waveguide.

Figure 4

Schematic of the simplified ${\mathrm{TM}}_{01}$ coupler optimization scheme, showing the coupler cross isolated from the idealized rf choke.

Figure 5

Reflection and extraction of the ${\mathrm{TM}}_{01}$ mode from the ${\mathrm{TM}}_{01}$ coupler. The extracted power is divided equally among the four rectangular waveguide outputs.

Figure 6

Transmission of the ${\mathrm{TE}}_{11}$ mode through the ${\mathrm{TM}}_{01}$ output coupler.

Figure 7

Reflection and extraction of the ${\mathrm{TE}}_{11}$ mode from the IOM in isolation. The extracted power is divided between the two rectangular waveguide outputs corresponding to the polarization of the incident ${\mathrm{TE}}_{11}$ mode.

Figure 8

${\mathrm{TE}}_{11}$ extraction and reflection from the transition section including the ${\mathrm{TM}}_{01}$ coupler before the IOM.

Figure 9

Isolation of the IOM output from the high power ${\mathrm{TM}}_{01}$ accelerating mode for the ${\mathrm{TE}}_{11}$ IOM coupler alone and for the transition section.

Figure 10

Power envelope of the incident ${\mathrm{TM}}_{01}$ mode from the output of the 0.5-m long CWG. Calculated with an estimated reduced copper conductivity of $\sigma =4\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$.

Figure 11

Maximum E-field (a) and H-field (b) for the incident ${\mathrm{TM}}_{01}$ mode from the CWG with 68 MW peak pulse power. Showing $E_{i,\max }=210\mathrm{M}\mathrm{V}{\mathrm{m}}^{-1}$ and $H_{i,\max }=448\mathrm{k}\mathrm{A}{\mathrm{m}}^{-1}$.

Figure 12

The $z$ component of the transition section wakefield impedance showing interaction with the trapped mode at 55 GHz.

Figure 13

Peak E-field (a) and H-field (b) of the trapped mode at 55 GHz, excited by a 10-nC bunch.

Figure 14

Steady-state heat load resulting from the 670-W ${\mathrm{TM}}_{01}$ incident rf power and the 55-GHz trapped mode for a 20-kHz repetition rate beam.

Figure 15

Transient surface temperature rise at location (b) of Fig. 14, showing a maximum of $\mathrm{\Delta }T=10.9°\mathrm{C}$ occurring 4.5 ns from the beginning of the pulse. Computed for a structure with electrical conductivity of $4\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$, $k_T=398\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, $\rho =8.9\mathrm{g}{\mathrm{cm}}^{-3}$, $c_{\epsilon }=389\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$.

Figure 16

Radial offset of the drive bunch center of charge propagating through the CWA.

Figure 17

Bunch trajectory through the fifth 0.5-m long CWG module in the CWA showing the center of charge of the electron bunch (top panel), the bunch curvature at three locations in the CWG (middle panel), and the 190-GHz ${\mathrm{HE}}_{11}$ mode at the end of the CWG module.

Figure 18

IOM output energies for bunch trajectories with 30, 40, and $50\mathrm{\mu }\mathrm{m}$ initial offsets, showing instability developing for the $50\text{−}\mathrm{\mu }\mathrm{m}$ initial offset case after module number 40.

Figure 19

IOM output energies for one quadrupole misalignment of 5, 6, and $7\mathrm{\mu }\mathrm{m}$, showing instability developing for the $7\text{−}\mathrm{\mu }\mathrm{m}$ misalignment case.

Figure 20

Cumulative baseline IOM energies for a bunch with $100\mathrm{\mu }\mathrm{m}$ vertical offset.

Figure 21

Baseline IOM energy spectrum for a bunch with $100\mathrm{\mu }\mathrm{m}$ vertical offset.