Transverse electron cooling of heavy molecular ions

Transverse electron cooling of heavy molecular ions has been studied at the Test Storage Ring (TSR). Electron beams from a cold GaAs:(Cs,O) photocathode, with kinetic energies down to 31 eV, have been used for cooling of singly-charged ions of masses up to 41 u. We believe that these are the heaviest singly-charged ions for which successful electron cooling has been reported so far. Transverse ion-beam emittances $\ll 1\mu \mathrm{m}$ were reached after typically several seconds of cooling time. The measured transverse cooling rates agree with a simple binary-collision model, assuming a transverse electron temperature of approximately $1\mathrm{meV}/k_{\mathrm{B}}$. The results serve as benchmark for electron cooling at the new Cryogenic Storage Ring, which uses the same photocathode electron source and is targeting singly-charged ions of even higher mass.

Figure 1

Overview of the heavy-ion storage ring TSR: After injection from a linear accelerator (1, not shown), singly-charged molecular ions were electron-cooled in the photocathode Electron Target (2). Recombination (3) led to neutral products that left the ring via an extraction beam line and were recorded by a fragment-imaging detector (4, not shown). The primary electron cooler of TSR (5) is shown only schematically, as it is not discussed here. The inset (6) shows the beta (${\beta }_x$ and ${\beta }_y$) and horizontal dispersion ($D_x$) functions of the TSR in standard operation mode [30]. The solid blue line in the graph indicates the position of the Electron Target.

Figure 2

Overview of the Electron Target (2 in Fig. 1). The electron beam (blue dashed line) was emitted from a cold GaAs:(Cs,O) photocathode (1) embedded in a strong axial magnetic field. Magnetic expansion of the beam took place at the entrance of the adiabatic acceleration section (2). For low ion velocities, as discussed here, the latter was not used, as electrons reached their final energy already in the electron gun. A toroidal coil (3) merged the electrons with the ion beam (solid red line). After a 1.5-m-long interaction section (4) the beams were separated by another toroid. After deceleration (5), the electrons were dumped into a Faraday cup (6). The GaAs:(Cs,O) emitter was illuminated in transmission mode by an 808-nm laser from the photocathode setup (7). The latter contains facilities for in-vacuum cleaning and reactivation of cathodes (8), allowing quasicontinuous operation.

Figure 3

Transverse electron cooling of ${}^{16}\mathrm{O}{}^{18}{\mathrm{O}}^{+}$ at 2.7 MeV ($79\mathrm{keV}/\mathrm{nucleon}$). The left and right subfigures show the horizontal ($x$) and vertical ($y$) ion motions, respectively. Electron cooling started directly at ion injection (0 s storage time). Recombination of the molecular ion in the cooler led to neutral fragments ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ that were detected via neutral-fragment imaging. The top left frames show the distribution of the reconstructed centers-of-mass (c.m.) of these fragments as a function of storage time. The density of dots in the histogram is proportional to the density of hits on the detector. For 1-s time intervals, normal distributions were fit to the vertical and horizontal c.m. histograms, as exemplified in frames (a), (b), and (c). The obtained standard deviations are shown in the lower left frames. From 7 s of storage time, the evolution of the horizontal and vertical beam envelopes can be fit by an exponential decay (solid red curve), yielding the cooling times ${\tau }_{\mathrm{cool}}$ and final envelope sizes ${\widehat{\sigma }}^{\mathrm{f}}$ (see text).

Figure 4

Transverse electron cooling of ${\mathrm{HS}}^{+}$ at 2.7 MeV ($81\mathrm{keV}/\mathrm{nucleon}$). Although electron cooling started directly at ion injection, data was recorded only for storage times $\ge 2\mathrm{s}$. The plots are analogous to the case of ${}^{16}\mathrm{O}{}^{18}{\mathrm{O}}^{+}$ from Fig. 3.

Figure 5

Measured transverse cooling times ${\tau }_{\mathrm{cool}}$ for beams of ${\mathrm{CF}}^{+}$ ($m_{\mathrm{i}}=31\mathrm{u}$) as a function of the electron density $n_e$. The short-dashed black curve is a simplified $1/n_e$-dependence as in Eq. (12). The other curves are fits of Eq. (11) using the cooling rates $\lambda$ from Eqs. (9) (long-dashed blue) and (8) (solid red), respectively, thus taking the density- and temperature-dependence of $L_C$ into account.

Figure 6

Cooling time ${\tau }_{\mathrm{cool}}$ for ${\mathrm{HF}}^{+}$ at 4.7-MeV ($233\mathrm{keV}/\mathrm{nucleon}$) as a function on the expansion factor $\alpha$ of the electron beam, with other Target parameters held fixed. Only the horizontal component of the betatron motion has been analyzed. The data is compared to a simplified ${\alpha }^{-1/2}$-law (short-dashed black curve) and to the models from Eqs. (9) (long-dashed blue) and (8) (solid red) as described in the text.

Figure 7

Overview of the measured normalized cooling rates for magnetic expansion $\alpha =20$. The dots represent the data from Table 1. The dotted-black curve is a fit of the measurement to a $1/m_{\mathrm{i}}$-model as expected from Eq. (12). The shaded areas delimit the expected rates in the electron temperature interval $0.5\mathrm{meV}/k_{\mathrm{B}}\le T_e\le 1.5\mathrm{meV}/k_{\mathrm{B}}$ for a flattened and isotropic electron velocity distribution, as indicated.

Figure 8

Steady-state beam diameters (68% envelopes) after electron cooling. The black dots represent the data from Table 2. The dashed red line indicates the expected ratio of diameters at equal horizontal and vertical divergence, given the amplitudes of the beta functions of the TSR at the Electron Target (see also Fig. 1). The blue dashed curve also accounts for the dispersion ($D_x=2.0\mathrm{m}$) in the Target, assuming a momentum spread $\delta p/p={\sigma }_y/{\beta }_y$ (see text).

Figure 9

Steady-state horizontal ($x$) and vertical ($y$) beam diameters $2\sigma$ as a function of ion mass. The shaded green area shows the span of expected horizontal beam diameters in equilibrium between electron cooling and IBS heating [Eq. (16)], given the observed ${\tau }_{\mathrm{cool}}$. The upper and lower limits correspond to ${10}^6$ and ${10}^4$ stored ions, respectively.

Figure 10

Horizontal and vertical transverse ion beam temperatures after electron cooling. The colored horizontal bars indicate the best-fit electron temperatures $T_e$ corresponding to the observed cooling rates, for flat and isotropic velocity distributions. The shaded green area is the expected ion temperature corresponding to the IBS limit (see text).