Cancellation of klystron-induced energy and arrival-time variations in linear accelerators with arc-type bunch compressors

We explain how the accelerating field amplitude and phase vary with modulator voltage in pulsed radio frequency high-power amplifiers based on klystron tubes. Changes in modulator voltage give rise to correlated changes of amplitude and phase, affecting the properties of the accelerated beam, in particular energy, arrival time, and bunch duration. We show, both theoretically and experimentally, that there exists a postcrest acceleration phase (the magic angle) where the changes of beam energy due to phase and amplitude shifts caused by modulator-voltage variations cancel out. When accelerating at the magic angle, the klystron modulator voltage jitter no longer contributes to energy and arrival-time jitter in the accelerator. Off-crest operation at the magic angle can be implemented for bunch compression schemes in accelerators with arc-type bunch compressors, which have positive momentum compaction. The experimental results, obtained at the MAX IV laboratory, show the benefit of operating close to the magic angle in arc-type bunch compressors. In a direct measurement of normalized electron-energy jitter, the energy jitter was reduced by a factor of 1.8 down to $8.2\times {10}^{-5}$ when operating at the magic angle.

Figure 1

Illustrations based on analytical calculations. (a) The relative energy gain variation for the nominal HV (blue curve) and for 1% lower HV (red curve). Both curves are normalized with respect to the crest energy for nominal HV. The curves intersect at a phase of 18.5°. (b) The difference between the gradient of the two curves in (a), i.e., the relative gradient change for a 1% difference in HV.

Figure 2

(a) Averaged amplitude and phase data plotted for a nominal HV setting of 1160V. During the measurement, the HV settings were changed as described in Sec. 5b. Amplitude data are plotted in blue, and phase is plotted in red. The marker sizes indicate the vertical standard deviation of the raw data. (b) Scatterplot representation of the same data, where each blue point corresponds to the measured amplitude and phase for one rf pulse. The dashed red line is a linear fit to the data points.

Figure 3

Photocathode gun (PG) electron bunches are accelerated up to $\sim 100\mathrm{MeV}$ electron energy in the first linac ($L_{00}$). In the following accelerating structure pair $L_{01A}$ and $L_{01B}$, the beam is further accelerated up to a nominal energy of 250 MeV. In the measurement described in Sec. 5b, the rf phase was varied and the sensitivity of energy to modulator high voltage was measured. For each phase, the K01 modulator high voltage was varied between 1180 and 1168 V, and the beam energy variations were recorded with the first BPM at maximum dispersion in BC1.

Figure 4

Normalized energy shift as a function of rf phase, when varying K01 modulator high voltage between 1180 and 1168 V. Measured data plotted with blue dots, linear fit to measured data plotted with a thin dotted line, and calculated values using Eq. (6) are plotted with a red dashed line.

Figure 5

Measured normalized energy jitter operating K01 at two phases, $\theta ={\theta }_{\text{magic}}$ is plotted in red and $\theta =-{\theta }_{\text{magic}}$ is plotted in blue.