Minimum Fisher Information Research Articles

Reconstruction of neutron spectrum emitted by portable 14 MeV neutron generator by a combination of different methods

The presented paper is a continuation of the Tikhonov Regularisation, Minimum Fisher Information, Maximum Entropy, and Maximum Likelihood methods application to unfolding the neutron spectra emitted by the fusion devices from activation measurement. The aim of the analysis is the evaluation of the possible uncertainty improvement. The developed algorithms and methodology were validated with 14 MeV portable neutron generators before application to the analysis of the neutron spectrum emitted from tokamak. The analysis concerns plasma-target generator did not provide satisfactory uncertainty of the results. The modification of the irradiation foils’ set and the improvement in the activity measurement precision progress the results. The sealed tube portable neutron generator irradiated the Al, Fe, Ni, Zr, Au, Mg, and Nb foils. The HPGe spectrometer measured the induced activity with an uncertainty of about 10 %. The synthetic data analysis was made to establish the ratio between the error of the spectrum reconstruction and the discrepancy between the input data and activities reconstructed for this spectrum by the FISPACT-II inventory code. Two bin structures were considered. One was compatible with the FISPACT-II code, but the energy resolution was not regular. The second was characterised by constant bin spacing connected with the modification requirement before simulation and additional uncertainty of about 5 %. The best results were obtained by calculation of the mean value from all methods. The corresponding reconstruction uncertainty is equal to 11 %. The reconstructed spectrum has a dominant deuterium tritium peak slightly shifted to the higher energies due to the beam-target reaction kinematics. The evaluation of the impact of the deuterium-deuterium reaction due to the long-term operation was not reachable due to the measured high intensity from scattered neutrons.

Transactional Interpretation and the Generalized Poisson Distribution

The aim of this paper is to study the quantum-like approach to the description of the market in the context of the principle of minimum Fisher information. We wish to investigate the validity of using squeezed coherent states as market strategies. For this purpose, we focus on the representation of any squeezed coherent state with respect to the basis of the eigenvectors of the observable of market risk. We derive a formula for the probability of being the squeezed coherent state in one of these states. The distribution that we call generalized Poisson establishes the relation between the squeezed coherent states and their description in the language of risk in quantum terms. We provide a formula specifying the total risk of squeezed coherent strategy. Then, we propose a risk of risk concept that is in fact the second central moment of the generalized Poisson distribution. This is an important numerical characterization of squeezed coherent strategies. We provide its interpretations on the basis of the uncertainty relation for time and energy.

Reconstruction of the emissivity and flow for Doppler coherence imaging spectroscopy (CIS) on J-TEXT

Doppler coherence imaging spectroscopy (CIS) has been installed on J-TEXT tokamak to provide a wealth of information for carbon impurity ions (CIII). To obtain the local emissivity and flow from the line-integrated information measured by the camera, the tomographic inversion needs to propose. However, besides the ill-conditioned nature of the inversion, the distribution of CIII (only in the narrow scrape-off-layer (SOL) and around the divertor) makes the inversion more challenging. And the error in the emissivity inversion may propagate to the flow inversion. In this article, we have introduced the two classical tomographic algorithms, Tikhonov regularization, and minimum Fisher information regularization. To estimate the uncertainty of these algorithms and study the error sources, two typical CIII distribution models were chosen to make benchmarks. Finally, these methods were applied to a J-TEXT experiment, demonstrating the emissivity and flow distribution in SOL and around the divertor.

Quantum illumination with definite photon-number entangled states

Quantum illumination employs entangled states to detect a weakly reflecting target in a thermal bath. The performance of a given entangled state is evaluated from the minimum error probability in the asymptotic limit, which is compared against the optimal coherent state scheme. Using a relationship between the minimum error probability and quantum Fisher information, we compare the optimal performance of definite photon-number entangled states against that of coherent states under local repetitive strategies. When optimized under the constraint of a fixed total energy, we find that a coherent state outperforms the definite photon-number entangled states with the same signal energy.

Application of the different deconvolution methods to the neutron spectrum reconstruction from activation measurement

The neutron activation method provides information about the total neutron emission, yet in many applications, the energy distribution of the produced particles is also required. In this paper, codes based on the methods popular in tomography (Tikhonov Regularization, Minimum Fisher Information, Maximum Entropy and Maximum Likelihood Methods) have been developed for the reconstruction of the energy spectra of neutrons emitted by a Gas-Plasma Target Neutron Generator manufactured by a Gradel-Fusion Company. To perform the measurements by the neutron activation analysis the following samples were selected: Al, Zn, Fe, Ni, Zr and Au. Before the analysis of the experimental results, the codes were tested with synthetic data. The correlation between the reconstruction error and the FISPACT-II inventory code simulation's agreement with the measurement data have been determined. The spectrum was reconstructed by all methods separately, and the final result was defined as a mean value of them. The uncertainty of the reconstructed neutron spectra for the activities with an error higher than 10% has been estimated at the level of 22%.

