ヒューマニズムとの関連における民主主義の倫理と教育(その一) : 教科書研究

TLDR: The S800 Spectrograph as discussed by the authors uses magnetic elements to direct the ions that pass through it and has wide-ranging applications for experimental nuclear physics, such as particle tracking and tuning.

Abstract: The S800 Spectrograph has wide-ranging applications for experimental nuclear physics. Of the many aspects of this apparatus, tuning and tracker have been focused on. This paper attempts a cursory inspection of the facets in both of these areas. For tuning, an explanation is given for charged particle beam optics as well as for the tuning software. Tracking devices such as the PPAC detector are discussed and a sample of one such calibration is given. I. The S800 Spectrograph Magnetic spectrographs have become very important for making measurements in nuclear physics. A magnetic spectrograph is an optical system for charged particles. It has an object and a focal plane, and it bends and focuses ions like lenses do for light. The S800 at the National Superconducting Cyclotron Laboratory (NSCL) is one such magnetic spectrograph. The S800 spectrograph uses magnetic elements to direct the ions that pass through it. The set-up for the S800, shown here, consists of several series of magnetic dipoles and quadrupoles whose magnetic fields may be configured and altered manually. To compare this magnetic spectrograph to an optical system, the target is the real image, the production target is the object, and the magnets are lenses, both bending and focusing the beam. II. The Optics of Charged Beam Particles A beam is a collection of moving charged particles all moving in the same direction with nearly the same momentum and is relatively close together transverse to the direction of motion. Moving charged particles will experience a force in a magnetic field dictated by the Lorentz force (F = qv x B). Thus magnets can be used to bend or focus a beam of charged particles. This is the basis for a magnetic spectrograph. In charged particle optics the goal is to determine the path the beam follows. Many different shapes and sizes of magnets are used in spectrometers. This figure shows three such cross sections for basic magnet types. The dipole has a uniform field across the central region of the magnet which will deflect charged particles as they pass through. A quadrupole has a zero magnetic field along the axis which focuses a charged particle beam, since the field strength is directly proportional to the distance from the axis. The S800 spectrograph is composed of several dipole and quadrupole magnets in series. III. TUNER Tuning is the process of adjusting the various magnets along the spectrograph in order that the beam to be used for the experiment will physically pass through all of the apparatus. Since each magnet in the system has its own characteristic matrix describing the transformation of trajectory coordinates as a particle passes through, the breadth or path of the beam can be predicted. The easiest way to calculate a beam trajectory is to use a computer program called Tuner. Tuner is a Linux based program which allows for user defined magnets to be ordered, their magnetic fields to be manipulated and will churn through the math giving both the transfer matrix and an excellent graphical representation of what the beam will look like. A sample configuration of the beam optics is shown in this figure. Each magnet has a set field that contributes towards the final overall transfer matrix which can be easily viewed and analyzed by the user. IV. Particle Tracking In a scattering experiment, the experimenter has to know the direction, energy (or momentum), and identity of the incoming and outgoing particles. Even if he knows where the beam is coming from, going to, and the path it takes; for the best results, he must know the beam on a particle-by-particle basis. This is the principle of particle tracking. The goal of a tracking system in a spectrograph such as the S800 is to keep tabs on relevant information about each particle in a particle beam. Information pieces such as position, angle of incidence, energy, momentum are all observable quantities that must be measured in order to obtain accurate and meaningful results from an experiment. V. PPAC’s Every spectrograph must have a mechanism for making position measurements. The S800 has one option through detectors called PPACs (Parallel Plate Avalanche). PPACs are two-dimensional position sensitive detectors developed specifically for use at the Cyclotron facility at Michigan State. The workings of a PPAC detector are quite simple. The detector was designed with several criteria in mind: particle resolution up to approximately 1mm, respond to a wide variety of ions, and be