Pressurized rf cavities in ionizing beams

A muon collider or Higgs factory requires significant reduction of the six dimensional emittance of the beam prior to acceleration. One method to accomplish this involves building a cooling channel using high pressure gas filled radio frequency cavities. The performance of such a cavity when subjected to an intense particle beam must be investigated before this technology can be validated. To this end, a high pressure gas filled radio frequency (rf) test cell was built and placed in a 400 MeV beam line from the Fermilab linac to study the plasma evolution and its effect on the cavity. Hydrogen, deuterium, helium and nitrogen gases were studied. Additionally, sulfur hexafluoride and dry air were used as dopants to aid in the removal of plasma electrons. Measurements were made using a variety of beam intensities, gas pressures, dopant concentrations, and cavity rf electric fields, both with and without a 3 T external solenoidal magnetic field. Energy dissipation per electron-ion pair, electron-ion recombination rates, ion-ion recombination rates, and electron attachment times to ${\mathrm{SF}}_6$ and ${\mathrm{O}}_2$ were measured.

Figure 1

The experimental setup housed within the bore of the superconducting solenoid. The beam enters from the right, passing through a scintillating screen and two collimators before impinging on the HPrf test cell. After traversing the test cell, the beam is stopped in a stainless steel cylinder. Toroids are mounted on both ends of the downstream collimator. The inset plot shows the radial distribution of the electric field amplitude and plasma density within the test cell.

Figure 2

Rf envelopes for various gas combinations. The beginning of the rf pulse has been omitted. The beam was sent through the test cell after the flat top electric field value had been reached. The magneta points are a rf pulse in which no beam was sent to the test cell. The blue points are a beam passing through the test cell filled with pure hydrogen. The green circles and black dashes represent hydrogen doped with dry air, both without and with a 3 T external magnetic field. The red crosses represent deuterium doped with dry air. The beam on and off, and rf off times are indicated by the dashed teal gridlines.

Figure 3

Electron drift velocity and thermal energy in hydrogen gas vs $E/p$ [38]. The thermal energy has been derived from measurements of the electron diffusion constant and mobility, and the Einstein relation. The vertical lines represent the range of $X_0$ in the HPrf beam test.

Figure 4

The equivalent circuit of a matched cavity where the impedance, $Z_0$, of the waveguide and source reflect the resistance, $R_c$, of the cavity (after applying Thévinin’s Theorem). The beam generated plasma within the cavity acts as a resistive component, $R_g$.

Figure 5

Energy dissipation measurements for pure hydrogen. The lines represent predictions based on Eq. (6) and electron drift velocity measurements from Ref. [30].

Figure 6

Energy dissipation measurements for pure deuterium. The lines represent predictions based on Eq. (6) and electron drift velocity measurements from Ref. [50].

Figure 7

Energy dissipation measurements for pure nitrogen and helium. The lines represent predictions based on Eq. (6) and electron drift velocity measurements from Refs. [30, 51].

Figure 8

Ratio of measured to predicted $dw$ vs $X_0$ for pure hydrogen [30].

Figure 9

Ratio of measured to predicted $dw$ vs $X_0$ for pure deuterium [50].

Figure 10

Ratio of measured to predicted $dw$ vs $X_0$ for pure nitrogen and helium [30, 51].

Figure 11

Energy dissipation measurements for 20.4 atm hydrogen doped with varying concentrations of dry air. The black lines are predictions for only electrons (solid) and only ions (dashed) [30, 46, 52].

Figure 12

Electron-ion recombination measurements vs $X_0$ for various pressures of hydrogen gas at the lowest beam intensity.

Figure 13

Electron-ion recombination measurements vs $X_0$ for various pressures of deuterium gas at the lowest beam intensity.

Figure 14

Electron-ion recombination measurements vs $X_0$ for nitrogen and helium gases at the highest beam intensity.

Figure 15

Electron attachment time as a function of $X_0$ at 20.4 atm for various dry air concentrations. The estimated error is 10% of the measurement value at 0.04% DA, 20% at 0.2% DA, 50% at 1% DA, and 100% at 5% DA.

Figure 16

Electron attachment time as a function of $X_0$ at 98.6 and 100 atm for various dry air concentrations. The estimated error is 20% of the measurement value at 0.001% DA, 50% at 0.002% DA, 100% at 0.01% DA, and 100% at 0.04% DA. The data points for larger concentrations can only be considered upper limits on the attachment time.

Figure 17

Electron attachment time as a function of $p$ at $X_0=(20\mathrm{MV}/\mathrm{m})/(160\mathrm{atm})$ for various dry air concentrations.

Figure 18

Electron attachment time as a function of $X_0$ at 20.4 atm and 1% dry air for deuterium and hydrogen. The estimated error is 50% of the measurement value.

Figure 19

Electron attachment time as a function of dry air concentration at $X_0=2.76\mathrm{V}/(\mathrm{cm}\mathrm{torr})$ for nitrogen gas at 47.6 atm and hydrogen gas at 20.4 atm.

Figure 20

Electron attachment time as a function of $X_0$ at 100 atm for 1% dry air doped helium.

Figure 21

Ion-ion recombination rate as a function of $X_0$ at 100 atm dry air doped hydrogen.

Figure 22

Ion-ion recombination rate as a function of $X_0$ at 100 atm ${\mathrm{SF}}_6$ doped hydrogen.

Figure 23

Ion-ion recombination rate as a function of $X_0$ at 20.4 atm for 1% dry air doped deuterium.

Figure 24

Percent of the total stored energy for 325 and 650 MHz cavities dissipated due to plasma loading in the HCC. One beam pulse is comprised of 21 bunches.