| 1. |
|
|
| 2. |
|
|
| 3. |
- Stahl, Adam, 1985, et al.
(author)
-
Kinetic modelling of runaway-electron dynamics
- 2015
-
In: Proceedings of the 14th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems.
-
Conference paper (other academic/artistic)abstract
- Improved understanding of runaway-electron formation and decayprocesses are of prime interest for the safe operation of large tokamaks, and theirdynamics during dynamical scenarios such as disruptions are of particular concern. Inthis contribution, we present kinetic modelling of scenarios with time-dependent plasmaparameters – in particular, we investigate hot-tail runaway generation during a rapiddrop in plasma temperature. With the goal of studying runaway-electron generationwith a self-consistent electric field-evolution, we also discuss the implementation ofa conservative collision operator and demonstrate its properties. An operator foravalanche runaway-electron generation which includes the proper energy dependenceof the runaway distribution, is investigated, and the avalanche growth rate is shownto be significantly affected in some parameter regimes. These developments all pavethe way for an improved modelling of runaway-electron dynamics during disruptionsor other dynamic events.
|
|
| 4. |
- Decker, Joan, 1977, et al.
(author)
-
Numerical characterization of bump formation in the runaway electron tail
- 2016
-
In: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 1361-6587 .- 0741-3335. ; 58:2, s. 025016-
-
Journal article (peer-reviewed)abstract
- Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham–Lorentz–Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting electron acceleration. The effect of the ALD force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker–Planck codes LUKE (Decker and Peysson 2004 Report EUR-CEA-FC-1736, Euratom-CEA), and CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847). The time evolution of the distribution function is analyzed as a function of the relevant parameters: parallel electric field, background magnetic field, and effective charge. Under the action of the ALD force, we find that runaway electrons are subject to an energy limit, and that the electron distribution evolves towards a steady-state. In addition, a bump is formed in the tail of the electron distribution function if the electric field is sufficiently strong. The mechanisms leading to the bump formation and energy limit involve both the parallel and perpendicular momentum dynamics; they are described in detail. An estimate for the bump location in momentum space is derived. We observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could, in turn, pump energy from runaway electrons and alter their confinement.
|
|
| 5. |
- Embréus, Ola, 1991, et al.
(author)
-
Numerical calculation of ion runaway distributions
- 2015
-
In: 42nd European Physical Society Conference on Plasma Physics, EPS 2015.
-
Conference paper (peer-reviewed)abstract
- Numerical solver of the 2D ion Fokker-Planck equation has been presented, and its usefulness demonstrated in investigating the conditions required for ion runaway in cold and hot tokamak plasmas. It is shown that Alfvénic activity observed in disruption experiments are unlikely to be explained by the runaway mechanism alone.
|
|
| 6. |
- Embréus, Ola, 1991, et al.
(author)
-
Numerical calculation of ion runaway distributions
- 2015
-
In: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 22:5, s. 052122-
-
Journal article (peer-reviewed)abstract
- Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments; however, limitations of previous analytic work have prevented definite conclusions. In this work, we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species, and temperatures, and the potential for excitation of toroidal Alfvén eigenmodes during tokamak disruptions is considered.
|
|
| 7. |
|
|
| 8. |
- Hesslow, Linnea, 1993, et al.
(author)
-
Effect of partially-screened nuclei on fast-electron dynamics
- 2017
-
In: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 118:25, s. article no. 5501-
-
Journal article (peer-reviewed)abstract
- We analyze the dynamics of fast electrons in plasmas containing partially ionized impurity atoms, where the screening effect of bound electrons must be included. We derive analytical expressions for the deflection and slowing-down frequencies, and show that they are increased significantly compared to the results obtained with complete screening, already at sub-relativistic electron energies. Furthermore, we show that the modifications to the deflection and slowing down frequencies are of equal importance in describing the runaway current evolution. Our results greatly affect fast-electron dynamics and have important implications, e.g. for the efficacy of mitigation strategies for runaway electrons in tokamak devices, and energy loss during relativistic breakdown in atmospheric discharges.
|
|
| 9. |
- Hesslow, Linnea, 1993, et al.
(author)
-
Kinetic effects of partially screened impurities in runaway-electron mitigation scenarios
- 2017
-
In: International Sherwood Fusion Theory Conference, Annapolis, USA.
