Beam cooling

Beam cooling is the technique of reducing the momentum spread and increasing the phase-space density of stored particle beams. This paper gives an introduction to beam cooling and Liouville’s theorem, and then it describes the three methods of active beam cooling that have been proven to work so far, namely electron cooling, stochastic cooling, and laser cooling. Ionization cooling is also mentioned briefly

NUMERICAL CALCULATIONS OF THE ELECTRON COOLING DRAG FORCE IN A MAGNETIC FIELD

Abstract The longitudinal drag force that the electrons in an electron cooler exert on a circulating ion beam has been measured at many electron-cooling installations and also at CRYRING. Although different theoretical models have been used for calculation of this drag force, the discrepancy between theory and experiment have sometimes been quite big due to the theoretical difficulty in treating the interaction between charged particles in a magnetic field. We here present the beginning of an attempt to numerically calculate the energy loss suffered by ions in binary collisions with electrons in the presence of a finite magnetic field. Results for the longitudinal drag force are presented for relative velocities between ions and electrons and magnetic fields that are relevant for electron cooling at CRYRING and similar storage rings. THE PROBLEM The magnitude of the drag force that an ion experiences when it moves through the electron beam of an electron cooler has been calculated, with or without the inclusion of a magnetic field, using a number of different approaches such as binary collisions [1], dielectric theory [2] or molecular-dynamics simulations In our case, the electron is more or less strongly bound to a field line and it can approach the ion several times during successive cyclotron orbits. For large impact parameters this is conventionally regarded as the ions colliding with an electron "disk", whose charge is smeared out over the cyclotron orbits and which has a very small transverse motion, leading to an increased drag force. Indeed, a drag force larger than what has been calculated from theories that do not take the magnetic field into account has been observed at several cooler installations. Another feature of magnetized collisions, in contrast to classical Rutherford scattering, is that negative and positive ions have different drag forces. This effect that also has been observed experimentally Here we present the beginning of an attempt to get accurate numerical values for the electron-cooling drag force in the presence of a finite magnetic field using a binarycollision approach. The aim is to calculate the energy loss for heavy ions passing through an electron gas that has the anisotropic temperature and the magnetization that are characteristic of an electron cooler. Outside the scope of this investigation, however, is the inclusion of plasma effects or electron-electron interactions. THE METHOD The method we use to calculate the energy loss of an ion colliding with an electron is simply to numerically integrate the classical equations of motion of the two particles. We define the magnetic field to be in the positive z direction, and the terms 'longitudinal' and 'transverse' refer to the direction of the field. The initial condition is that the electron is performing gyro motion on a circle around the origin in the plane z = 0 with velocity v e,0 . The ion starts far below that plane and moves toward it with a velocity v i,0 directed along the z axis. It scatters against the electron and continues until it no longer is influenced by the force of the electron, whereupon the energy loss suffered by the ion is computed. The energy loss thus gives the longitudinal drag force for an ion that has an initial velocity that is purely longitudinal. This energy loss or drag force is then integrated over all impact parameters of the ion and over all phases of the electron gyro motion (or, equivalently, over an impact-parameter plane assuming that the electron always starts in the same (x, y) coordinate). The drag force is finally normalized to an electron density of 1 × 10 14 m −3 . The force acting between the ion and the electron is a screened Coulomb force, and the Debye length is used as the screening length. Since the Debye length depends on the electron density n e and the electron temperature T , there are two additional choices to be made here. We have used an electron density of 1 × 10 13 m −3 , which is typical for CRYRING, and as the electron temperature we have taken kT e = m e v 2 e,0 /2. However, for a few different combinations of v e,0 and v i,0 other values of λ D were also used in order to test how sensitive the results are to the choice of λ D , see below. The calculations were performed for a magnetic field of 0.1 T, but the results can easily be transformed to other fields. It is readily seen that the equations of motion ar

GEANT4 Studies of Magnets Activation in the HEBT Line for the European Spallation Source

The High Energy Beam Transport (HEBT) line for the European Spallation Source is designed to transport the beam from the underground linac to the target at the surface level while keeping the beam losses small and providing the requested beam footprint and profile on the target. This paper presents activation studies of the magnets in the HEBT line due to backscattered neutrons from the target and beam interactions inside the collimators producing unstable isotopes

