Operational tests of CRYRING@ESR without electron cooler solenoid compensation

We have tested operation of FAIR’s low-energy ion storage ring CRYRING@ESR with uncompensated electron cooler solenoid. With its standard working point on the lowest-order difference resonance, a second solenoid is normally used to cancel betatron coupling introduced by the cooler’s magnetic field. In operation with a D+ test beam, we found that omission of the compensation solenoid did not lead to a notable deterioration of beam intensity, quality, or cooling time, though the expected coupling of betatron motion is then clearly observed.


Introduction
CRYRING is a heavy-ion storage ring initially designed and operated by Manne Siegbahn Laboratory (MSL), Stockholm [1].As an in-kind contribution to FAIR, the ring has been transferred to GSI, Darmstadt.Recommissioned within the CRYRING@ESR project, it complements the existing GSI facilities by a storage ring optimised for low ion energies [2].The ring is able to store highly-charged heavy ions produced by the SIS18 synchrotron after deceleration in the Experimental Storage Ring (ESR).Additionally, a local low-energy injector linac allows stand-alone operation with light ions.Electron cooling is a central beam preparation technique and is routinely employed with the full variety of ion beams available at CRYRING@ESR [3].
With the standard working point (Q h , Q v ) close to the lowest-order difference resonance, the longitudinal magnetic field of the electron cooler solenoid is expected to introduce strong coupling of horizontal and vertical betatron motion.Hence, the cooler is accompanied by a second, compensation solenoid of equal integral field, but inverted polarity, to cancel that coupling effect [4].The compensation solenoid largely occupies one of the six drift sections of the ring (cf.Fig. 1).With four more drifts occupied by the injection bumpers, the extraction system, the bunching rf electrode, and the electron cooler itself, this leaves a single section of the ring free for installation of in-ring experiments.
Naturally, the question arises whether removal of the compensation solenoid in favour of additional experimental inserts could be a viable option.Except for a small class of use-cases involving polarised beams, most experiments proposed at CRYRING@ESR are not thought to be inherently disturbed by longitudinal field components, provided a high beam quality can be maintained also in presence of strong betatron coupling.As this mode of operation had never been attempted at MSL, we have performed a series of machine experiments to study the effectiveness of the compensation solenoid and the potential impact of its omission on the properties of stored and cooled beams.

Basic ring operation
At the most fundamental level, solenoid-induced coupling could adversely affect the ring's ability to accept and store beam because of the associated horizontal and vertical emittance exchange [4].As a test, we injected a beam of D + from CRYRING@ESR's local ion source and RFQ linac at 300 keV/u.A few 10 7 ions were then accelerated to 1 MeV/u and stored for typically 2 s.The low rigidity of 0.29 Tm promised high sensitivity to coupling by the electron cooler field, which was set to its typical value of 0.03 T once the ions had been accelerated.The cooler's electron beam, and thus electron cooling itself, was disabled to enhance sensitivity to potential acceptance limits.
The ring operated at its standard working point of (Q h , Q v ) = (2.42,2.42), which was kept identical through all phases of injection, acceleration, and storage.As, in the machine model presently underlying the accelerator controls, the mapping between working point and strengths of the two quadrupole families is imperfect, the magnet settings were manually refined using direct tune measurements by narrow-band transverse radio-frequency knock-out (RF-KO).The sextupole magnets, normally used to correct chromaticities, were left unpowered to exclude their possible contributions to any amount of betatron coupling observed.
Starting from this configuration, the compensation magnet was disconnected from the cooler's main solenoid, with which it is normally powered in series.We then scanned the quadrupole strengths such as to map-out a matrix of working points covering the expected stable region around (Q h , Q v ) = (2.42,2.42) (cf.Fig. 2a).For each setting, we measured the intensity of the accelerated 1-MeV/u D + beam, integrating over 1.5 s of storage.Again, the set tunes during injection, acceleration, and storage were kept identical and varied in-sync during the measurement series.
The results are shown in Fig. 2b, with brighter colours indicating higher stored beam intensities.The second and third order stop-bands surrounding the nominal working point (2.42, 2.42) on all sides are clearly visible.The relatively small area of the stable region is due to For comparison, Fig. 2c shows the same measurement in the standard magnetic configuration of the ring, i.e. with the cooler solenoid compensated and with the sextupole magnets optimised for vanishing horizontal and vertical chromaticities.While the area of the stable region is clearly larger overall, stored beam intensity near the difference resonance, especially at (Q h , Q v ) = (2.42,2.42), is not affected.

