Numerical solution of linear models in economics: The SP-DG model revisited

In general, complex and large dimensional models are needed to solve real economic problems. Due to these characteristics, there is either no analytical solution for them or they are not attainable. As a result, solutions can be only obtained through numerical methods. Thus, the growing importance of computers in Economics is not surprising. This paper focuses on an implementation of the SP-DG model, using Matlab,developed by the students as part of the Computational Economics course. We also discuss some of our teaching/learning experience within the course, given for the first time in the FEP Doctoral Programme in Economics.SP-DG Model, Output, Inflation, Numerical Simulation, Teaching of Economics

Spectroscopic properties and radiation damage investigation of a diamond based Schottky diode for ion-beam therapy microdosimetry

In this work, a detailed analysis of the properties of a novel microdosimeter based on a synthetic single crystal diamond is reported. Focused ion microbeams were used to investigate the device spectropscopic properties as well as the induced radiation damageeffects. A diamond based Schottky diode was fabricated by chemical vapor deposition with a very thin detecting region, about 400 nm thick (approximately 1.4 μm water equivalent thickness), corresponding to the typical size in microdosimetric measurements. A 200 × 200 μm2 square metallic contact was patterned on the diamond surface by standard photolithography to define the sensitive area. Experimental measurements were carried out at the Ruder Boškovic′ Institute microbeam facility using 4 MeV carbon and 5 MeV silicon ions. Ion beam induced charge maps were employed to characterize the microdosimeter response in terms of its charge collection properties. A stable response with no evidence of polarization or memory effects was observed up to the maximum investigated ion beam flux of about 1.7 × 109 ions·cm−2·s−1. A homogeneity of the response about 6% was found over the sensitive region with a well-defined confinement of the response within the active area. Tests of the radiation damageeffect were performed by selectively irradiating small areas of the device with different ion fluences, up to about 1012 ions/cm2. An exponential decrease of the charge collection efficiency was observed with a characteristic decay constant of about 4.8 MGy and 1 MGy for C and Si ions, respectively. The experimental data were analyzed by means of GEANT4 Monte Carlo simulations. A direct correlation between the diamond damaging effect and the Non Ionizing Energy Loss (NIEL) fraction was found. In particular, an exponential decay of the charge collection efficiency with an exponential decay as a function of NIEL is observed, with a characteristic constant of about 9.3 kGy-NIEL for both carbon and silicon ions

Measurement and modelling of anomalous polarity pulses in a multi-electrode diamond detector

In multi-electrode detectors, the motion of excess carriers generated by ionizing radiation induces charge pulses at the electrodes, whose intensities and polarities depend on the geometrical, electrostatic and carriers transport properties of the device. The resulting charge sharing effects may lead to bipolar currents, pulse height defects and anomalous polarity signals affecting the response of the device to ionizing radiation. This latter effect has recently attracted attention in commonly used detector materials, but different interpretations have been suggested, depending on the material, the geometry of the device and the nature of the ionizing radiation. In this letter, we report on the investigation in the formation of anomalous polarity pulses in a multi-electrode diamond detector with buried graphitic electrodes. In particular, we propose a purely electrostatic model based on the Shockley-Ramo-Gunn theory, providing a satisfactory description of anomalous pulses observed in charge collection efficiency maps measured by means of Ion Beam Induced Charge (IBIC) microscopy, and suitable for a general application in multi-electrode devices and detectors.Comment: 8 pages, 4 figure

Dedicated multichannel readout ASIC coupled with single crystal diamond for dosimeter application

This paper reports on the tests of a low-noise, multi-channel readout integrated circuit used as a readout electronic front-end for a diamond multi-pixel dosimeter. The system is developed for dose distribution measurement in radiotherapy applications. The first 10-channel prototype chip was designed and fabricated in a 0.18 um CMOS process. Every channel includes a charge integrator with a 10 pF capacitor and a double slope A/D converter. The diamond multi-pixel detector, based on CVD synthetic single crystal diamond Schottky diodes, is made by a 3 × 3 sensor matrix. The overall device has been tested under irradiation with 6 MeV radio therapeutic photon beams at the Policlinico ``Tor Vergata'' (PTV) hospital. Measurements show a 20 fA RMS leakage current from the front-end input stage and a negligible dark current from the diamond detector, a stable temporal response and a good linear behaviour as a function of both dose and dose rate. These characteristics were common to each tested channel

