Michael Taylor

PhD Applied Mathematics
IERSD-NOA

Research interests

  • Interests
    Environmental Analysis, Neural Analyzers, Scientometrics, Research 2.0

Publications

  • Volterra network modeling of the nonlinear finite-impulse response of the radiation belt flux

    Michael Taylor, Ioannis A. Daglis, Anastassios Anastasiadis, Dimitris Vassiliadis

    American Institute of Physics Conference Series. 01/2011; 1320:221-226.

    We show how a general class of spatio-temporal nonlinear impulse-response forecast networks (Volterra networks) can be constructed from a taxonomy of nonlinear autoregressive integrated moving average with exogenous inputs (NARMAX) input-output equations, and used to model the evolution of energetic... [more] We show how a general class of spatio-temporal nonlinear impulse-response forecast networks (Volterra networks) can be constructed from a taxonomy of nonlinear autoregressive integrated moving average with exogenous inputs (NARMAX) input-output equations, and used to model the evolution of energetic particle f uxes in the Van Allen radiation belts. We present initial results for the nonlinear response of the radiation belts to conditions a month earlier. The essential features of spatio-temporal observations are recovered with the model echoing the results of state space models and linear f nite impulse-response models whereby the strongest coupling peak occurs in the preceding 1–2 days. It appears that such networks hold promise for the development of accurate and fully data-driven space weather modelling, monitoring and forecast tools.
  • Understanding the role of open peer-review and dynamic articles

    Pandelis Perakakis, Michael Taylor, Marco G. Mazza, Varvara Trachana

    Scientometrics. 01/2011;

    We welcome the commentary by L. Egghe (Scientometrics, this issue) stimulating discussion on our recent article “Natural selection of academic papers” (NSAP) (Scientometrics, 85(2):553–559, 2010) that focuses on an important modern issue at the heart of the scientific enterprise—the open and continu... [more] We welcome the commentary by L. Egghe (Scientometrics, this issue) stimulating discussion on our recent article “Natural selection of academic papers” (NSAP) (Scientometrics, 85(2):553–559, 2010) that focuses on an important modern issue at the heart of the scientific enterprise—the open and continuous evaluation and evolution of research. We are also grateful to the editor of Scientometrics for giving us the opportunity to respond to some of the arguments by L. Egghe that we believe are inaccurate or require further comment.
  • Natural selection of academic papers

    Pandelis Perakakis, Michael Taylor, Marco G. Mazza, Varvara Trachana

    Scientometrics. 01/2010; 85:553-559.

    Academic papers, like genes, code for ideas or technological innovations that structure and transform the scientific organism and consequently the society at large. Genes are subject to the process of natural selection which ensures that only the fittest survive and contribute to the phenotype of th... [more] Academic papers, like genes, code for ideas or technological innovations that structure and transform the scientific organism and consequently the society at large. Genes are subject to the process of natural selection which ensures that only the fittest survive and contribute to the phenotype of the organism. The process of selection of academic papers, however, is far from natural. Commercial for-profit publishing houses have taken control over the evaluation and access to scientific information with serious consequences for the dissemination and advancement of knowledge. Academic authors and librarians are reacting by developing an alternative publishing system based on free-access journals and self-archiving in institutional repositories and global disciplinary libraries. Despite the emergence of such trends, the journal monopoly, rather than the scientific community, is still in control of selecting papers and setting academic standards. Here we propose a dynamical and transparent peer review process, which we believe will accelerate the transition to a fully open and free-for-all science that will allow the natural selection of the fittest ideas.
  • The roads to open access

    Pandelis Perakakis, Michael Taylor, Varvara Trachana

    UNESCO World Social Science Report 2010. 01/2010; 1:307-309.

    One of the most important technological achievements of the 20th century was the invention of the internet and the immense potential it created for information sharing. Now, at the dawn of the 21st century when a large fraction of the world’s population has instantaneous access to vast amounts of da... [more] One of the most important technological achievements of the 20th century was the invention of the internet and the immense potential it created for information sharing. Now, at the dawn of the 21st century when a large fraction of the world’s population has instantaneous access to vast amounts of data, it is ironic that access to new research papers should only be available to those who work at elite institutions able to cope with the burden of high journal subscription fees. This barrier to the world’s academic output not only blocks interested readers and authors; it also slows the development of knowledge. Current trends suggest, however, that this is likely to change dramatically.
  • Towards a Unified Source-Propagation Model of Cosmic Rays

    Michael Taylor, Mercedes Molla

    Astronomical Society of the Pacific Conference Series. 01/2010; 424:98.

