Beam dynamics design studies of a superconducting radioactive ion beam postaccelerator

The HIE-ISOLDE project at CERN proposes a superconducting upgrade to increase the energy range and quality of the radioactive ion beams produced at ISOLDE, which are currently postaccelerated by the normal conducting radioactive ion beam experiment linac. The specification and design choices for the HIE-ISOLDE linac are outlined along with a comprehensive beam dynamics study undertaken to understand and mitigate the sources of beam emittance dilution. The dominant cause of transverse emittance growth was attributed to the coupling between the transverse and longitudinal motions through the phase dependence of the rf defocusing force in the accelerating cavities. A parametric resonance induced by the coupling was observed and its excitation surveyed as a function of transverse phase advance using numerical simulations and analytic models to understand and avoid the regions of transverse beam instability. Other sources of emittance growth were studied and where necessary ameliorated, including the beam steering force in the quarter-wave resonator and the asymmetry of the rf defocusing forces in the solenoid focusing channel. A racetrack shaped beam port aperture was shown to improve the symmetry of the fields in the high-$\beta$ quarter-wave resonator and reduce the loss of acceptance under the offset used to compensate the steering force. The methods used to compensate the beam steering are described and an optimization routine written to minimize the steering effect when all cavities of a given family are offset by the same amount, taking into account the different velocity profiles across the range of mass-to-charge states accepted. The assumptions made in the routine were shown to be adequate and the results well correlated with the beam quality simulated in multiparticle beam dynamics simulations. The specification of the design tolerances is outlined based on studies of the sensitivity of the beam to misalignment and errors, with particular emphasis on the phase and amplitude stability required for the independently phased quarter-wave resonators.

Figure 1

A first-order calculation of the energy profile along the linac for $A/q=2.5$ and 4.5 in both acceleration and deceleration modes.

Figure 2

The accelerating properties of the low-$\beta$ (${\beta }_g=6.3\%$) and high-$\beta$ (${\beta }_g=10.3\%$) cavities.

Figure 3

The layout of the low (a) and high (b) energy cryomodules. Distances are in units of mm.

Figure 4

The lattice design of the HIE-ISOLDE linac.

Figure 5

The longitudinal acceptance in the complete upgrade with different intercryomodule distances. The nominal beam at injection is presented and the acceptance quantified by maximizing the emittance of the nominal beam as well as by fitting an rms ellipse to the accepted particle distribution.

Figure 6

The transverse emittance growth as a function of transverse phase advance per focusing period with an intercryomodule distance of 80 cm.

Figure 7

The first-order analytic prediction of the emittance growth in the high energy section calculated using Eq. (9) assuming a longitudinal emittance of $2\pi \mathrm{keV}/\mathrm{u}\mathrm{ns}$. Alongside, the second-order prediction is plotted.

Figure 8

The resonant growth in transverse emittance at output as a function of the focusing strength in the low energy section.

Figure 9

The nominal beam parameters simulated at first order using the LANA code: $A/q=4.5$ to $10\mathrm{MeV}/\mathrm{u}$.

Figure 10

The position of the center of the noses relative to the center of the beam port aperture parametrized by $\Delta$.

Figure 11

The geometry of the nominal (NOM) high-$\beta$ cavity. The beam offset ($\delta$) inside the nominal aperture is shown inset on the left and a positive value of $\Delta$ shows a vertical offset of the noses with respect to the center of the beam port on the top right.

Figure 12

The steering effect in the high-$\beta$ cavity for $A/q=4.5$ operating at a synchronous phase of $-20°$.

Figure 13

Contours of ${\sigma }_{\Delta y^{\prime }}$ (mrad) in the high energy section as a function of $y_0$ and $\delta$, with the beam ports centered on the nose ($\Delta =0\mathrm{mm}$).

Figure 14

A comparison of the single-particle optimization routine with TRACK as a function of $y_0$ and $\delta$, with the beam ports centered on the nose ($\Delta =0\mathrm{mm}$).

Figure 15

The consequence of positioning the beam port 2 mm above and below the center of the noses ($\Delta =\pm 2\mathrm{mm}$).

Figure 16

The cavity variants. Dimensions are in mm.

Figure 17

The asymmetry of the rf defocusing forces in the vertical and horizontal planes for the nominal cavity and the two variants investigated.

Figure 18

A comparison of the emittance growth in the high energy section, representing the intermediate upgrade, as a function of focusing strength in the LANA and TRACK codes.

Figure 19

A survey of the loss in acceptance operating at 90° phase advance per period as a function of the solenoid alignment tolerance for BPM tolerances in the range 0.1–0.5 mm and cavity tolerances in the range 0.1–1.0 mm.

Figure 20

The time-averaged rms emittance growth as a function of the number of high-$\beta$ cavities in the intermediate upgrade for a total jitter of 1° and 1% in amplitude and phase, respectively.

Figure 21

The time-averaged rms longitudinal emittance growth factor as a function of the rf stability in the high energy section.