Lateral IBIC characterization of single crystal synthetic diamond detectors

In order to evaluate the charge collection efficiency (CCE) profile of single-crystal diamond devices based on a p-type/intrinsic/metal configuration, a lateral Ion Beam Induced Charge (IBIC) analysis was performed over their cleaved cross sections using a 2 MeV proton microbeam. CCE profiles in the depth direction were extracted from the cross-sectional maps at variable bias voltage. IBIC spectra relevant to the depletion region extending beneath the frontal Schottky electrode show a 100% CCE, with a spectral resolution of about 1.5%. The dependence of the width of the high efficiency region from applied bias voltage allows the constant residual doping concentration of the active region to be evaluated. The region where the electric field is absent shows an exponentially decreasing CCE profile, from which it is possible to estimate the diffusion length of the minority carriers by means of a drift-diffusion model. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A diamond detector based dosimetric system for instantaneous dose rate measurements in FLASH electron beams

Objective. A reliable determination of the instantaneous dose rate (I-DR) delivered in FLASH radiotherapy treatments is believed to be crucial to assess the so-called FLASH effect in preclinical and biological studies. At present, no detectors nor real-time procedures are available to do that in ultra high dose rate (UH-DR) electron beams, typically consisting of μs pulses characterized by I-DRs of the order of MGy/s. A dosimetric system is proposed possibly overcoming the above reported limitation, based on the recently developed flashDiamond (fD) detector (model 60025, PTW-Freiburg, Germany). Approach. A dosimetric system is proposed, based on a flashDiamond detector prototype, properly modified and adapted for very fast signal transmission. It was used in combination with a fast transimpedance amplifier and a digital oscilloscope to record the temporal traces of the pulses delivered by an ElectronFlash linac (SIT S.p.A., Italy). The proposed dosimetric systems was investigated in terms of the temporal characteristics of its response and the capability to measure the absolute delivered dose and instantaneous dose rate (I-DR). A ‘standard’ flashDiamond was also investigated and its response compared with the one of the specifically designed prototype. Main results. Temporal traces recorded in several UH-DR irradiation conditions showed very good signal to noise ratios and rise and decay times of the order of a few tens ns, faster than the ones obtained by the current transformer embedded in the linac head. By analyzing such signals, a calibration coefficient was derived for the fD prototype and found to be in agreement within 1% with the one obtained under reference 60Co irradiation. I-DRs as high as about 2 MGy s−1 were detected without any undesired saturation effect. Absolute dose per pulse values extracted by integrating the I-DR signals were found to be linear up to at least 7.13 Gy and in very good agreement with the ones obtained by connecting the fD to a UNIDOS electrometer (PTW-Freiburg, Germany). A good short term reproducibility of the linac output was observed, characterized by a pulse-to-pulse variation coefficient of 0.9%. Negligible differences were observed when replacing the fD prototype with a standard one, with the only exception of a somewhat slower response time for the latter detector type. Significance. The proposed fD-based system was demonstrated to be a suitable tool for a thorough characterization of UH-DR beams, providing accurate and reliable time resolved I-DR measurements from which absolute dose values can be straightforwardly derived

Design, realization, and characterization of a novel diamond detector prototype for FLASH radiotherapy dosimetry

Purpose: FLASH radiotherapy (RT) is an emerging technique in which beams with ultra-high dose rates (UH-DR) and dose per pulse (UH-DPP) are used. Commercially available active real-time dosimeters have been shown to be unsuitable in such conditions, due to severe response nonlinearities. In the present study, a novel diamond-based Schottky diode detector was specifically designed and realized to match the stringent requirements of FLASH-RT. Methods: A systematic investigation of the main features affecting the diamond response in UH-DPP conditions was carried out. Several diamond Schottky diode detector prototypes with different layouts were produced at Rome Tor Vergata University in cooperation with PTW-Freiburg. Such devices were tested under electron UH-DPP beams. The linearity of the prototypes was investigated up to DPPs of about 26 Gy/pulse and dose rates of approximately 1 kGy/s. In addition, percentage depth dose (PDD) measurements were performed in different irradiation conditions. Radiochromic films were used for reference dosimetry. Results: The response linearity of the diamond prototypes was shown to be strongly affected by the size of their active volume as well as by their series resistance. By properly tuning the design layout, the detector response was found to be linear up to at least 20 Gy/pulse, well into the UH-DPP range conditions. PDD measurements were performed by three different linac applicators, characterized by DPP values at the point of maximum dose of 3.5, 17.2, and 20.6 Gy/pulse, respectively. The very good superimposition of three curves confirmed the diamond response linearity. It is worth mentioning that UH-DPP irradiation conditions may lead to instantaneous detector currents as high as several mA, thus possibly exceeding the electrometer specifications. This issue was properly addressed in the case of the PTW UNIDOS electrometers. Conclusions: The results of the present study clearly demonstrate the feasibility of a diamond detector for FLASH-RT applications