    It is well known that the cosmic ray energy spectrum is multifractal with the analysis of cosmic ray fluxes as a function of energy revealing a first “knee” slightly below 10^16 eV, a second knee slightly below 10^18 eV and an “ankle” close to 10^19 eV. The behaviour of the highest energy cosmic ray... [more] It is well known that the cosmic ray energy spectrum is multifractal with the analysis of cosmic ray fluxes as a function of energy revealing a first “knee” slightly below 10^16 eV, a second knee slightly below 10^18 eV and an “ankle” close to 10^19 eV. The behaviour of the highest energy cosmic rays around and above the ankle is still a mystery and precludes the development of a unified source-propagation model of cosmic rays from their source origin to Earth. A variety of acceleration and propagation mechanisms have been proposed to explain different parts of the spectrum the most famous of course being Fermi acceleration in magnetised turbulent plasmas (Fermi 1949). Many others have been proposd for energies at and below the first knee (Peters & Cimento (1961); Lagage & Cesarsky (1983); Drury et al. (1984); Wdowczyk & Wolfendale (1984); Ptuskin et al. (1993); Dova et al. (0000); Horandel et al. (2002); Axford (1991)) as well as at higher energies between the first knee and the ankle (Nagano & Watson (2000); Bhattacharjee & Sigl (2000); Malkov & Drury (2001)). The recent fit of most of the cosmic ray spectrum up to the ankle using non-extensive statistical mechanics (NESM) (Tsallis et al. (2003)) provides what may be the strongest evidence for a source-propagation system deviating significantly from Boltmann statistics. As Tsallis has shown (Tsallis et al. (2003)), the knees appear as crossovers between two fractal-like thermal regimes. In this work, we have developed a generalisation of the second order NESM model (Tsallis et al. (2003)) to higher orders and we have fit the complete spectrum including the ankle with third order NESM. We find that, towards the GDZ limit, a new mechanism comes into play. Surprisingly it also presents as a modulation akin to that in our own local neighbourhood of cosmic rays emitted by the sun. We propose that this is due to modulation at the source and is possibly due to processes in the shell of the originating supernova. We report that the entire spectrum, spanning cosmic rays of local solar origin and those eminating from galactic and extra-galactic sources can be explained using a new diagnostic — the gradient of the log-log plot. This diagnostic reveals the known Boltmann statistics in the solar-terrestrial neighbourhood but at the highest energies — presumably at the cosmic ray source, with clearly separated fractal scales in between. We interpret this as modulation at the source followed by Fermi acceleration facilitated by galactic and extra-galactic magnetic fields with a final modulation in the solar-terrestrial neighbourhood. We conclude that the gradient of multifractal curves appears to be an excellent detector of fractality.
  • 1.14
    Impact points
    KARDIA: A Matlab software for the analysis of cardiac interbeat intervals.

    Pandelis Perakakis, Mateus Joffily, Michael Taylor, Pedro Guerra, Jaime Vila

    Computer methods and programs in biomedicine. 11/2009;

    This article presents KARDIA, a Matlab (MathWorks Inc., MA) software developed for the analysis of cardiac interbeat interval (IBI) data. Available functions are called through a graphical user interface and permit the study of phasic cardiac responses (PCRs) and the estimation of time and frequency... [more] This article presents KARDIA, a Matlab (MathWorks Inc., MA) software developed for the analysis of cardiac interbeat interval (IBI) data. Available functions are called through a graphical user interface and permit the study of phasic cardiac responses (PCRs) and the estimation of time and frequency domain heart rate variability (HRV) parameters. Scaling exponents of heartbeat fluctuations are calculated with the detrended fluctuation analysis (DFA) algorithm. Grand average and individual subject results can be exported to spreadsheets for further statistical analysis. KARDIA is distributed free of charge under the terms of GNU public license so that other users can modify the code and adjust the program's performance according to their own scientific requirements.
  • 4.36
    Impact points
    Breathing Frequency Bias in Fractal Analysis of Heart Rate Variability.