Transactional Interpretation for the Principle of Minimum Fisher Information.

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information. The second, we call it transactional, expresses Fisher information from the perspective of the constant risk of market strategies. The orders of the market strategies derived from these two descriptions are different. From a market standpoint, minimizing Fisher information is equivalent to minimizing risk.

Relativistic Quantum Information of Anyons

In this paper, a method is developed to investigate the relativistic quantum information of anyons. Anyons are particles with intermediate statistics ranging between Bose-Einstein and Fermi-Dirac statistics, with a parameter $\alpha$ ($0<\alpha<1$) characteristic of this intermediate statistics. A density matrix is also introduced as a combination of the density matrices of bosons and fermions with a continuous parameter, $\alpha$, that represents the behavior of anyons. This density matrix reduces to bosonic and fermionic density matrices in the limits $\alpha\rightarrow 0$ and $\alpha\rightarrow 1$,respectively. We compute entanglement entropy, negativity, and coherency for anyons in non-inertial frames as a function of $\alpha$. We also computed quantum fisher information for these particles. Semions, which are particles with $\alpha = 0.5$, were found to have minimum quantum fisher information with respect to $\alpha$ than those with other values of fractional parameter.

Comparative analysis and new post-processing methods for plasma tomography at tokamaks

The JET tokamak is equipped with extensive diagnostic systems for tomography, including bolometers and soft X-ray (SXR) detectors. The tomographic reconstructions presented in this contribution were obtained using an algorithm based on Tikhonov regularisation and Minimum Fisher information. A new method for subsequent interpretative analysis of the tomographic reconstructions will be introduced. It is based on a comparison of radiated power from different regions of reconstruction, that can be defined by a rectangle or by a flux surface. The method was also used for comparative analysis of data obtained by reconstructing signals from different detectors. Both combined and separate reconstructions will be analysed. Example applications are presented, showing electron temperature drop, sawteeth instability and transport after laser blow-off.

Experimental validation of plasma tomography algorithms at ISTTOK

Plasma tomography is an ill-conditioned inversion problem. Algorithms based on Tikhonov regularization and minimum Fisher information try to overcome this issue by introducing regularization parameters that require empirical tuning. In general, to validate the implementation of these algorithms, either artificial phantoms are used, or one must rely on information provided by other diagnostics. In this work, an experimental setup was developed that allows the use of physical phantoms to tune and validate the reconstruction algorithms. The setup was assembled in a replica of the ISTTOK tokamak with a cylindrical cold cathode lamp placed perpendicular to the poloidal plane at multiple radial and angular positions. It is assumed that this physical phantom acts approximately as a point source in the emissivity profile. Knowing these profiles a priori, it is possible to compare them with the reconstructions produced by the algorithms, in order to tune and optimize the reconstruction parameters. After validation with these physical phantoms, several reconstructions were successfully computed for some tokamak discharges.

Gaussian interferometric power in the localized two-mode Gaussian states

With localized two-mode Gaussian quantum states in a relativistic setting, we study how to use the Gaussian interferometric power, which is given by the minimum quantum Fisher information, to guarantee the precision of the estimation of the Unruh temperature. We note that the interferometric power will be reduced with increase in the Unruh temperature because the Unruh radiation acts as a thermal bath on the probe state and it will destroy available quantum resources. By comparing the interferometric power with the entanglement, we also find that the larger squeezing parameter, the more similar the variation of entanglement and interferometric power. The maximum value of entanglement and interferometric power appears in the same condition. That is, for the states with larger entanglement, we can get higher precision of estimation. Moreover, we find that the interferometric power remains nonzero even for high Unruh temperature. This reflects the robust behavior of the Gaussian interferometric power against thermal noises.

Time-dependent pair density from the principle of minimum Fisher information.

The Euler equation for the time-dependent pair density is derived from the principle of minimum Fisher information. The same Euler equation is also derived from the recently introduced time-dependent pair density functional theory. The concept of steric effect to electron pairs is proposed and the steric pair energy is defined as the Weizsäcker kinetic energy of electron pairs.

Thermodynamical transcription of density functional theory with minimum Fisher information

Ghosh, Berkowitz and Parr designed a thermodynamical transcription of the ground-state density functional theory and introduced a local temperature that varies from point to point. The theory, however, is not unique because the kinetic energy density is not uniquely defined. Here we derive the expression of the phase-space Fisher information in the GBP theory taking the inverse temperature as the Fisher parameter. It is proved that this Fisher information takes its minimum for the case of constant temperature. This result is consistent with the recently proven theorem that the phase-space Shannon information entropy attains its maximum at constant temperature.