-
Conference paper (other academic/artistic)abstract
- Runaway electrons constitute a significant threat to tokamak devices. Their mitigation by heavy-impurity injection has been experimentally shown to be more effective than would be expected from standard collisional theory [1]. In order to understand this effect and develop runaway mitigation schemes, more accurate kinetic models are needed to describe the interaction between electrons and partially ionized atoms. Such models require the partial screening of the nuclei by the bound electrons to be taken into account.In this contribution, we analyze the dynamics of fast electrons in plasmas containing partially ionized impurity atoms. A generalized collision operator is derived from first principles using quantum-mechanical models. We obtain analytical expressions for the deflection and slowing-down frequencies. Even at sub-relativistic energies, these are increased by more than an order of magnitude compared to the results obtained with complete screening. Moreover, we implement the generalized collision operator in the continuum kinetic-equation solver CODE [2, 3] and demonstrate that interaction with partially ionized atoms greatly affects fast-electron dynamics by enhancing the rates of angular deflection and energy loss. In particular, we investigate the decay of a runaway-electron current coupled to a self-consistent electric field. The effect of the interaction with partially ionized impurities has important implications for the efficacy of mitigation strategies for runaway electrons in tokamak devices.References[1] E. M. Hollmann et al., Physics of Plasmas 22, 056108 (2015).[2] M. Landreman, A. Stahl and T. Fülöp, Comp. Phys. Comm. 185, 847 (2014).[3] A. Stahl et al., Nuclear Fusion 56, 112009 (2016).
|
|
| 10. |
- Hirvijoki, Eero, 1985, et al.
(author)
-
Radiation reaction induced non-monotonic features in runaway electron distributions
- 2015
-
In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:5, s. 475810502-
-
Journal article (peer-reviewed)abstract
- Runaway electrons, which are generated in a plasma where the induced electric field exceeds acertain critical value, can reach very high energies in the MeV range. For such energetic electrons,radiative losses will contribute significantly to the momentum space dynamics. Under certainconditions, due to radiative momentum losses, a non-monotonic feature – a “bump” – can formin the runaway electron tail, creating a potential for bump-on-tail-type instabilities to arise. Herewe study the conditions for the existence of the bump. We derive an analytical threshold conditionfor bump appearance and give an approximate expression for the minimum energy at which thebump can appear. Numerical calculations are performed to support the analytical derivations.
|
|
| 11. |
- Newton, Sarah, 1981, et al.
(author)
-
Numerical calculation of ion runaway distributions
- 2015
-
In: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. CP12.00118-
-
Conference paper (other academic/artistic)abstract
- Ion acceleration by electric fields is of interest in many plasma scenarios. Limitations of analytic descriptions prevent their general use in following the evolution of such ``runaway ion'' populations. Therefore we have implemented an initial value solver, CODION, for the linearized ion drift kinetic equation, with a non-relativistic Fokker-Planck collision operator. A spectral-Eulerian discretization scheme is used for 2D velocity space. The background plasma is taken to be homogeneous and static, with arbitrary composition. We demonstrate the use of the numerical distribution function to study ion acceleration in solar flares and tokamak plasmas. The variation of the strength and duration of the electric field required to produce a significant fast ion population is illustrated. Low frequency magnetic activity, indicative of toroidal Alfv\'{e}n eigenmode excitation, has been observed during tokamak disruptions. Taking typical disruption parameters, we show that accelerated bulk ions are unlikely to reach a sufficient velocity to provide the resonant drive.
|
|
| 12. |
|
|
| 13. |
|
|
| 14. |
- Pokol, Gergö, 1979, et al.
(author)
-
Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons
- 2014
-
In: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 21:10, s. 102503-
-
Journal article (peer-reviewed)abstract
- Runaway electrons with strongly anisotropic distributions present in post-disruption tokamak plasmas can destabilize the extraordinary electron (EXEL) wave. The present work investigates the dynamics of the quasi-linear evolution of the EXEL instability for a range of different plasma parameters using a model runaway distribution function valid for highly relativistic runaway electron beams produced primarily by the avalanche process. Simulations show a rapid pitch-angle scattering of the runaway electrons in the high energy tail on the 100–1000 μs time scale. Due to the wave-particle interaction, a modification to the synchrotron radiation spectrum emitted by the runaway electron population is foreseen, exposing a possible experimental detection method for such an interaction.
|
|
| 15. |
|
|
| 16. |
- Stahl, Adam, 1985, et al.