    Pandelis Perakakis, Michael Taylor, Eduardo Martinez-Nieto, Ioanna Revithi, Jaime Vila

    Biological psychology. 07/2009;

    Detrended Fluctuation Analysis (DFA) is an algorithm widely used to determine fractal long-range correlations in physiological signals. Its application to heart rate variability (HRV) has proven useful in distinguishing healthy subjects from patients with cardiovascular disease. In this study we exa... [more] Detrended Fluctuation Analysis (DFA) is an algorithm widely used to determine fractal long-range correlations in physiological signals. Its application to heart rate variability (HRV) has proven useful in distinguishing healthy subjects from patients with cardiovascular disease. In this study we examined the effect of respiratory sinus arrhythmia (RSA) on the performance of DFA applied to HRV. Predictions based on a mathematical model were compared with those obtained from a sample of 14 normal subjects at three breathing frequencies: 0.1Hz, 0.2Hz and 0.25Hz. Results revealed that: 1) the periodical properties of RSA produce a change of the correlation exponent in HRV at a scale corresponding to the respiratory period, 2) the short-term DFA exponent is signi_cantly reduced when breathing frequency rises from 0.1Hz to 0.2Hz. These findings raise important methodological questions regarding the application of fractal measures to short-term HRV.
  • Tutorial: Exact Solutions for the Populations of the n-level Ion

    Michael Taylor, Jose Manuel Vilchez

    Publications of the Astronomical Society of the Pacific. 01/2009; 121:1257-1266.

    This tutorial presents a review of the analytical approach to obtain exact solutions for the populations of n-level ions, and summarizes the ideas behind detailed balance and the statistical physics of collisionally-excited ions. Seaton’s analytical solution for the populations of the 3-level ion ha... [more] This tutorial presents a review of the analytical approach to obtain exact solutions for the populations of n-level ions, and summarizes the ideas behind detailed balance and the statistical physics of collisionally-excited ions. Seaton’s analytical solution for the populations of the 3-level ion has been supplanted by matrix methods such as the master equation approach, which are now central to astronomy since there is a need to maintain a parity between improvements in quantum-mechanically calculated values for collision strengths and transition probabilities on the one hand, and three-dimensional (3D) photoionization codes used by astrophysicists for producing nebular diagnostics on the other. We show that the analytical method of solution to the problem using matrices and symbolic mathematics is straightforward, and we illustrate through theoretical, numerical, and empirical checks the validity of its results. First, we recast the equations of thermal statistical equilibrium for the energy level populations of collisionally-excited ions in the form of a well-defined matrix equation. We then show how symbolic mathematics is efficient in the inversion of equations and is able to provide the exact analytical solutions for the sought-after level populations. We present the matrices for the 5-level ion as an example of how to extend the exact solution for the 3-level ion to illustrate the general technique. We then show how the analytical results faithfully reduce to the Seaton solution when appropriate limits are taken. Spectrophotometric observations of a real ionized gas (the planetary nebula A39) are then used to obtain empirical values of forbidden line ratios and level populations for the 5-level [O III] ion. These values are compared with: (1) a best-fit 3D Monte Carlo photoionization model, and (2) the exact solution for the 5-level ion, using the symbolic mathematics approach, the exact Seaton 3-level ion solution, and a numerical approximation for the 5-level ion. It is shown that in every case, the analytical solution agrees with results obtained using observed nebular conditions to within the standard error. We provide a MATLAB code that can be adapted and tailored by astrophysicists to calculations of other n-level ions.
  • A matrix generalisation of dimensional analysis: new similarity transforms to address the problem of uniqueness

    Michael Taylor, Angeles I. Diaz, Lucas A. Jodar-Sanchez, Raphael J. Villanueva-Mico

    Advanced Studies in Theoretical Physics. 01/2008; 2:979-995.

    On the verge of the centenary of dimensional analysis (DA), we present a new matrix generalisation of the Buckingham Theorem on which it is based. The proof is based on a solution we have found for inverting non-square block matrices and gives rise naturally to a new pair of transforms - the similar... [more] On the verge of the centenary of dimensional analysis (DA), we present a new matrix generalisation of the Buckingham Theorem on which it is based. The proof is based on a solution we have found for inverting non-square block matrices and gives rise naturally to a new pair of transforms - the similarity transform (S) that converts physical dimensional data into dimensionless space and its inverse (S’). Although it is well known that DA: a) reduces the number of free parameters, b) guarantees scale invariance through dimensional homogeneity and c) extracts functional information encoded in the dimensionless grouping of variables, scientists seem to be unaware that the scaling laws provided by DA are degenerate and therefore not unique. We demonstrate that the inverse transform S’ is responsible for the non-uniqueness and we show how reference to observational data is sufficient to to break the degeneracy inherent in transforming back to dimensional (physical) space. As an example, we show how the underlying functional form of the Planck Radiation Law can be deduced in only a few lines using the matrix method and without appealing to first principles - thus demonstrating the possibility of a priori knowledge discovery; but that subsequent data analysis is still required in order to identify the exact causal law. This opens the door to a new semi-empirical methodology for the discovery of empirical laws encoded in observational data. It is hoped that the proof presented here will provide a new impetus to the pursuit of inverse problems in physics.
  • The Siege of Science

    M. Taylor, P. Perakakis, V. Trachana

    Ethics in Science and Environmental Politics. 01/2008; 8:17-40.