SXR measurement and W transport survey using GEM tomographic system on WEST

Measuring Soft X-Ray (SXR) radiation (0.1–20 keV) of fusion plasmas is a standard way of accessing valuable information on particle transport. Since heavy impurities like tungsten (W) could degrade plasma core performances and cause radiative collapses, it is necessary to develop new diagnostics to be able to monitor the impurity distribution in harsh fusion environments like ITER. A gaseous detector with energy discrimination would be a very good candidate for this purpose. The design and implementation of a new SXR diagnostic developed for the WEST project, based on a triple Gas Electron Multiplier (GEM) detector is presented. This detector works in photon counting mode and presents energy discrimination capabilities. The SXR system is composed of two 1D cameras (vertical and horizontal views respectively), located in the same poloidal cross-section to allow for tomographic reconstruction. An array (20 cm × 2 cm) consists of up to 128 detectors in front of a beryllium pinhole (equipped with a 1 mm diameter diaphragm) inserted at about 50 cm depth inside a cooled thimble in order to retrieve a wide plasma view. Acquisition of low energy spectrum is insured by a helium buffer installed between the pinhole and the detector. Complementary cooling systems (water) are used to maintain a constant temperature (25̂C) inside the thimble. Finally a real-time automatic extraction system has been developed to protect the diagnostic during baking phases or any overheating unwanted events. Preliminary simulations of plasma emissivity and W distribution have been performed for WEST using a recently developed synthetic diagnostic coupled to a tomographic algorithm based on the minimum Fisher information (MFI) inversion method. First GEM acquisitions are presented as well as estimation of transport effect in presence of ICRH on W density reconstruction capabilities of the GEM.

On a gas electron multiplier based synthetic diagnostic for soft x-ray tomography on WEST with focus on impurity transport studies

The tokamak WEST aims at testing ITER divertor high heat flux component technology in long pulse operation. Unfortunately, heavy impurities like tungsten (W) sputtered from the plasma facing components can pollute the plasma core by radiation cooling in the soft x-ray (SXR) range, which is detrimental for the energy confinement and plasma stability. SXR diagnostics give valuable information to monitor impurities and study their transport. The WEST SXR diagnostic is composed of two new cameras based on the Gas Electron Multiplier (GEM) technology. The WEST GEM cameras will be used for impurity transport studies by performing 2D tomographic reconstructions with spectral resolution in tunable energy bands. In this paper, we characterize the GEM spectral response and investigate W density reconstruction thanks to a synthetic diagnostic recently developed and coupled with a tomography algorithm based on the minimum Fisher information (MFI) inversion method. The synthetic diagnostic includes the SXR source from a given plasma scenario, the photoionization, electron cloud transport and avalanche in the detection volume using Magboltz, and tomographic reconstruction of the radiation from the GEM signal. Preliminary studies of the effect of transport on the W ionization equilibrium and on the reconstruction capabilities are also presented.

Fisher information framework for time series modeling

A robust prediction model invoking the Takens embedding theorem, whose working hypothesis is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz, central to the working hypothesis satisfy a time independent Schrödinger-like equation in a vector setting. The inference of (i) the probability density function of the coefficients of the working hypothesis and (ii) the establishing of constraint driven pseudo-inverse condition for the modeling phase of the prediction scheme, is made, for the case of normal distributions, with the aid of the quantum mechanical virial theorem. The well-known reciprocity relations and the associated Legendre transform structure for the Fisher information measure (FIM, hereafter)-based model in a vector setting (with least square constraints) are self-consistently derived. These relations are demonstrated to yield an intriguing form of the FIM for the modeling phase, which defines the working hypothesis, solely in terms of the observed data. Cases for prediction employing time series’ obtained from the: (i) the Mackey–Glass delay-differential equation, (ii) one ECG signal from the MIT-Beth Israel Deaconess Hospital (MIT-BIH) cardiac arrhythmia database, and (iii) one ECG signal from the Creighton University ventricular tachyarrhythmia database. The ECG samples were obtained from the Physionet online repository. These examples demonstrate the efficiency of the prediction model. Numerical examples for exemplary cases are provided.

Optimized tomography methods for plasma emissivity reconstruction at the ASDEX Upgrade tokamak.