(author)
-
Effective Critical Electric Field for Runaway-Electron Generation
- 2015
-
In: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 114:11, s. 115002-
-
Journal article (peer-reviewed)abstract
- In this Letter we investigate factors that influence the effective critical electric field for runaway-electrongeneration in plasmas. We present numerical solutions of the kinetic equation and discuss the implications forthe threshold electric field. We show that the effective electric field necessary for significant runaway-electronformation often is higher than previously calculated due to both (1) extremely strong dependence of primarygeneration on temperature, and (2) synchrotron radiation losses. We also address the effective critical field inthe context of a transition from runaway growth to decay. We find agreement with recent experiments, but showthat the observation of an elevated effective critical field can mainly be attributed to changes in the momentum-space distribution of runaways, and only to a lesser extent to a de facto change in the critical field.
|
|
| 17. |
- Stahl, Adam, 1985, et al.
(author)
-
Kinetic modelling of runaway electrons in dynamic scenarios
- 2016
-
In: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 56:11, s. 112009-
-
Journal article (peer-reviewed)abstract
- Improved understanding of runaway-electron formation and decay processes are of prime interest for the safe operation of large tokamaks, and the dynamics of the runaway electrons during dynamical scenarios such as disruptions are of particular concern. In this paper, we present kinetic modelling of scenarios with time-dependent plasma parameters; in particular, we investigate hot-tail runaway generation during a rapid drop in plasma temperature. With the goal of studying runaway-electron generation with a self-consistent electric-field evolution, we also discuss the implementation of a conservative collision operator and demonstrate its properties. An operator for avalanche runaway-electron generation, which takes the energy dependence of the scattering cross section and the runaway distribution into account, is investigated. We show that the simpler avalanche model of Rosenbluth & Putvinskii [Nucl. Fusion 37, 1355 (1997)] can give very inaccurate results for the avalanche growth rate (either lower or higher) for many parameters, especially when the average runaway energy is modest, such as during the initial phase of the avalanche multiplication. The developments presented pave the way for an improved modelling of runaway-electron dynamics during disruptions or other dynamic events.
|
|
| 18. |
- Stahl, Adam, 1985, et al.
(author)
-
Reaction of runaway electron distributions to radiative processes
- 2015
-
In: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. PP12.00103 -
-
Conference paper (other academic/artistic)abstract
- The emission of electromagnetic radiation by a charged particle in accelerated motion is associated with a reduction in its energy, accounted for by the inclusion of a radiation reaction force in the kinetic equation. For runaway electrons in plasmas, the dominant radiative processes are the emission of bremsstrahlung and synchrotron radiation. In this contribution, we investigate the impact of the associated radiation reaction forces on the runaway electron distribution, using both analytical and numerical studies, and discuss the corresponding change to the runaway electron growth rate, which can be substantial. We also report on the formation of non-monotonic features in the runaway electron tail as a consequence of the more complicated momentum-space dynamics in the presence of radiation reaction.
|
|
| 19. |
- Stahl, Adam, 1985, et al.
(author)
-
Runaway-electron formation and electron slide-away in an ITER post-disruption scenario
- 2016
-
In: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 775:1
-
Conference paper (peer-reviewed)abstract
- Mitigation of runaway electrons is one of the outstanding issues for a reliable operation of ITER and other large tokamaks, and accurate estimates for the expected runaway- electron energies and current are needed. Previously, linearized tools, assuming the runaway population to be small, have been used to study the runaway dynamics, but these tools are not valid in the cases of most interest, i.e. when the runaway population becomes substantial. We study runaway-electron formation in a post-disruption ITER plasma using the newly developed non-linear code NORSE , and nd that the entire electron population is converted to runaways in the scenario considered. A new non-linear feedback mechanism is also described, by which a transition to electron slide-away can be induced at eld strengths signi cantly lower than previously expected. We nd the exact time to the transition to be highly dependent on the details of the mechanisms removing heat from the thermal electron population.
|
|
| 20. |
- Stahl, Adam, 1985, et al.