Application of a novel diamond detector for commissioning of FLASH radiotherapy electron beams

Purpose: A diamond detector prototype was recently proposed by Marinelli et al. (Medical Physics 2022, https://doi.org/10.1002/mp.15473) for applications in ultrahigh-dose-per-pulse (UH-DPP) and ultrahigh-dose-rate (UH-DR) beams, as used in FLASH radiotherapy (FLASH-RT). In the present study, such so-called flashDiamond (fD) was investigated from the dosimetric point of view, under pulsed electron beam irradiation. It was then used for the commissioning of an ElectronFlash linac (SIT S.p.A., Italy) both in conventional and UH-DPP modalities. Methods: Detector calibration was performed in reference conditions, under 60 Co and electron beam irradiation. Its response linearity was investigated in UH-DPP conditions. For this purpose, the DPP was varied in the 1.2-11.9 Gy range, by changing either the beam applicator or the pulse duration from 1 to 4 μs. Dosimetric validation of the fD detector prototype was then performed in conventional modality, by measuring percentage depth dose (PDD) curves, beam profiles, and output factors (OFs). All such measurements were carried out in a motorized water phantom. The obtained results were compared with the ones from commercially available dosimeters, namely, a microDiamond, an Advanced Markus ionization chamber, a silicon diode detector, and EBT-XD GAFchromic films. Finally, the fD detector was used to fully characterize the 7 and 9 MeV UH-DPP electron beams delivered by the ElectronFlash linac. In particular, PDDs, beam profiles, and OFs were measured, for both energies and all the applicators, and compared with the ones from EBT-XD films irradiated in the same experimental conditions. Results: The fD calibration coefficient resulted to be independent from the investigated beam qualities. The detector response was found to be linear in the whole investigated DPP range. A very good agreement was observed among PDDs, beam profiles, and OFs measured by the fD prototype and reference detectors, both in conventional and UH-DPP irradiation modalities. Conclusions: The fD detector prototype was validated from the dosimetric point of view against several commercial dosimeters in conventional beams. It was proved to be suitable in UH-DPP and UH-DR conditions, for which no other commercial real-time active detector is available to date. It was shown to be a very useful tool to perform fast and reproducible beam characterizations in standard clinical motorized water phantom setups. All of the previously mentioned demonstrate the suitability of the proposed detector for the commissioning of UH-DR linac beams for preclinical FLASH-RT applications

S-band hybrid amplifiers based on hydrogenated diamond FETs

The first realizations of S-band hybrid amplifiers based on hydrogenated-diamond (H-diamond) FETs are reported. As test vehicles of the adopted H-diamond technology at microwave frequencies, two designs are proposed: one, oriented to low-noise amplification, the other, oriented to high-power operation. The two amplifying stages are so devised as to be cascaded into a two-stage amplifier. The activities performed, from the technological steps to characterization, modelling, design and realization are illustrated. Measured performance demonstrates, for the low-noise stage, a noise figure between 7 and 8 dB in the 2–2.5 GHz bandwidth, associated with a transducer gain between 5 and 8 dB. The OIP3 at 2 GHz is 21 dBm. As to the power-oriented stage, its transducer gain is 5–6 dB in the 2–2.5 GHz bandwidth. The 1-dB output compression point at 2 GHz is 20 dBm whereas the OIP3 is 33 dBm. Cascading the measured S-parameters of the two stages yields a transducer gain of 15 ± 1.2 dB in the 2–3 GHz bandwidth