Marek Gasior

Improving FFT Frequency Measurement Resolution by Parabolic and Gaussian Spectrum Interpolation

Discrete spectra can be used to measure frequencies of sinusoidal signal components. Such a measurement consists of digitizing a compound signal, performing windowing of the signal samples and computing their discrete magnitude spectrum, usually by means of the Fast Fourier Transform algorithm. Frequencies of individual components can be evaluated from their locations in the discrete spectrum with a resolution depending on the number of samples. However, the frequency of a sinusoidal component can be determined with improved resolution by fitting an interpolating parabola through the three largest consecutive spectrum bins corresponding to the component. The abscissa of its maximum constitutes a better frequency approximation. Such a method has been used for tune measurement systems in circular accelerators. This paper describes the efficiency of the method, depending on the windowing function applied to the signal samples. A typical interpolation gain is one order of magnitude. Better results are obtained with Gaussian interpolation, offering frequency resolution improvement by more than two orders of magnitude when used with windows having fast sidelobe decay. An improvement beyond three orders of magnitude is possible with steep Gaussian windows. These results are confirmed by laboratory measurements. Both methods assume the measured frequency to be constant during acquisition and the spectral peak corresponding to the measured component to constitute a local maximum in a given band of the input signal discrete spectrum.

Transverse impendance of LHC collimators

The transverse impedance in the LHC is expected to be dominated by the numerous collimators, most of which are made of Fibre-Reinforced-Carbon to withstand the impacts of high intensity proton beams in case of failures, and which will be moved very close to the beam, with full gaps of few millimetres, in order to protect surrounding super-conducting equipments. We present an estimate of the transverse resistive-wall impedance of the LHC collimators, the total impedance in the LHC at injection and top energy, the induced coupled-bunch growth rates and tune shifts, and finally the result of the comparison of the theoretical predictions with measurements performed in 2004 and 2006 on a prototype collimator installed in the SPS.

The FPGA-based continuous FFT tune measurement system for the LHC and its test at the CERN SPS

A base band tune (BBQ) measurement system has recently been developed at CERN based on a high- sensitivity direct-diode detection technique followed by a high resolution FFT algorithm implemented in an FPGA. The FPGA based digital processing allows the acquisition of continuous real-time spectra with 32-bit resolution, while a digital frequency synthesiser (DFS) can provide acquisition synchronised chirp excitation. All the implemented algorithms support dynamic reconfiguration of processing and excitation parameters. Results from both laboratory measurements and tests performed with beam at the CERN SPS will be presented.

Measurements of the LHC Collimator Impedance with Beam in the SPS

The transverse impedance of the LHC collimators will likely dominate the overall transverse impedance in the LHC at high energies and potentially limit the maximum intensity. A prototype collimator was recently tested in the SPS. Small, but significant tune shifts depending on the collimator position have been observed using different independent high resolution tune measurement methods. In addition trapped modes predicted from numerical simulation at the ends of the collimator jaws have been identified by bench measurement techniques as well as with the beam. We present a description of the measurements and an analysis of the results.

Influence of varying tune width on the robustness of the LHC tune PLL and its application for continuous chromaticity measurement

Tune and chromaticity measurement is an integral part of safe and reliable LHC operation. Tight tolerances on the maximum transverse beam excursions allow oscillation amplitudes of less than 30 mum. This leaves only a small margin for transverse beam and momentum excitations required for measuring tune and chromaticity. This contribution discusses a robust tune phase-locked-loop (PLL) operation in the presence of non-linearities and varying chromaticity. The loop design was tested at the SPS, using the LHC PLL prototype system. The system was also used to continuously measure tune width and chromaticity, using resonant transverse excitations of the tune side-slopes.

Application of avalanche generators in laboratory measurements

Nanosecond pulses of large amplitudes are required for laboratory measurements in several domains, including particle accelerator beam instrumentation. Producing such pulses can be efficiently achieved with so called avalanche generators. In these generators an external delay line, charged to relatively high voltage, is periodically discharged to the generator output exploiting the avalanche breakdown effect in a bipolar junction transistor. This paper describes a number of avalanche generators built and used by the authors, including versions with trigger and amplitude modulation inputs. The described generators were constructed primarily to produce pulses simulating beam-induced signals from the Large Hadron Collider. They can, however, be useful for any measurements where nanosecond pulses with amplitudes of tens of volts are required.

Simultaneous Tune and Coupling Feedback during RHIC Run 6

The Relativistic Heavy Ion Collider (RHIC) is a versatile facility, capable of operating with both polarized protons and a variety of ion species over a broad range of energies. Acceleration ramp requirements change frequently to meet the needs of the physics experiments. There has been an ongoing effort at RHIC to implement reliable betatron tune feedback as a tool for ramp development, and possibly to control tune during routine operations. Vertical orbit fluctuations in the chromaticity correction sextupoles during ramping are sufficient to fully couple the tunes. This complicates tune control, and with tune feedback causes the basis in which tune errors are reported to not match the basis used to correct the quadrupole currents, leading to feedback instability. This problem has been overcome by using realtime measurements of the coupling projections of both betatron eigenmodes to close feedback loops onto two skew quadrupole families. This minimizes coupling and matches the tune and coupling reporting basis to the correction basis. We report on successful simultaneous tune and coupling feedback during RHIC ramp development and implications of this effort for the LHC.

Differential phase detector for precise phase alignment

This paper presents a differential phase detector circuit, whose phase-to-voltage characteristic has an extremum when its two input signals are exactly in phase. In this condition all its digital signals are of 50% duty cycle so that the circuit characteristic does not have a dead zone. This feature allows a precise indication of the zero-phase condition, which is independent of the detector power supply and the offset of its ADC readout. Such a detector is used for a phase alignment of two reference clock signals with frequency about 11 kHz in front-ends processing signals from beam position monitors of the Large Hadron Collider (LHC) at CERN. The detector output voltage is digitized with a 24-bit ADC at the rate of the reference signals. The resulting samples are processed in the front-end FPGA and transmitted to the control system using an Ethernet data stream. After a detailed description of the differential phase detector its performance is demonstrated with laboratory measurements. The results show that this simple circuit allows a phase alignment resolution of the 11.2 kHz clock signals in the order of 0.0001° with a measurement bandwidth of 1 Hz.