Gold-gold luminosity increase in RHIC for a beam energy scan with colliding beam energies extending below the nominal injection energy

The Beam Energy Scan phase II (BES-II), performed in the Relativistic Heavy Ion Collider (RHIC) from 2019 to 2021, explored the phase transition between quark-gluon plasma and hadronic gas. BES-II exceeded the goal of a fourfold increase in the average luminosity over that achieved during Beam Energy Scan phase I (BES-I), at five gold beam energies: 9.8, 7.3, 5.75, 4.59, and $3.85\mathrm{GeV}/\mathrm{nucleon}$. This was accomplished by addressing several beam dynamics effects, including intrabeam scattering, beam-beam, space charge, beam instability, and field errors induced by superconducting magnet persistent currents. Some of these effects are especially detrimental at low energies. BES-II achievements are presented, and the measures taken to improve RHIC performance are described. These measures span the whole RHIC complex, including ion beam sources, injectors, beam lifetime improvements in RHIC, and operation with the world’s first bunched beam Low Energy RHIC electron Cooler (LEReC).

Figure 1

The initial and average luminosities at five gold beam energies achieved during BES-I and BES-II. Red dots and blue squares represent the average luminosity. A small horizontal bar marks the initial luminosity. The average luminosity at $4.59\mathrm{GeV}/\mathrm{nucleon}$ during BES-I is interpolated based on data collected at 3.85 and $5.75\mathrm{GeV}/\mathrm{nucleon}$.

Figure 2

The longitudinal vertex distribution for a long bunch (${\sigma }_s=2.5\mathrm{m}$) with the lower frequency cavities (9 MHz) and a short bunch (${\sigma }_s=1.5\mathrm{m}$) with the higher frequency cavities (28 MHz). The red vertical lines indicate the vertex cut range of $\pm 0.7\mathrm{m}$ about the detector center. This cut reduces the instantaneous luminosity by $\sim 70\%$ and $\sim 50\%$ for long and short bunches, respectively.

Figure 3

Schematic of the Low Energy RHIC electron Cooling accelerator. Electron beam is accelerated by a 704 MHz superconducting rf cavity to the required energy and then transported to the RHIC cooling sections. First they merge with ion bunches in the Yellow ring cooling section, before turning around and merging with ion bunches in the Blue RHIC ring. Finally they are transported to a beam dump.

Figure 4

The LEReC electron beam and RHIC ion beam time structure, showing the overlap of 30 to 36 electron bunches (blue) with a single gold ion bunch (red). The electron bunches are spaced by 1.4 nsec (704 MHz), with a charge of 0.13 nC and a length of 0.4 nsec. The gold ion bunch has a charge of 7.5 nC and a bunch repetition frequency of 9 MHz.

Figure 5

Ion beam emittance evolution, with and without electron cooling. Upper plot: rms bunch length. Lower plot: vertical beam size. The blue and yellow traces are without cooling, while the black and red traces are with cooling. The Yellow beam was injected about 3 min before the Blue beam. The time origin marks the start of physics data taking, soon after both rings were filled.

Figure 6

Collision rates during stores at $3.85\mathrm{GeV}/\mathrm{nucleon}$, with (red trace) and without (black trace) cooling. The store length with cooling was usually about 10 min longer. The vertical line indicates the time when the $\beta$ function at the collision point was squeezed, with cooling.

Figure 7

The experimental collision rates for stores at $3.85\mathrm{GeV}/\mathrm{nucleon}$ with different fractional betatron tunes. The blue data were taken with fractional tunes of 0.23, when the electron cooling efficiency was higher. The red data correspond to fractional tunes of 0.12, when the cooling efficiency was reduced but the ion beam lifetime was increased. The black data were taken after fine betatron tune adjustments and with smaller electron beam currents, further improving the ion beam lifetime with less heating.

Figure 8

Longitudinal phase space distribution for a single rf system (28 MHz) and a double rf system (28 and 9 MHz), before and after 7000 turns. The double rf system (b) provides a larger central bucket area than the single rf system (a). Debunched beam after 7000 turns is negligible in the double rf case (d), compared to the single rf case (c).

Figure 9

Evolution of the bunched beam intensity with a single rf system (red trace) and with a double rf system (blue trace).

Figure 10

Incoherent space charge tune shift in BES-I and BES-II at various beam energies. The lines connecting the data points are for the purpose of guiding the viewer’s eye and have no physical meaning.

Figure 11

Beam-beam parameters in BES-I and BES-II at various beam energies.

Figure 12

Transverse emittance blowup due to the space charge effect. A 50% increase was observed with the fractional part of betatron tunes at 0.09 (a) compared to the emittance with the fractional part of betatron tunes later raised to 0.12 (b). The blowup can be seen in the initial values comparing the left and right plots. The horizontal emittance is shown in blue and the vertical emittance is shown in red. The vertical emittance was reported to be higher than the horizontal likely due to the calibration of measurement devices.

Figure 13

Gaussian longitudinal profile (the black curve) for a single rf system and flattened longitudinal profile (the red curve) for a double rf system, with the third harmonic cavities phased opposite to the primary rf.

Figure 14

Nominal chromaticity settings at various energies during BES-II, required to suppress the coupled bunch instability.

Figure 15

Suppressing turn-by-turn orbit oscillations with the bunch-by-bunch damper in a test. The oscillation begins at turn 512 when the tune meter kicker excites the beam. (a) Without damper (b) With damper.

Figure 16

The conventional magnetic cycle (a) and the demagnetization cycle (b) for beam operations at an RHIC main dipole current of 473 A. The demagnetization cycle removed a large fraction of the persistent current. Similar demagnetization cycles were implemented at all other BES-II energies.

Figure 17

Initial ${\beta }^{*}$ values were smaller during BES-II than during BES-I, at all beam energies. The ${\beta }^{*}$ values were reduced even more during stores with electron cooling: once at $3.85\mathrm{GeV}/\mathrm{nucleon}$ and twice at $4.59\mathrm{GeV}/\mathrm{nucleon}$.

Figure 18

The bunch intensity during BES-I and BES-II at various beam energies.

Figure 19

The bucket acceptances achieved by the rf systems during BES-I and BES-II and the longitudinal emittance of bunches coming out of the AGS during BES-II.