Coupling strength
The question how well coupling introduced in the cooler is cancelled by the compensation solenoid is interesting in view of experiments sensitive to longitudinal field components acting on the ions.
We measured the betatron coupling strength in both configurations, with and without compensation, by the method of 'closest tune approach' [5].We prepared a series of quadrupole settings that, in the uncoupled case, correspond to a diagonal scan of (Q h , Q v ), crossing the coupling resonance at (2.42, 2.42) (cf.Fig. 3).With coupling, the measured betatron frequencies exhibit an avoided-crossing behaviour, the smallest difference in the observed tunes being equal to the magnitude of the coupling coefficient |C − |.
Again, the probe beam was D + at 1 MeV/u.Also in this measurement, the sextupole lenses were disabled.The electron cooler solenoid operated at 0.03 T, but the ion beam was uncooled.As shown in Fig. 3a, no coupling is observed with the compensation solenoid enabled: Q h and Q v can cross smoothly within the uncertainty of the RF-KO-based tune measurement, which we determined to be ±3 × 10 −3 .
With the compensation solenoid disabled, the avoided crossing of Q h and Q v near (2.42, 2.42) becomes very apparent, as visible in Fig. 3b.The measurement also shows that, in vicinity of the coupling resonance, any single RF-KO kicker (horizontal or vertical) effectively excites betatron motion in both planes, a clear sign of energy redistribution among the two degrees of freedom of ion motion.From the perturbative coupling theory of Guignard [5], and using the approxima-  tions developed by Simonsson for the CRYRING case [4], we expect a coupling coefficient Therein, B cool is the flux density of the cooler field, L eff its effective length, and (Bρ) 0 the rigidity of the ion beam.With L eff ≈ 2 m and the field set to 0.03 T, we expect |C − | ≈ 0.033 for the 0.29-Tm D + beam, in good agreement with the measured value |C − | exp = 0.032 (3).The dashed and dash-dotted lines in Fig. 3b are betatron tunes computed using MAD/X, given a simplified model of the cooler magnets.

Electron cooling
A central goal of the machine study was to quantify the performance of the electron cooler and the achievable quality of cooled beams in presence of coupling.For the electron cooling tests, we increased the energy of the stored D + beam to 2 MeV/u, allowing the cooler high-voltage supply to operate in a more typical regime, while still keeping the ion rigidity at a low 0.41 Tm.The set working point was kept at (2.42, 2.42) and chromaticity correction was re-enabled.Effectively, betatron coupling leads to entanglement of the horizontal and vertical cooling forces, as ion energy is redistributed among both planes.We tested this by purposely misaligning the cooler's electron beam with respect to the ion axis.The corresponding response of the ion beam is very different for the cases of compensated and uncompensated cooler solenoid, as depicted in Fig. 4. The top panels show the horizontal and vertical projected beam profiles as a function of storage time t, as measured using ionisation profile monitors.Directly after beam injection and acceleration (at t ∼ 2 s), the electron cooler was switched on with its beam vertically misaligned by an angle of ∼2 mrad.
With the compensation solenoid enabled, the resulting non-linear vertical drag leads to strong excitation of betatron oscillation in that plane, while, horizontally, betatron motion is damped by the still properly centred cooling force along that direction, as previously observed in MSL operation [6].Without solenoid compensation, isolated excitation of a single component of betatron motion is not possible.Hence, the vertical drag force widens the beam envelope in both planes.However, as that vertical drag is now partly compensated by the horizontal cooling force, the emittance blow-up along any direction is weaker compared to the isolated vertical excitation in the uncoupled case.
After several seconds of storage, the misalignment of the electron beam was abruptly corrected (dashed lines in Fig. 4), so that the ions were transversely cooled in both planes.The final stage of electron cooling is characterised by exponential shrinking of the beam envelope with time constant τ .Equilibrium of electron cooling and intra-beam scattering defines the final beam size σ ∞ [7].No significant differences in either τ or σ ∞ were found between operation with and without coupling compensation, as shown in the lower panels of Fig. 4.Both measurements were done at an electron density n e = 2.7 × 10 6 cm −3 and the magnetic expansion factor of the electron gun was 50.
The apparently weaker response of the ion envelopes to a misaligned electron beam could make optimal set-up of electron cooling more difficult in presence of coupling.As a check for this, we aligned the cooler beam in both configurations, starting with the assumed 'difficult' case of a disabled compensation solenoid.In both cases, we measured the longitudinal electron drag force via the bunched-beam phase shift method [8].The measurements are shown in Fig. 5, along with fits of Parkhomchuk's semi-empirical cooling force formula, using the effective electron temperature T eff as only free parameter [9].No significant difference in T eff is found, indicating equal cooling force in both cases.The electron density n e was 9.5 × 10 6 cm −3 at expansion 50.

Conclusion
We have tested operation of CRYRING@ESR with disabled cooler solenoid compensation, finding no indication of reduced acceptance or stability near the standard working point.Electron cooling works reliably also in presence of strong betatron coupling.The observed impact on the betatron tunes near the difference resonance is found to be in good agreement with theoretical expectations, and is reduced by at least an order of magnitude with the compensation solenoid enabled.

Figure 1 .
Figure 1.Schematic overview of CRYRING@ESR, with its drift sections labeled according to their main functions.

14thFigure 2 .
Figure 2. Stored beam intensity (D + , 1 MeV/u) measured for a matrix of working points (Q h , Q v ) centred on (2.42, 2.42) as indicated by the shaded area (a), with cooler solenoid compensation and chromaticity correction disabled (b), and for normal magnetic configuration (c).Brighter colours indicate greater ion numbers.

Figure 3 .
Figure 3. Measured tunes for diagonal scans of the set working point across the coupling resonance, as indicated in the inset, with (a) and without (b) compensation of the cooler solenoid.The probe beam was D + at 1.0 MeV/u.

Figure 4 .
Figure 4. Response of the D + beam envelopes to transverse drag and cooling forces with (left) and without (right) the compensation solenoid active.See text.

Figure 5 .
Figure 5. Measured drag force acting on the D + ions as a function of the velocity detuning ∆v between electron and ion beams (black dots), at electron density n e = 9.5 × 10 6 cm −3 (expansion factor 50), after cooler alignment with (top) and without (bottom) coupling compensation.