Design of a cylindrical corrugated waveguide for a collinear wakefield accelerator

We present the design of a cylindrical corrugated waveguide for use in the A-STAR accelerator under development at Argonne National Laboratory. A-STAR is a high gradient, high bunch repetition rate collinear wakefield accelerator that uses a 1-mm inner radius corrugated waveguide to produce a $90\mathrm{MV}{\mathrm{m}}^{-1}$, 180-GHz accelerating field when driven by a 10-nC drive bunch. To select a corrugation geometry for A-STAR, we analyze three types of corrugation profiles in the overmoded regime with $a/\lambda$ ranging from 0.53 to 0.67, where $a$ is the minor radius of the corrugated waveguide and $\lambda$ is the free-space wavelength. We find that the corrugation geometry that optimizes the accelerator performance is a rounded profile with vertical sidewalls and a corrugation period $p\ll a$. Trade-offs between the peak surface fields and thermal loading are presented along with calculations of pulse heating and steady-state power dissipation. In addition to the ${\mathrm{TM}}_{01}$ accelerating mode, properties of the ${\mathrm{HEM}}_{11}$ mode and contributions from higher order modes are discussed.

Figure 1

Two 0.5-m long modules of the CWA connected in series, showing the module on the left with the quadrupole wiggler removed.

Figure 2

Cylindrical corrugated waveguide (CWG) with minor radius $a$. The specific design used in A-STAR has $a=1\mathrm{mm}$.

Figure 3

Dimensions for corrugation types: (a) minimum radii corners, (b) maximum radii corners, (c) rounded with unequal radii corners connected by tangent sidewalls, where $t=2r_t$ and $g=2r_g$.

Figure 4

Corrugation variation with the spacing parameter $\xi$ and sidewall parameter $\zeta$ for the minimum radii (top), maximum radii (middle), and unequal radii (bottom) profiles at fixed period and depth.

Figure 5

Corrugation depths calculated for minimum radii corrugations (top) and maximum radii corrugations (bottom) for aperture ratios of $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue). See Fig. 4 for cell geometries.

Figure 6

Corrugation depths calculated for unequal radii corrugations with $\zeta =0.85$ (dashed), $\zeta =1.0$ (solid), and $\zeta =1.15$ (dotted) where the aperture ratios are $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue). See Fig. 4 for cell geometries.

Figure 7

Loss factor $\kappa$, normalized group velocity ${\beta }_g=v_g/c$, and attenuation constant $\alpha$ for the maximum radii geometry with $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue). Plotted for a CWG with minor radius $a=1\mathrm{mm}$ and electrical conductivity $\sigma =4\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$.

Figure 8

Peak electric field distribution (a) and magnetic field distribution (b) of the $90\mathrm{MV}{\mathrm{m}}^{-1}$ ${\mathrm{TM}}_{01}$ accelerating mode in the A-STAR corrugated waveguide.

Figure 9

Normalized peak surface E fields of the minimum radii rectangular corrugation geometry with $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue).

Figure 10

Normalized peak surface E ($\mathrm{V}{\mathrm{m}}^{-1}$) and H ($\mathrm{A}{\mathrm{m}}^{-1}$) fields of the maximum radii corrugation geometry with $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue).

Figure 11

Normalized peak surface E ($\mathrm{V}{\mathrm{m}}^{-1}$) and H ($\mathrm{A}{\mathrm{m}}^{-1}$) fields of the unequal radii corrugation geometry for aperture ratio $a/\lambda =0.60$ and $\zeta =0.85$ (dashed), $\zeta =1.0$ (solid), and $\zeta =1.15$ (dotted).

Figure 12

Pulse heating maximum temperature rise for the maximum radii corrugation with $a=1\mathrm{mm}$, $E_{\mathrm{acc}}=100\mathrm{MV}{\mathrm{m}}^{-1}$, and conductivity $\sigma =4\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$ for $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue).

Figure 13

Comparison of wake impedance for maximum radii structures with $p/a=0.4$ (left panel) and $p/a=0.7$ (right panel) and aperture ratio $a/\lambda =0.60$. The HOMs are seen as additional peaks for the larger period structure on the right.

Figure 14

Ratio of the HOM wakefield to the total wakefield for an impulse excitation with $a/\lambda =0.53$ (red), $a/\lambda =0.60$ (black), and $a/\lambda =0.67$ (blue).

Figure 15

A-STAR CWG dimensions.

Figure 16

A 10-nC doorstep charge distribution and resulting wake potential of the ${\mathrm{TM}}_{01}$ mode for the A-STAR CWG, showing a transformer ratio $\mathcal{R}=5$ and peak accelerating gradient $E_{\mathrm{acc}}=90\mathrm{MV}{\mathrm{m}}^{-1}$.

Figure 17

rf power envelope at the end of a 0.5-m section of the A-STAR CWG made from copper ($5.8\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$), aluminum ($3.8\times {10}^7\mathrm{S}{\mathrm{m}}^{-1}$), and stainless steel ($1.35\times {10}^6\mathrm{S}{\mathrm{m}}^{-1}$).