Study of the beam-cavity interaction in the PS 10 MHz RF system

The eleven main accelerating cavities of the Proton Synchrotron (PS) at CERN consist of two ferrite-loaded coaxial lambda/4 resonators each. Both resonators oscillate in phase, as their gaps are electrically connected by short bars. They are in addition magnetically coupled via the bias loop used for cavity tuning. The cavities are equipped with a wide-band feedback system, limiting the beam loading, and a further reduction of the beam induced voltage is achieved by relays which short-circuit each half-resonator gap when the cavity is not in use. Asymmetries of the beam induced voltage observed in the two half-cavities indicate that the coupling between the two resonators is not as tight as expected. The total cavity impedance coupling to the beam may be affected differently by the contributions of both resonators. A dedicated measurement campaign with high-intensity proton beam and numerical simulation have been performed to investigate the beam-cavity interaction. This paper reports the result of the study and the work aiming at the development of a model of the system, including the wide-band feedback, which reproduces this interaction

The PS 10 MHz High Level RF System Upgrade

In view of the upgrade of the injectors for the High Luminosity LHC, significantly higher bunch intensity is required for LHC-type beams. In this context an upgrade of the main accelerating RF system of the Proton Synchrotron (PS) is necessary, aiming at reducing the cavity impedance which is the source of longitudinal coupled-bunch oscillations. These instabilities pose as a major limitation for the increase of the beam intensity as planned after LS2. The 10 MHz RF system consists in 11 ferrite loaded cavities, driven by tube-based power amplifiers for reasons of radiation hardness. The cavity-amplifier system is equipped with a wide-band feedback that reduces the beam induced voltage. A further reduction of the beam loading is foreseen by upgrading the feedback system, which can be reasonably achieved by increasing the loop gain of the existing amplification chain. This paper describes the progress of the design of the upgraded feedback system and shows the results of the tests on the new amplifier prototype, installed in the PS during the 2015-16 technical stop. It also reports the first results of its performance with beam, observed in the beginning of the 2016 run

Implementation of synchronised PS-SPS transfer with barrier buckets

For the future intensity increase of the fixed-target beams in the CERN accelerator complex, a barrier-bucket scheme has been developed to reduce the beam loss during the 5-turn extraction from the PS towards the SPS, the so-called Multi-Turn Extraction. The low-level RF system must synchronise the barrier phase with the PS extraction and SPS injection kickers to minimise the number of particles lost during the rise times of their fields. As the RF voltage of the wide-band cavity generating the barrier bucket would be too low for a conventional synchronisation, a combination of a feedforward cogging manipulation and the real-time control of the barrier phase has been developed and tested. A deterministic frequency bump has been added to compensate for the imperfect circumference ratio between PS and SPS. This contribution presents the concept and implementation of the synchronised barrier-bucket transfer. Measurements with high-intensity beam demonstrate the feasibility of the proposed transfer scheme.Comment: Talk presented at LLRF Workshop 2022 (LLRF2022, arXiv:2208.13680

Electron Cloud Mitigation by Fast Bunch Compression in the CERN PS

A fast transverse instability has been observed with nominal LHC beams in the CERN Proton Synchrotron (PS) in 2006. The instability develops within less than 1 ms, starting when the bunch length decreases below a threshold of 11.5 ns during the RF procedure to shorten the bunches immediately prior to extraction. An alternative longitudinal beam manipulation, double bunch rotation, has been proposed to compress the bunches from 14 ns to the 4 ns required at extraction within 0.9 ms, saving some 4.5 ms with respect to the present compression scheme. The resultant bunch length is found to be equivalent for both schemes. In addition, electron cloud and vacuum measurements confirm that the development of an electron cloud and the onset of an associated fast pressure rise are delayed with the new compression scheme. Beam dynamics simulations and measurements of the double bunch rotation are presented as well as evidence for its beneficial effect from the electron cloud standpoint

Controlled Longitudinal Emittance Blow-Up in the CERN PS

The longitudinal emittance of the bunches in the CERN PS must be increased before transition crossing to avoid beam loss due to a fast vertical instability. This controlled blow-up is essential for all high-intensity beams in the PS, including those for transfer to the LHC. The higher harmonic 200MHz RF system (six cavities) used for this blow-up has to generate a total RF voltage which, for the most demanding blow-up, is comparable to the voltage of the main RF cavities. The system is presently subject to a major upgrade and a possible reduction in the number of higher harmonic RF cavities installed is under consideration. To determine the minimum required, detailed simulations and machine development studies to optimize the longitudinal blow-up have been performed. Further options to produce the required longitudinal emittance using other RF systems are also analyzed. The results obtained for the different scenarios for the longitudinal blow-up are presented and compared in this paper

Commissioning and performance of a phase-compensated optical link for the AWAKE experiment at CERN

In this work, we analyze the performance of the solution adopted for the compensation of the phase drift of a 3 km optical fiber link used for the AWAKE experiment at CERN. The link is devoted to transmit the reference signals used to synchronize the SPS beam with the experiment to have a fixed phase relation, regardless of the external conditions of the electronics and the link itself. The system has been operating for more than a year without observed drift in the beam phases. Specific measurements have proven that the jitter introduced by the system is lower than 0.6 ps and the maximum phase drift of the link is at the picosecond level.Comment: Poster presented at LLRF Workshop 2017 (LLRF2017, arXiv:1803.07677

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}<H<H_{c2}$. The critical behaviour in the vicinity of the critical points is of the Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.Comment: 90 pages, 33 figures, extensive revisio

Dependence of e-cloud on the longitudinal bunch profile: studies in the PS & extension to the HL-LHC

Recent studies have shown that the prospects for significantly increasing bunch intensities in the LHC for the luminosity upgrade (HL-LHC) may be severely limited by the available cryogenic cooling capacity and the electron-cloud (EC) driven beam instability. However, it is planned that during the HL-LHC era the bunch intensities in the LHC will go up by nearly a factor of two compared to the LHC-design values. This motivates the exploration of additional EC mitigation techniques that can be adopted in addition to those already in place. Preliminary simulations indicated that long flat bunches can be beneficial over Gaussian bunches to reduce the EC build up. Rigorous studies using realistic bunch profiles have never been done. Therefore, we have undertaken an in-depth investigation in the CERN 26 GeV PS to see if we can validate the previous findings and, in particular, if flattening the bunch can mitigate the EC. Here we present the results from dedicated EC measurements in the PS using a variety of bunch shapes and a comparison with simulations. Finally, we investigate if reshaping the bunch profiles using a 2nd harmonic rf cavity can mitigate EC in the HL-LHC

Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.Comment: 32 pages, 7 figures; references added, minor corrections, final versio

Short-distance thermal correlations in the XXZ chain

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < \Delta < 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure