Ion Beam In Storage Ring Research Articles

Polarization-dependent disappearance of a resonance signal: Indication for optical pumping in a storage ring?

We report on laser spectroscopic measurements on ${\mathrm{Li}}^{+}$ ions in the experimental storage ring ESR at the GSI Helmholtz Centre for Heavy Ion Research. Driving the $2s\text{ }{^{3}S}_{1}(F=3/2)\ensuremath{\leftrightarrow}2p\text{ }{^{3}P}_{2}(F=5/2)\ensuremath{\leftrightarrow}2s\text{ }{^{3}S}_{1}(F=5/2)$ $\mathrm{\ensuremath{\Lambda}}$-transition in $^{7}{\mathrm{Li}}^{+}$ with two superimposed laser beams it was found that the use of circularly polarized light leads to a disappearance of the resonance structure in the fluorescence signal. This can be explained by optical pumping into a dark state of polarized ions. We present a detailed theoretical analysis of this process that supports the interpretation of optical pumping and demonstrates that the polarization induced by the laser light must then be at least partially maintained during the round trip of the ions in the storage ring. Such polarized ion beams in storage rings will provide opportunities for new experiments, especially on parity violation.

Colliding or co-rotating ion beams in storage rings for EDM search

A new approach to search for and measure the electric dipole moment (EDM) of the proton, deuteron and some other light nuclei is presented. The idea of the method is to store two ion beams, circulating with different velocities, in a storage ring with crossed electric and magnetic guiding fields. One beam is polarized and its EDM is measured using the so-called ‘frozen spin’ method. The second beam, which is unpolarized, is used as a co-magnetometer, sensitive to the radial component of the ring’s magnetic field. The particle’s magnetic dipole moment (MDM) couples to the radial magnetic field and mimics the EDM signal. Measuring the relative vertical orbit separation of the two beams, caused by the presence of the radial magnetic field, one can control the unwanted MDM spin precession. Examples of the parameters for EDM storage rings for protons and other species of ions are presented. The use of crossed electric and magnetic fields helps to reduce the size of the ring by a factor of 10–20. We show that the bending radius of such an EDM storage ring could be about 2–3 m. Finally, a new method of increasing the spin coherence time, the so-called ‘spin wheel’, is proposed and its applicability to the EDM search is discussed.

Cooling force on ions in a magnetized electron plasma

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. In the common rest frame of the ion and the electron beam, the ion is subjected to a drag force and it experiences a loss or a gain of energy which eventually reduces the energy spread of the ion beam. A calculation of this process is complicated as the electron velocity distribution is anisotropic and the cooling process takes place in a magnetic field which guides the electrons. In this paper the cooling force is calculated in a model of binary collisions (BC) between ions and magnetized electrons, in which the Coulomb interaction is treated up to second order as a perturbation to the helical motion of the electrons. The calculations are done with the help of an improved BC theory which is uniformly valid for any strength of the magnetic field and where the second-order two-body forces are treated in the interaction in Fourier space without specifying the interaction potential. The cooling force is explicitly calculated for a regularized and screened potential which is both of finite range and less singular than the Coulomb interaction at the origin. Closed expressions are derived for monochromatic electron beams, which are folded with the velocity distributions of the electrons and ions. The resulting cooling force is evaluated for anisotropic Maxwell velocity distributions of the electrons and ions.

Light sources based on relativistic ion beams

Possible parameters of Light Sources (LS) based on Backward Rayleigh scattering (BRS) of laser photons on relativistic ion beams in storage rings are discussed. It was shown that the parameters of the LS based on the RHIC storage ring (dedicated to high energy physics now) satisfy the requirements of the 2nd generation LS. Using the ordinary or enhanced radiative cooling of ion beams in storage rings by broad-band lasers will permit to decrease essentially their emittance, dimensions, angular and energy spreads and convert them to the next generation of LS.

Linear polarization of x-ray photons in HFQ transitions of polarized He-like ions with application to the search for parity nonconservation effects

Theoretical concepts in the production and controlling of polarized highly charged ion beams in storage rings are investigated. A scheme for the control of the degree of ion beam polarization, based on the observation of the linear polarization of emitted x-ray photons in hyperfine quenched (HFQ) decay of excited levels of polarized He-like ions, is presented. One of the important motivations for the production of polarized ion beams is the possibility of observing the parity nonconservation (PNC) effects in HFQ transitions in He-like highly charged ions, where these effects can reach an unprecedented high value for atomic physics. The measurement of these effects requires online diagnostics of the degree of ion beam polarization. The possible schemes for such experiments as well as estimates of the magnitude of the observable PNC effects are presented.