    Science is in a state of siege. The traditional stage for scientific ideas through peer-reviewed academic journals has been hijacked by an overpriced journal monopoly. After a wave of mergers and take-overs, big business publishing houses now exercise economic control over access to knowledge and fr... [more] Science is in a state of siege. The traditional stage for scientific ideas through peer-reviewed academic journals has been hijacked by an overpriced journal monopoly. After a wave of mergers and take-overs, big business publishing houses now exercise economic control over access to knowledge and free scientific discourse. Their ‘all is number’ rationale, made possible and perpetuated by single-parameter bibliometric indices like the Impact Factor and the h-index has led to a measurement of scientists, science and science communication with quality being reduced to quantity and with careers hanging in the balance of column totals. Other multi-parameter indices like the subscription-based Index Copernicus have not helped to resolve the situation. The patented and undisclosed black box algorithm of the Index Copernicus has just replaced one yardstick by another even less accessible one. Moreover, the academic as author, editor and/or reviewer, under intense competitive pressure, is forced to play the publishing game where such numbers rule, leading to frequent abuses of power. However, there are also deep paradoxes at the heart of this siege. Electronic software for producing camera-ready-copy, LaTeX style files, the internet and technology mean that it has never been easier or cheaper to publish than it is today. Despite this, top journals are charging exorbitant prices for authors to publish and for readers to access their articles. Academic libraries are feeling the pinch the most and are being forced to cut journal subscriptions. Not surprisingly, scholars in droves are declaring their independence from commercial publishers and are moving to open access journals or are self-archiving their articles in public domain pre-print servers. That this movement is starting to hurt the big publishing houses is evidenced by their use of counter-tactics such as proprietary pre-print servers and pure propaganda in their attempts to guard against profit loss. Whether or not bibliometry will be an artefact in the future depends on the outcome of this battle. Here, we review the current status of this siege, how it arose and how it is likely to evolve.
  • A 3D Study of Combined Density and Temperature Fluctuations in Gaseous Nebulae I: Theory

    Michael Taylor, Jose Manuel Vilchez

    12/2007;

    This draft (in preparation) has been withdrawn so as to be combined with its second part (work also in preparation), to produce a single paper, that includes further analysis and revisions done after new important results obtained.... [more] This draft (in preparation) has been withdrawn so as to be combined with its second part (work also in preparation), to produce a single paper, that includes further analysis and revisions done after new important results obtained.
  • On the deduction of galaxy abundances with evolutionary neural networks

    Michael Taylor, Angeles I. Diaz

    10/2007;

    A growing number of indicators are now being used with some confidence to measure the metallicity(Z) of photoionisation regions in planetary nebulae, galactic HII regions(GHIIRs), extra-galactic HII regions(EGHIIRs) and HII galaxies(HIIGs). However, a universal indicator valid also at high metallici... [more] A growing number of indicators are now being used with some confidence to measure the metallicity(Z) of photoionisation regions in planetary nebulae, galactic HII regions(GHIIRs), extra-galactic HII regions(EGHIIRs) and HII galaxies(HIIGs). However, a universal indicator valid also at high metallicities has yet to be found. Here, we report on a new artificial intelligence-based approach to determine metallicity indicators that shows promise for the provision of improved empirical fits. The method hinges on the application of an evolutionary neural network to observational emission line data. The network's DNA, encoded in its architecture, weights and neuron transfer functions, is evolved using a genetic algorithm. Furthermore, selection, operating on a set of 10 distinct neuron transfer functions, means that the empirical relation encoded in the network solution architecture is in functional rather than numerical form. Thus the network solutions provide an equation for the metallicity in terms of line ratios without a priori assumptions. Tapping into the mathematical power offered by this approach, we applied the network to detailed observations of both nebula and auroral emission lines in the optical for a sample of 96 HII-type regions and we were able to obtain an empirical relation between Z and S23 with a dispersion of only 0.16 dex. We show how the method can be used to identify new diagnostics as well as the nonlinear relationship supposed to exist between the metallicity Z, ionisation parameter U and effective (or equivalent) temperature T*.
  • 100 Years of dimensional analysis: New steps toward empirical law deduction