European Spallation Source Lattice Design Status

The accelerator of the European Spallation Source (ESS) will deliver 62.5 mA proton beam of 2.0 GeV onto the target, offering an unprecedented beam power of 5 MW. Since the technical design report (TDR) was published in 2013, work has continued to further optimise the accelerator design. We report on the advancements in lattice design optimisations after the TDR to improve performance and flexibility, and reduce cost of the ESS accelerato

Induced activation in accelerator components

The residual activity induced in particle accelerators is a serious issue from the point of view of radiation safety as the long-lived radionuclides produced by fast or moderated neutrons and impact protons cause problems of radiation exposure for staff involved in the maintenance work and when decommissioning the facility. This paper presents activation studies of the magnets and collimators in the High Energy Beam Transport line of the European Spallation Source due to the backscattered neutrons from the target and also due to the direct proton interactions and their secondaries. An estimate of the radionuclide inventory and induced activation are predicted using the GEANT4 code

Experimental N V and Ne VIII low-temperature dielectronic recombination rate coefficients

The dielectronic recombination rate coefficients of N V and Ne VIII ions have been measured at a heavy-ion storage ring. The investigated energy ranges covered all dielectronic recombination resonances attached to 2s -> 2p (Delta n=0) core excitations. The rate coefficients in a plasma are derived and parameterized by using a convenient fit formula. The experimentally derived rate coefficients are compared with theoretical data by Colgan et al. (2004, A&A, 417, 1183) and Nahar & Pradhan (1997, ApJ, 111, 339) as well as with the recommended rate coefficients by Mazzotta et al. (1998, A&A, 133, 403). The data of Colgan et al. and Nahar & Pradhan reproduce the experiment very well over the temperature ranges where N V and Ne VIII are expected to exist in photoionized as well as in collisionally ionized plasmas. In contrast, the recommendation of Mazzotta et al. agrees with the experimental rate coefficient only in the temperature range of collisional ionization. At lower temperatures it deviates from the measured rate coefficient by orders of magnitude. In addition the influence of external electric fields with field strengths up to 1300 V/cm on the dielectronic recombination rate coefficient has been investigated.Comment: 9 pages, 9 figures, to be published in Astronomy & Astrophysic

Diagnostic criterion for crystallized beams

Small ion crystals in a Paul trap are stable even in the absence of laser cooling. Based on this theoretically and experimentally well-established fact we propose the following diagnostic criterion for establishing the presence of a crystallized beam: Absence of heating following the shut-down of all cooling devices. The validity of the criterion is checked with the help of detailed numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR

THE ESS LINAC DESIGN

Abstract The European Spallation Source (ESS) is a 5 MW, 2.5 MeV long pulse proton machine. It represents a big jump in power compare to the existing spallation facilities. The design phase is well under way, with the delivery of a Conceptual Design Report published in the beginning of 2012, and a Technical Design Report in December 2012. Why and how the 5 MW goal influences the parameter choices will be described

A Very Intense Neutrino Super Beam Experiment for Leptonic CP Violation Discovery based on the European Spallation Source Linac: A Snowmass 2013 White Paper

Very intense neutrino beams and large neutrino detectors will be needed in order to enable the discovery of CP violation in the leptonic sector. We propose to use the proton linac of the European Spallation Source currently under construction in Lund, Sweden to deliver, in parallel with the spallation neutron production, a very intense, cost effective and high performance neutrino beam. The baseline program for the European Spallation Source linac is that it will be fully operational at 5 MW average power by 2022, producing 2 GeV 2.86 ms long proton pulses at a rate of 14 Hz. Our proposal is to upgrade the linac to 10 MW average power and 28 Hz, producing 14 pulses/s for neutron production and 14 pulses/s for neutrino production. Furthermore, because of the high current required in the pulsed neutrino horn, the length of the pulses used for neutrino production needs to be compressed to a few $\mu$s with the aid of an accumulator ring. A long baseline experiment using this Super Beam and a megaton underground Water Cherenkov detector located in existing mines 300-600 km from Lund will make it possible to discover leptonic CP violation at 5 $\sigma$ significance level in up to 50% of the leptonic Dirac CP-violating phase range. This experiment could also determine the neutrino mass hierarchy at a significance level of more than 3 $\sigma$ if this issue will not already have been settled by other experiments by then. The mass hierarchy performance could be increased by combining the neutrino beam results with those obtained from atmospheric neutrinos detected by the same large volume detector. This detector will also be used to measure the proton lifetime, detect cosmological neutrinos and neutrinos from supernova explosions. Results on the sensitivity to leptonic CP violation and the neutrino mass hierarchy are presented.Comment: 28 page