Is laser cooling for heavy-ion fusion feasible?

Heavy-ion beams, each with current in the kiloampere range and particle energy in the giga-electronvolt range, must be focused onto a millimetre-size spot to provide the power required for ignition of high-gain targets for inertial confinement fusion. However, the focal spot size is always enlarged by chromatic aberration generated by the thermal spread of the beam ions in the direction of beam propagation. Enlarged focal spot degrades the target performance. For high-current beams, the conventional remedy for chromatic aberration using sextupole magnets has been shown to be ineffective. If novel correction schemes can be found, then the spot size can be reduced to below that previously believed possible. Smaller spots can mean lower energy targets so that the heavy-ion fusion (HIF) scenario can look more attractive. Success in laser cooling of ion beams in storage rings has inspired us to explore the feasibility of applying laser cooling for HIF, and the recirculator configuration proposed for HIF appears to be well suited for this purpose. However, using particle-in-cell simulations and theoretical arguments, we demonstrate in this paper that although laser cooling of heavy-ion beams is feasible in principle, the rapid velocity-space diffusion of ions in the bump-in-tail distribution, set up by the cooling lasers, limits the velocity-space compressibility of the thermal spread along the beam. Consequently, laser cooling is impractical for high-current, heavy-ion beams for the proposed recirculator configuration. Nevertheless, if the recirculator architecture or the target requirement can reduce the beam current, then the cooling scheme described here would be useful. This scheme may also be applicable to the RF linac and storage ring approach to HIF.

Cooling of ions and antiprotons with magnetized electrons

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. More recently antiprotons have been cooled in traps, first by electrons and then by positrons in order to produce antihydrogen atoms as simplest form of antimatter for CPT-tests. During these cooling processes the light particles are guided by strong external magnetic fields which imposes a challenge to the theoretical description. Within the binary collision model we treat the Coulomb interaction as second-order perturbation to the helix motion of the light particles and also by numerical simulations. In the complementary dielectric theory we calculate the polarization of the light particles by solving the nonlinear Vlasov–Poisson equation as well as linear response. It turns out that the linearization becomes dubious at low ion velocities. In the presence of a strong magnetic field the numerically expensive solution of the Vlasov–Poisson equation is the method of choice, alternatively one may employ the binary collision model. Within this approach simulations must be employed for a repulsive interaction, e.g. antiproton–electron, or for highly charged ions. Drag forces F→ are given as functions of the ion velocity v→i and can be used as input for codes to calculate cooling times.

Schemes for radiative polarization of ion beams in storage rings

It is argued that in storage rings hydrogen-like ions can be polarized due to their large magnetic moment and the existence of hyperfine ground-state levels. While spontaneous spin-flip transitions between the Zeeman sublevels in magnetic fields of the order of a few T lead to unacceptable building-up times of the polarization, this time is drastically reduced by radiative transitions between selectively laser-excited sublevels of different hyperfine states. Model calculations for 15163Eu with nuclear spin 5/2 show that under realistic experimental conditions the electron and the nucleus will be polarized close to 100% within several minutes. The proposed scheme can easily be applied to other ions with nuclear spin >1/2.

Drag force on ions in magnetized electron plasmas

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. In the common rest frame of the ion and the electron beam the ion is subjected to a drag force and it experiences a loss or a gain of energy which eventually reduces the energy spread of the ion beam. A calculation of this process is complicated as the electron velocity distribution is anisotropic and the cooling process takes place in a magnetic field which guides the electrons. In this paper the drag force and the energy loss are calculated in a model of binary collisions between ions and magnetized electrons, in which the Coulomb interaction is treated up to second order as a perturbation to the helical motion of the electrons. The energy loss is related to the transfer of relative velocity in a collision. Particular attention must be paid to the non-conservation of the center-of-mass motion in the presence of a magnetic field. Three kinetic regimes can be identified, depending on the relative magnitude of the distance of closest approach, the cyclotron radius and the pitch of the helical motion. Closed expressions for the energy loss are derived for monochromatic electron beams, which are folded with the velocity distribution of the electrons. Hard collisions are taken into account by regularizing the integrals with respect to the impact parameter at small distances. The resulting energy loss of the ion and the drag force are evaluated for anisotropic Maxwell velocity distributions of the electrons. The influence of the magnetic field is as follows: the energy loss is reduced if the ion moves parallel to the field, while it is enhanced if the ion velocity has a component transverse to the field. This enhancement is not as large as in the dielectric theory and in previous kinetic models.