    Michael Taylor, Angeles I. Diaz, Lucas A. Jodar-Sanchez, Rafael J. Villanueva-Mico

    09/2007;

    On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free parameters, b) guarantees scale invariance through dimensional ... [more] On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free parameters, b) guarantees scale invariance through dimensional homogeneity and c) extracts functional information encoded in the dimensionless grouping of variables. Less known are the results of Rudolph and co-workers that DA also gives rise to a new pair of transforms - the similarity transform (S) that converts physical dimensional data into dimensionless space and its inverse (S'). Here, we present a new matrix generalisation of the Buckingham Theorem, made possible by recent developments in the theory of inverse non-square matrices, and show how the transform pair arises naturally. We demonstrate that the inverse transform S' is non-unique and how this casts doubt on scaling relations obtained in cases where observational data has not been referred to in order to break the degeneracy inherent in transforming back to dimensional (physical) space. As an example, we show how the underlying functional form of the Planck Radiation Law can be deduced in only a few lines using the matrix method and without appealing to first principles; thus demonstrating the possibility of a priori knowledge discovery; but that subsequent data analysis is still required in order to identify the exact causal law. It is hoped that the proof presented here will give theoreticians confidence to pursue inverse problems in physics using DA. Comment: 14 pages, 3 figures. Submitted to New Journal of Physics (IOP)
  • Exact solutions for the populations of the n-level ion

    Michael Taylor, Jose Manuel Vilchez

    09/2007;

    We present a matrix solution to the full equations of statistical equilibrium that give the energy level populations of collisionally-excited ions in photoionised gaseous nebulae. The rationale for such a calculation is to maintain a parity between improvements in the quantum-mechanically evaluated ... [more] We present a matrix solution to the full equations of statistical equilibrium that give the energy level populations of collisionally-excited ions in photoionised gaseous nebulae. The rationale for such a calculation is to maintain a parity between improvements in the quantum-mechanically evaluated values for collision strengths and transition probabilities from the Iron and Opacity Projects on the one hand, and 3D photoionisation codes such as MOCASSIN and astrophysical software for producing nebular diagnostics such as the Nebular package for IRAF, on the other. We have taken advantage of the fact that mathematics programs such as MATLAB and Mathematica have proven to be very adept at symbolic manipulation providing a route to exact solutions for the n-level ion. In particular, we have avoided the substitution of estimated values. We provide the matrix solution for the 5-level ion as an example and show how the equations faithfully reduce to the exact solution for the 3-level ion. Through the forbidden line ratio R23, we compare the exact solution with a) that obtained from the observed emission of the spherical planetary nebula Abell 39, b) 3D Monte-Carlo photoionisation modelling of the same nebula, c) the approximate 5-level program TEMDEN and d) the exact 3-level ion. The general solution presented here means that programs for the calculation of level populations can obtain solutions for ions with a user-specified number of excited levels. The use of a separate and updatable database of atomic and ionic constants such as that provided by NIST, means that software of more general application can now be made available; particularly for the study of high excitation objects such as active galactic nebulae (AGNs) and supernovae (SNs) where higher excited levels become significant.
  • Measuring internationality: reflections and perspectives on academic journals

    Gualberto Buela-Casal, Pandelis Perakakis, Michael Taylor, Purificacion Checa

    Scientometrics. 01/2006; 67:45-65.

    Internationality as a concept is being applied ambiguously, particularly in the world of academic journal publication. Although different criteria are used by scientometrists in order to measure internationality and to supplement its minimal literal meaning, the present study suggests that no single... [more] Internationality as a concept is being applied ambiguously, particularly in the world of academic journal publication. Although different criteria are used by scientometrists in order to measure internationality and to supplement its minimal literal meaning, the present study suggests that no single criterion alone is sufficient. This paper surveys, critically-assesses and extends the existing measures of internationality in the context of academic publishing and identifies those criteria that are most clearly resolved and amenable to quantitative analysis. When applied, however, to a case study of four thematically-connected journals from the field of Health and Clinical Psychology using descriptive statistics and the Gini Coefficient, the measurement of internationality using these criteria was found to be ambiguous. We conclude that internationality is best viewed as a mathematically fuzzy entity and that a single measure Internationality Index, constructed from a combination of suitably weighted criteria, is the only way to unambiguously quantify the degree of internationality.
  • An AI approach to quantitative modelling in Astrophysics

    Michael Taylor

    Congreso Español de Informática Symposium on Fuzzy Logic and Soft Computing. 01/2005; 1:69-81.