The soft X-ray (SXR) emission provides valuable insight into processes happening inside of high-temperature plasmas. A standard method for deriving the local emissivity profiles of the plasma from the line-of-sight integrals measured by pinhole cameras is the tomographic inversion. Such an inversion is challenging due to its ill-conditioned nature and because the reconstructed profiles depend not only on the quality of the measurements but also on the inversion algorithm used. This paper provides a detailed description of several tomography algorithms, which solve the inversion problem of Tikhonov regularization with linear computational complexity in the number of basis functions. The feasibility of combining these methods with the minimum Fisher information regularization is demonstrated, and various statistical methods for the optimal choice of the regularization parameter are investigated with emphasis on their reliability and robustness. Finally, the accuracy and the capability of the methods are demonstrated by reconstructions of experimental SXR profiles, featuring poloidal asymmetric impurity distributions as measured at the ASDEX Upgrade tokamak.

A beacon configuration optimization method based on Fisher information for Mars atmospheric entry

The navigation capability of the proposed Mars network based entry navigation system is directly related to the beacon number and the relative configuration between the beacons and the entry vehicle. In this paper, a new beacon configuration optimization method is developed based on the Fisher information theory and this method is suitable for any number of visible beacons. The proposed method can be used for the navigation schemes based on range measurements provided by radio transceivers or other sensors for Mars entry. The observability of specific state is defined as its Fisher information based on the observation model. The overall navigation capability is improved by maximizing the minimum average Fisher information, even though the navigation system is not fully observed. In addition, when there is only one beacon capable of entry navigation and the observation information is relatively limited, the optimization method can be modulated to maximize the Fisher information of the specific state which may be preferred for the guidance and control system to improve its estimation accuracy. Finally, navigation scenarios consisted of 1–3 beacons are tested to validate the effectiveness of the developed optimization method. The extended Kalman filter (EKF) is employed to derive the state estimation error covariance. The results also show that the zero-Fisher information situation should be avoided, especially when the dynamic system is highly nonlinear and the states change dramatically.

Optimization of soft X-ray tomography on the COMPASS tokamak

Abstract The COMPASS tokamak is equipped with the soft X-ray (SXR) diagnostic system based on silicon photodiode arrays shielded by a thin beryllium foil. The diagnostic is composed of two pinhole cameras having 35 channels each and one vertical pinhole camera with 20 channels, which was installed recently to improve tomographic inversions. Lines of sight of the SXR detectors cover almost complete poloidal cross section of the COMPASS vessel with a spatial resolution of 1-2 cm and temporal resolution of about 3 μs. Local emissivity is reconstructed via Tikhonov regularization constrained by minimum Fisher information that provides reliable and robust solution despite limited number of projections and ill-conditionality of this task. Improved border conditions and numerical differentiation matrices suppressing artifacts in reconstructed radiation were implemented in the code. Furthermore, a fast algorithm eliminating iterative processes was developed, and it is foreseen to be tested in real-time plasma control.

Tomographic capabilities of the new GEM based SXR diagnostic of WEST

The tokamak WEST (Tungsten Environment in Steady-State Tokamak) will start operating by the end of 2016 as a test bed for the ITER divertor components in long pulse operation. In this context, radiative cooling of heavy impurities like tungsten (W) in the Soft X-ray (SXR) range [0.1 keV; 20 keV] is a critical issue for the plasma core performances. Thus reliable tools are required to monitor the local impurity density and avoid W accumulation. The WEST SXR diagnostic will be equipped with two new GEM (Gas Electron Multiplier) based poloidal cameras allowing to perform 2D tomographic reconstructions in tunable energy bands. In this paper tomographic capabilities of the Minimum Fisher Information (MFI) algorithm developed for Tore Supra and upgraded for WEST are investigated, in particular through a set of emissivity phantoms and the standard WEST scenario including reconstruction errors, influence of noise as well as computational time.

Infrared Imaging Bolometer for the HL-2A Tokamak**supported by National Natural Science Foundation of China (Nos. 10805016 and 11175061), and the Chinese National Fusion Project for ITER (No. 2014GB109001)

An infrared imaging bolometer diagnostic has been upgraded recently to be adapted for the complications of the signal-to-noise ratio arising from the low level of plasma radiation and high reflectivity of low energy photon (<6.2 eV). It utilizes a platinum foil, blackened on both sides with graphite spray, as the bolometer detector. The advantage of the blackened foil is the light absorption extending into the infrared. After a careful calibration of the foil, the incident power density distribution on the foil is determined by solving the heat diffusion equation with a numerical technique. The local plasma radiated power density is reconstructed with a minimum fisher information regularization method by assuming plasma emission toroidal symmetry. Comparisons of the results and the profiles measured by an ordinary bolometric detector demonstrate that this method is good enough to provide the plasma radiated power pattern. The typical plasma radiated power density distribution before and after high mode (H-mode) transition is firstly reconstructed with the infrared imaging bolometer. Moreover, during supersonic molecular beam injection (SMBI), an enhanced radiation region is observed at the edge of the plasma.