Crystalline beam emulations in a pulse-excited linear Paul trap

This paper considers a pulsed voltage excitation of the quadrupole electrodes of a linear Paul ion trap. The transverse dynamics of ions in this time-varying electric field is analogous to that of charged particles in the strong focusing magnetic lattice of a storage ring. By laser cooling ions stored in a pulse-excited linear Paul trap theoretical results on the stability of crystalline ion beams in storage rings can be tested. The stability of ion motion in a pulse-excited trap is derived in (q,a)-parameter formalism and we show where in (q,a) space to expect the formation of Coulomb crystals according to the theory of crystalline ion beams.

Tapered laser cooling of stored coasting ion beams

We propose a scheme for tapered laser cooling of coasting ion beams in storage rings. Tapered cooling has recently been shown to be crucial for attaining crystalline ion beams. The scheme proposed here, based on a relative displacement of a co- and a counterpropagating Gaussian laser beam, gives a radial variation in the equilibrium velocities to which particles are cooled. The variation is approximately linear in a relatively large range transverse to the laser beams. Expressions for the spatially dependent equilibrium velocities and the range of the tapered cooling forces are derived. We discuss the dependence on laser beam parameters as well as the limitations of this cooling scheme.

Particle-in-cell simulation of the stopping power in the presence of a magnetic field

In the last years electron cooling has become a well established method to reduce the phase space volume of ion beams in storage rings. We use a Particle-In-Cell (PIC) simulation to study the interaction between the ion beam and the electron plasma in the cooler. We investigate the energy loss of heavy, highly charged ions in magnetized electron plasmas and focus on the influence of the magnetic field.

Diagnostic methods to detect the properties of cooled heavy ion beams in storage rings

Non-destructive diagnostics for the determination of the beam properties are crucial for experiments with cooled heavy ion beams in storage rings. The techniques presently available to measure the longitudinal momentum spread and the transverse emittances are briefly described. The experimental achievements in the preparation of cooled heavy ions are summarized. Intrabeam scattering heating is the main limitation for attaining highest beam quality as stronger compression in phase space causes a correspondingly increased heating rate. In the low intensity regime a suppression of intrabeam scattering was observed as a sudden reduction of the momentum spread. This effect opens possibilities for precision experiments with beams of unprecedented quality.

Radiative cooling of ion beams in storage rings by broad-band lasers.

A scheme for cooling nonfully stripped ions in storage rings is described in which photons in a counterpropagating laser beam are resonantly scattered by atomic electrons. The laser frequency is near one of the ion's transition frequencies, with a sufficiently broad bandwidth to cover the ions' full Doppler spectrum. Except for the resonance, this cooling is similar to radiative cooling in electron storage rings and works in all three directions. The scheme is distinct from the usual laser cooling which uses narrow-band lasers to resolve the line shape of individual ions. Explicit examples show that the scheme provides an efficient cooling of the beams, while producing intense $\ensuremath{\gamma}$ rays or x rays.

Simulation of the formation and detection of one-dimensional ordered ion beams.

Ion beam ordering in a realistic cooler storage ring was investigated using a molecular dynamics computer code developed for this study. A parameter C(T) was introduced to quantify ordering effects in ion beams as a function of temperature. The code was applied to singly (${\mathrm{Li}}^{+}$) and highly (${\mathrm{Ar}}^{18+}$) charged ion beams under the action of longitudinal (laser) and uniform (electron) cooling in CRYRING (Stockholm storage ring). It was found that one-dimensional (1D) ordering can be formed in dilute (\ensuremath{\sim}${10}^{6}$ particles) ${\mathrm{Li}}^{+}$ and ${\mathrm{Ar}}^{18+}$ beams at longitudinal temperatures \ensuremath{\sim}1 and \ensuremath{\sim}${10}^{2}$ mK, respectively, even for relatively high transverse temperatures. The heat exchange between longitudinal and transverse degrees of freedom in singly and highly charged ion systems was compared under similar conditions. High-frequency longitudinal Schottky spectra are derived by fast Fourier transforms, to illustrate a possible method of observing 1D ordering of ion beams in storage rings.

Longitudinal Equilibrium Distributions of Ion Beams in Storage Rings with Internal Targets and Electron Cooling

A derivation of the model used to describe the longitudinal drag rate is presented along with analytic equations to describe various aspects of the longitudinal equilibrium of an ion beam in a storage ring with internal targets and electron cooling. The effects of transverse and longitudinal heating, cathode power supply ripple voltage, and the electron beam space charge depression are discussed.