    This paper presents a new approach in astrophysics based on artificial intelligence (AI) to quantitatively model complex or nonlinear phenomena. Some of the new developments in dimensional analysis allow for the development of similarity networks that can be used to exploit high resolution obsevatio... [more] This paper presents a new approach in astrophysics based on artificial intelligence (AI) to quantitatively model complex or nonlinear phenomena. Some of the new developments in dimensional analysis allow for the development of similarity networks that can be used to exploit high resolution obsevational data in the determination of power laws or in the extraction of fuzzy logic rules to create smart simulators. Dimensional analysis is shown to lie at the heart of a holistic object description and similarity theory and hierarchical modeling techniques are presented to show how knowledge can be transferred between system scales and between subsystems in aggregated models. The methodology offered here is an AI-based alternative to the semi-empirical scientific modeling approach currently practised - where simulations are limited by truncated mathematical theories, computional power and runtime.
  • A neuro-fuzzy system to calculate a journal internationality index

    Pandelis Perakakis, Michael Taylor, Gualberto Buela-Casal, Purificacion Checa

    Congreso Español de Informática Symposium on Fuzzy Logic and Soft Computing. 01/2005; 1:157-163.

    Internationality as a concept is being applied ambiguously and erroneously, particularly in the world of academic journal publication where it is often used as a quality indicator. Although different qualitative criteria have been used by scientometrists in order to attempt a measure of internationa... [more] Internationality as a concept is being applied ambiguously and erroneously, particularly in the world of academic journal publication where it is often used as a quality indicator. Although different qualitative criteria have been used by scientometrists in order to attempt a measure of internationality in various contexts, it is now clear that the literal definition of internationality is a minimal one while other proposed measures based on individual criteria fail to provide a complete and accurate assessment. As such, internationality remains to be defined. Here, we present a holistic approach to the problem based on fuzzy logic. We surveyed, critically-assessed and pruned the set of internationality criteria in the context of academic publishing, selecting those that are semantically precise and amenable to quantitative measure. We have tested the ability of each criterion to measure internationality by applying them to four thematically-connected journals from the field of Health and Clinical Psychology, using descriptive statistics and the Gini Coefficient. The results of this case study revealed that, in the absence of a method of numerically weighting the criteria, any measurement of internationality remains ambiguous and incorrect. We propose that internationality is best represented by a neuro-fuzzy system of fuzzy sets of the weighted criteria linked by fuzzy rules in a multi-layer perceptron, whose output defuzzification gives a new measure – a Journal Internationality Index akin to the Impact Factor for citations. Viewing internationality in this way as an approximated fuzzy function means a quantitative measure can be found while keeping intact its semantic rule origins and meaning.
  • Wave-particle dynamics in a hot inhomogeneous fusion plasma

    Michael Taylor

    01/1996

    Degree: Ph.D.

    Supervisor: Professor R. Alan Cairns

  • Wave propagation through cyclotron resonance in the presence of large Larmor radius particles

    R. Alan Cairns, Helen Holt, Darren C. McDonald, Michael Taylor, Chris N. Lashmore-Davies

    Physics of Plasmas. 01/1995; 2:3702-3708.

    Absorption of waves propagating across an inhomogenous magnetic field is of crucial importance for cyclotron resonance heating. When the Larmor radius of the resonant particles is small compared to the wavelength then the propagation is described by differential equations, a comparatively simple met... [more] Absorption of waves propagating across an inhomogenous magnetic field is of crucial importance for cyclotron resonance heating. When the Larmor radius of the resonant particles is small compared to the wavelength then the propagation is described by differential equations, a comparatively simple method for obtaining which has recently been given by Cairns et al. [Phys. Fluids B 3, 2953 (1991)]. In a fusion plasma there may, however, be a significant population of ions whose Larmor radius is not small compared to the wavelength. In this case the system is described by integro‐differential equations, reflecting the fact that the plasma response at a given position is determined by the wave field over a region of width of the order of the Larmor radius. The simplified method referred to above is adapted to this case and used to obtain various forms of the equations. Methods of simplifying the equations while still retaining information from the non‐local response, are discussed and some illustrated numerical results presented.

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