Wakefield effects and mitigation techniques for nanobeam production at the KEK Accelerator Test Facility 2

The ATF2 beam line at KEK was built to validate the operating principle of a novel final-focus scheme devised to demagnify high-energy beams in future linear lepton colliders; to date vertical beam sizes as small as 41 nm have been demonstrated. However, this could only be achieved with an electron bunch intensity $\sim 10\%$ of nominal, and it has been found that wakefield effects limit the beam size for bunch charges approaching the design value of ${10}^{10}{e}^{-}$. We present studies of the impact of wakefields on the production of “nanobeams” at the ATF2. Wake potentials were evaluated for the ATF2 beam line elements and incorporated into a realistic transport simulation of the beam. The effects of both static (component misalignments and rolls, magnet strength errors and beam position monitor resolution) and dynamic (position and angle jitter) imperfections were included and their effects on the beam size evaluated. Mitigation techniques were developed and applied, including orbit correction, dispersion-free steering, wakefield-free steering, and interaction point tuning knobs. Explicit correction knobs to compensate for wakefield effects were studied and applied, and found to significantly decrease the intensity dependence of the beam size.

Figure 1

Schematic layout of ATF2 beam line.

Figure 2

Transverse wake potential $W$ (V/pC/mm) of the ATF2 bellows (red), C-BPMs (black) and flanges (orange) calculated with gdfidl for a Gaussian bunch of 7 mm rms length and a 1 pC charge with a vertical offset of 1 mm. For reference, the distribution of the electrons in one bunch is shown (blue). The head of the bunch points towards negative $z$.

Figure 3

IPBSM laser fringe modulation depth vs beam size, illustrating the dynamic ranges of the IPBSM modes [20].

Figure 4

Difference between the measured horizontal dispersion ($D_x$) and the target dispersion ($D_{x,\text{target}}$) vs BPM number before (red) and after (blue) applying DFS correction.

Figure 5

Difference between the measured vertical dispersion ($D_y$) and the target dispersion ($D_{y,\text{target}}$) vs BPM number before (red) and after (blue) DFS correction.

Figure 6

Norm of the difference ($\mu \mathrm{m}$) between the vertical orbit at high intensity, $6.0\times {10}^9$ electrons (${\mathrm{y}}_{HQ}$) and at low intensity, $2.0\times {10}^9$ electrons, (${\mathrm{y}}_{LQ}$) vs the number of iterations of the WFS correction.

Figure 7

Measured average vertical IP beam size ($\overline{{\sigma }_y^{*}}$) vs the beam intensity without correction and with DFS and WFS corrections. For each experimental data point the longer error bar shows the quadratic sum of the statistical and the systematic errors and the shorter error bar shows the systematic error. The lines show fits of Eq. (1).

Figure 8

Average vertical beam size at the IP ($\overline{{\sigma }_y^{*}}$) vs correction step: Orbit, DFS, WFS corrections and IP tuning knobs. The error bars represent the standard error of 100 machines. The red dashed line shows the 37 nm IP vertical beam size for a perfect machine.

Figure 9

Effect of both incoming 0.1, 0.3, 0.5 and $1.0{\sigma }_y$ beam position and 0.1, 0.3, 0.5 and $1.0{\sigma }_{y^{\prime }}$ beam angle jitters on the average vertical IP beam size ($\overline{{\sigma }_y^{*}}$) vs the beam intensity, calculated with placet incorporating wakefields. The error bars represent the standard error for 100 machines and 200 pulses per machine. The dashed lines (w) show fits of Eq. (1).

Figure 10

Comparison between measurements and simulations of the average IP vertical beam size ($\overline{{\sigma }_y^{*}}$) vs the beam intensity. For each experimental data point the longer error bar shows the quadratic sum of the statistical and the systematic errors and the shorter error bar shows the systematic error. The lines show fits of Eq. (1).

Figure 11

Schematic of the ATF2 wakefield knobs system between BPM QD10BFF and QD10AFF.

Figure 12

Average vertical IP beam size ($\overline{{\sigma }_y^{*}}$) vs the position of the bellows, for one machine at ${1.0\times 10}^{10}{e}^{-}$.

Figure 13

Average vertical IP beam size ($\overline{{\sigma }_y^{*}}$) vs the position of the C-BPMs, for one machine at ${1.0\times 10}^{10}{e}^{-}$.

Figure 14

Contour plot of the simulation of the impact of the position of the C-BPMs and the bellows on the average vertical beam size at the IP, $\overline{{\sigma }_y^{*}}$, for one machine and for a beam intensity of $1.0\times {10}^{10}{e}^{-}$.

Figure 15

Average vertical beam size at the IP $\overline{{\sigma }_y^{*}}$ vs the beam intensity, for 100 machines, with (blue) and without (red) application of the wakefield knobs at ${1.0\times 10}^{10}{e}^{-}$. The error bars represent the standard error for 100 machines and 200 pulses per machine. The lines show fits of Eq. (1).

Figure 16

$\overline{{\sigma }_y^{*}}$ vs wakefield knob mover position for four consecutive mover iterations. (a) First iteration of the bellows mover (b) First iteration of the C-BPMs mover (c) Second iteration of the bellows mover (d) Second iteration of the C-BPMs mover.

Figure 17

Measured vertical IP beam size (${\sigma }_y^{*}$) vs the beam intensity before (red) and after (blue) applying wakefield knobs. For each experimental data point the longer error bar shows the quadratic sum of the statistical and the systematic errors and the shorter error bar shows the systematic error. The lines show fits of Eq. (1).