Beam intensity effects in Fermilab Booster synchrotron

Detrimental beam dynamics effects limit the performance of high-intensity rapid cycling synchrotrons (RCSs) such as the 8 GeV proton Fermilab Booster. Here we report the results of comprehensive experimental studies of various beam intensity dependent effects in the Booster. In the first part, we report the dependencies of the Booster beam intensity losses on the total number of protons per pulse and on key operational parameters, such as the machine tunes and chromaticities. Then we cross check two methods of the beam emittance measurements (the MultiWires proportional chambers and the ionization profile monitors). Finally, we used the intensity dependent emittance growth effects to analyze the ultimate performance of the machine in the present configuration, with the maximum space-charge tuneshift parameter $\mathrm{\Delta }{Q}_{\mathrm{SC}}\sim 0.6$, and after its injection energy is upgraded from 0.4 to 0.8 GeV.

Figure 1

Schematics of the Fermilab Booster synchrotron. Sectors, each consisting of four combined function magnets, are numerated 1 to 24. Indicated are locations of the ionization profile monitors (IPMs), MultiWires (MWs) beam profile monitors in the 8 GeV proton transport line and the 400 MeV $H^{-}$ beam injection line.

Figure 2

Booster ramp: kinetic energy (black), rf voltage (blue) and frequency (red).

Figure 3

Measured Booster beam characteristics during the acceleration cycle: (top) the horizontal (blue) and vertical (red) betatron tunes $Q_{x,y}$; (bottom) the horizontal (blue) and vertical (red) chromaticities $Q_{x,y}^{\prime }$.

Figure 4

Booster beam losses in the acceleration cycle: (top) the BCHG0 intensity monitor signal (blue, left axis) and the S06 beam loss monitor (BLM) readings (red, right axis) for nominal operational 14 turns injection intensity; (bottom) the same for higher intensity 19 turns injection.

Figure 5

Booster resistive wall monitor traces sampled every 1 ns (index $j$) for the bunch beam current profiles right before (dashed blue) and 40 turns after (solid red) the extraction gap clearing.

Figure 6

Intensity-dependent fractional Booster beam intensity loss at injection vs total number of protons.

Figure 7

Transmission efficiency 1 ms after injection for different chromaticities $Q_{x,y}^{\prime }$ vs $N_p$.

Figure 8

Tune scans of the transmission efficiency over the first millisecond after injection: (a) (top left) at the $N_p=0.95\times {10}^{12}$ and $Q_{x,y}^{\prime }=-6/–6$; (b) (top right) $N_p=0.95\times {10}^{12}$ and $Q_{x,y}^{\prime }=-20/–20$; (c) (bottom left) $N_p=4.3\times {10}^{12}$ and $Q_{x,y}^{\prime }=-16/–4$; (d) (bottom right) $N_p=4.3\times {10}^{12}$ and $Q_{x,y}^{\prime }=-20/–20$.

Figure 9

Comparison of the measured rms IPM vertical beam sizes at extraction for different beam intensities with the rms sizes measured by the MWs and recalculated to the IPM location.

Figure 10

An example of reconstruction of vertical (top plot) and horizontal (bottom plot) rms proton beam sizes in the 33 ms (20 000 turns) acceleration cycle of the Fermilab 8 GeV Booster synchrotron with the total beam intensity of $N_p=4.6\times {10}^{12}$: time dependence of the original IPM data ${\sigma }_{m,\mathrm{IPM}}^2$, the data corrected for smearing effects ${\sigma }^{*}$ and the same data after additional correction for the space-charge expansion ${\sigma }_0$ with parameters $D=103\mathrm{mm}$, $d=52\mathrm{mm}$, $V=24\mathrm{kV}$—see text and Eqs. (4) and (5).

Figure 11

Booster bunching factor over the accelerator ramp (ratio of the peak to average proton beam current).

Figure 12

Booster beam emittance measured by MWs at extraction vs the total proton intensity.

Figure 13

Evolution of the IPM vertical emittance in the Booster cycle at different intensities $N_p$ from $0.5\times {10}^{12}$ (2 turns injection) to $6.2\times {10}^{12}$ (20 turns injection). All the data are smoothed by a 100 turn running window averaging.

Figure 14

Vertical rms emittance growth vs $N_p$: (red circles) over the first 3000 turns; (black squares) from 3000 to 19000 turns. The data points are calculated for the IPM emittance values averaged over 500 turns 0–500, 3000–3500, 19000–19500. The error bars indicate estimated statistical uncertainty. Red and black solid line are for the approximations Eqs. (8) and (9), respectively.

Figure 15

Calculated vertical space-charge tuneshift parameter for the Booster cycle with $N_p=4.6\times {10}^{12}$. (The shaded area indicates 10% uncertainty, mostly due to the IPM emittance calculations.)