easy to fix and durable. This figure shows a cross section of on PPAC. Each PPAC has two separate parallel planar electrodes on either side of a central biased electrode to measure the positions of particles which travel normal to these electrodes. Two avalanches are created when a particle passes through the detector and these four signals hitting the edge of the foils produces an electronic signal, the size of which returns the position of the particle. When in use the detectors are biased with around 600 Volts across the central gap so that when a charged particle creates a signal, the avalanches will be accelerated quickly and grow rapidly. PPACs are an excellent two-dimensional position measurement for a majority of heavy-ions used in the cyclotron. VI. SpecTcl SpecTcl is a Linux based software program designed in TCL (Tool Command Language) for the purpose of reading and displaying data from nuclear physics experiments graphically. SpecTcl is an incredibly flexible and customizable program that takes data and brings it alive in a graphical form. User-defined parameters based on experiment, test, or detector allow for almost anything that can be measured to be represented with a histogram of some sort. The above figure is a screenshot from SpecTcl and shows the viewing panel with several spectra being analyzed. Among the many boons of the program are the ability to update variables in real-time, the elimination of undesired data points or noise, regional summations or centroid calculations, and plotting many spectra simultaneously. Continually expanding into a more powerful program, SpecTcl is already an invaluable tool when it comes to experiments with the S800. VII. Calibration of a PPAC The measurements of the PPACs are only useful when they are properly calibrated. The calibration is a simple iterative process that improves the synchronization between the readouts on SpecTcl and the position measurements made by the PPACs. Patterned masks were placed in front of the PPACs in order to give us a standard to go by. Although the masks are not used in experiments, they give us a theoretical or predicted positional measurement, which make them essential for calibration. This figure shows the layout of the PPAC detectors (located at the intermediate image on the S800) and the masks in front of them ready for calibration. A simple alpha source is then used to collect sample data into the PPACs and stored as a trial run. The run is then read and graphed with SpecTcl. Through a simple calculation this data is then compared with the predicted measurements. Using a linear correlation between the two a correction coefficient is determined and re-entered into SpecTcl in real-time. The trial run is sampled and graphed again, and the process repeats. Each time the actual comes closer and closer to matching the predicted. The following figures illustrate one such iteration of a calibration calculation. The raw data run is fed into SpecTcl. The centroids of several points corresponding to the holes in the mask are then calculated with a region sum. The table shows the simple following calculation where the measured positions are figured. The final figure shows the graph of predicted versus measured and the calculation of the correction coefficient. This correction coefficient could be fed back into SpecTcl thus adjusting the readout to a more proper fit better approximating the predicted measurements, leading to a better calibration. x y x (mm) y (mm) x (theory) y (theory) 278.8 373.7 4.453125 22.98828 0 30 279.9 340.1 4.667969 16.42578 0 20 278.9 310.1 4.472656 10.56641 0 10 277.8 281.6 4.257813 5 0 0 278.8 249.4 4.453125 -1.28906 0 -10 279.2 215.4 4.53125 -7.92969 0 -20 279.6 189.2 4.609375 -13.0469 0 -30 251.1 310.2 -0.95703 10.58594 -10 10 251.2 278.7 -0.9375 4.433594 -10 0 307.3 280.1 10.01953 4.707031 10 0 225.2 281 -6.01563 4.882813 -20 0 334.6 277.9 15.35156 4.277344 20 0 197.4 281.8 -11.4453 5.039063 -30 0 It was found during the course of calibrating several PPACs that no fewer than two and no more than three iterations of this process were needed in order to get a calibration that was within the desired resolution range (1 mm). Further calibrations are necessary in order to determine angular correlations between PPACs and the angular momentum of individual particles. A simple trigonometric calculation could be made when calibrating the intermediate image PPACs to calculate the angular correlation. VIII. Acknowledgements I would like to thank Professors Daniel Bazin and Brad Sherrill for all of their work and guidance. I would also like to thank the Michigan State University Physics department for hosting the REU program and making this a most memorable and enjoyable learning experience.