Compensation of head-on beam-beam induced resonance driving terms and tune spread in the Relativistic Heavy Ion Collider

A head-on beam-beam compensation scheme was implemented for operation in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory [Phys. Rev. Lett. 115, 264801 (2015)]. The compensation consists of electron lenses for the reduction of the beam-beam induced tune spread, and a lattice for the minimization of beam-beam generated resonance driving terms. We describe the implementations of the lattice and electron lenses, and report on measurements of lattice properties and the effect of the electron lenses on the hadron beam.

Figure 1

Reproduced from Ref. [1]. (a) Head-on beam-beam compensation in a phase space view. A defocusing kick $\mathrm{\Delta }{r}_{pp}^{\prime }$ a proton receives from the other proton beam is reversed by a focusing kick $\mathrm{\Delta }{r}_{pe}^{\prime }$ from the electron lens after a phase advance $\pi$. (b) Amplitude dependence of the beam-beam kick $\mathrm{\Delta }{r}^{\prime }$ on the radius $r$ [18, 19, 20].

Figure 2

General layout of RHIC with locations of the head-on beam-beam interactions and electron lenses [1].

Figure 3

Peak and average store luminosity in polarized proton operation at 100 GeV beam energy in 2012 and 2015.

Figure 4

Operational use of the electron lenses in 2015. The top plot shows the luminosities of both experiments, the middle plot the rms emittances as measured by the IPMs, and the bottom plot the electron beam current of both lenses (left scale) as well as the signal from the backscattered electrons (eBSD, right scale). The numbers “1” through “4” indicate times for certain events that are explained in the text.

Figure 5

RHIC Blue ring ATS lattice for 100 GeV protons. Only a fraction of the 3.8 km circumference is shown.

Figure 6

Blue (top) and Yellow (bottom) non-linear tune dependence on the momentum deviation $\delta p/p$ for the 2012 lattice and the 2015 ATS optics. The black line in both plots corresponds to a linear chromaticity $Q^{\prime }=+1$.

Figure 7

Phase space vector $\overrightarrow{R}$ at IP10 as a function of the initial coordinates $(r_i,r_i^{\prime })$ at IP8 without head-on beam-beam compensation in part (a), and deviation from full compensation in part (b) and (c). Part (b) shows the case of a matched electron beam size and current, part (c) has an additional linear phase error of $+5$ deg between the $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{e}$ interactions.

Figure 8

Simulated dynamic aperture as a function of the vertical tune $Q_y$ without beam-beam interactions. B denotes the Blue, and Y the Yellow ring.

Figure 9

Simulated dynamic aperture as a function of bunch intensity including beam-beam interactions.

Figure 10

Measured phase error $(\mathrm{\Delta }\psi /\psi {)}_{x,y}$ for the Blue horizontal and vertical planes (top) and the Yellow horizontal and vertical planes (bottom).

Figure 11

Measured $\beta$-beat $(\mathrm{\Delta }\beta /\beta {)}_{x,y}$ for the Blue horizontal and vertical planes (top) and the Yellow horizontal and vertical planes (bottom).

Figure 12

Change of gold beam tunes $Q_{x,y}$ (top) and vertical closed orbit angle at the electron lens (bottom) in response to a vertical displacement.

Figure 13

Reconstructed tune distribution widths from BTF measurements without beam-beam interaction (solid black), with electron lens (solid red), with 1 (dashed black) and 2 (dotted black) beam-beam interactions, and with 2 beam-beam interactions and an electron lens (dotted red). The widths is of colliding beam distributions is determined by the distance of the coherent modes, not by the incoherent tune distributions.

Figure 14

Measured p beam tune distribution width as a function of the electron beam current without beam-beam collisions and with an electron beam size of ${\sigma }_e=0.55\mathrm{mm}$. The proton beam size is ${\sigma }_p=0.60\mathrm{mm}$. The curves are aligned to the left with an offset for better visibility of the effect [1].

Figure 15

Measured p beam tune distribution width as a function of the electron beam size ${\sigma }_e$ without beam-beam collisions and with an electron current of 900 mA. The proton beam size is ${\sigma }_p=0.60\mathrm{mm}$. The curves are aligned to the left with an offset for better visibility of the effect.

Figure 16

Comparison of measured and calculated increase in the tune spread of the electron lens in an electron beam current scan (a) and electron beam size scan (b). The measured width of the tune distribution is taken at $|\mathrm{Im}(R)/(R)|=0.1$, the calculation is for an amplitude range $a$ from zero to 2.5 ${\sigma }_p$.

Figure 17

Tune distribution width reduction with the electron lens, measured in the proton beam with $\mathrm{p}+\mathrm{Al}$ collisions. The distribution widens due to two beam-beam interactions, and narrows again with the electron lens. The curves are aligned to the left with an offset for better visibility of the effect.

Figure 18

Total tune spread $\mathrm{\Delta }{Q}_{\mathrm{tot}}$ as a function of the electron beam current $I_e$. The measured total tune spread is based on BTF measurements.The expected total tune spread is based on the measured tune spread $Q_0$ and the beam-beam parameters ${\xi }_{\mathrm{Al}}$ and ${\xi }_e$ using Eq. (13), and shown for $a\le 2.5{\sigma }_p$ and $a\le 3.5{\sigma }_p$.

Figure 19

Yellow beam loss rate of 30 stores. The two red marked stores had the Yellow electron lens on for 6.75 h and 5.28 h respectively, for all other stores the lenses were on between 0.45 to 1.83 h.

Figure 20

Horizontal (top) and vertical (bottom) rms emittance of 30 stores. The two red marked stores had the Yellow electron lens on for 6.75 h and 5.28 h respectively, for all other stores the lenses were on between 0.45 to 1.83 h.

Figure 21

Average store luminosity ${\mathcal{L}}_{\mathrm{avg}}$ as a function of the Blue and Yellow average electron lens on-time for the last 40 stores of the 2015 run with a store length of 6 h or longer.

Figure 22

Location of two experimental background monitors (scintillators), N2 and N3, in the PHENIX interaction region.

Figure 23

PHENIX N2 background signal. The two red marked stores had the Yellow electron lens on for 6.75 h and 5.28 h respectively, all other stores had the lenses on between 0.45 to 1.83 h. Zero (the beginning of the store) is suppressed on the horizontal axis to better show the change in the background signal when the lenses are turned off.