(author)
-
Self-consistent nonlinear kinetic modeling of runaway-electron dynamics
- 2017
-
Conference paper (peer-reviewed)abstract
- Runaway electrons represent the greatest threat to the plasma-facing components of atokamak when they are highly energetic and constitute a significant fraction of the electronpopulation, a regime which has not been previously accessible in modelling since it requiresa nonlinear relativistic treatment. To address this problem, we present an efficient numericaltool called NORSE for the study of runaway-electron momentum-space dynamics.The kinetic equation solved in NORSE includes a fully nonlinear relativistic collision operator, making it possible to consider scenarios where the electric field is comparableto the Dreicer field (or larger), or the electron distribution function is otherwise far froma Maxwellian (which can be the case already in present-day runaway experiments). Thiscapability makes NORSE unique in the field of runaway-electron studies.Using NORSE, we investigate the transition to a regime where the entire electronpopulation experiences continuous acceleration, so-called electron slide-away. Forthe first time, we apply a nonlinear kinetic-equation solver to study the evolution ofthe electron distribution in an ITER disruption. We use an electric field calculated self consistently,and show that the runaway-electron density becomes substantial, makingthe nonlinear treatment essential. In addition, we find that Ohmic heating and the rateof heat loss play an important role in determining the electron dynamics, with the latteraffecting the average energy reached by the runaways by several orders of magnitude.
|
|
| 21. |
- Stahl, Adam, 1985, et al.
(author)
-
Synchrotron radiation from a runaway electron distribution in tokamaks
- 2013
-
In: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 20:9, s. 093302-
-
Journal article (peer-reviewed)abstract
- The synchrotron radiation emitted by runaway electrons in a fusion plasma provides information regarding the particle momenta and pitch-angles of the runaway electron population through the strong dependence of the synchrotron spectrum on these parameters. Information about the runaway density and its spatial distribution, as well as the time evolution of the above quantities, can also be deduced. In this paper, we present the synchrotron radiation spectra for typical avalanching runaway electron distributions. Spectra obtained for a distribution of electrons are compared with the emission of mono-energetic electrons with a prescribed pitch-angle. We also examine the effects of magnetic field curvature and analyse the sensitivity of the resulting spectrum to perturbations to the runaway distribution. The implications for the deduced runaway electron parameters are discussed. We compare our calculations to experimental data from DIII-D and estimate the maximum observed runaway energy.
|
|
| 22. |
|
|
| 23. |
- Embréus, Ola, 1991, et al.
(author)
-
Conservative large-angle collision operator for runaway avalanches
- 2015
-
In: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. PP12.00107-
-
Conference paper (other academic/artistic)abstract
- Avalanche runaway generation is the phenomenon whereby runaway electrons (REs) are generated due to large-angle collisions of thermal electrons with existing REs, leading to an exponential growth of the runaway current. These large-angle collisions are not described by the Fokker-Planck operator commonly employed to model collisions in plasmas, and have previously been accounted for by the addition of a particle source term in the kinetic equation [M. Rosenbluth et al., 1997, Nucl. Fusion 37, 1355; S. C. Chiu et al. 1998, Nucl. Fusion 38, 1711]. In this contribution we describe a new large-angle collision operator, derived as the high-energy limit of the linearized relativistic Boltzmann collision integral. This operator generalizes previous models of large-angle collisions to account for the full momentum dependence of the primary distribution and conserves particle number, momentum and energy, while also avoiding double counting of small- and large-angle collisions. The new operator is implemented in the 2D Fokker-Planck solver CODE [M. Landreman et al. 2014, Comp. Phys. Comm. 185, 847], with which we investigate its effect on the evolution of the runaway distribution.
|
|
| 24. |
- Embréus, Ola, 1991, et al.
(author)
-
Effect of bremsstrahlung radiation emission on fast electrons in plasmas
- 2016
-
In: 43rd European Physical Society Conference on Plasma Physics, EPS 2016.
-
Conference paper (peer-reviewed)abstract
- Bremsstrahlung radiation emission is an important energy loss mechanism for energetic electrons in plasmas. In this contribution we investigate the effect of spontaneous bremsstrahlung emission on the momentum-space structure of the electron distribution, using a Boltzmanntransport model fully accounting for the emission of finite-energy photons. We implement the model in a 2D continuum kinetic-equation solver, and study the solutions to determine the effect of bremsstrahlung on the electron distribution function. We find that electrons acceleratedby electric fields can reach significantly higher energies than predicted in previous work,which considered only the average energy loss of a test particle. We demonstrate that significantfractions of electrons reach twice the expected energy or more, due to the difference betweenthe average and Boltzmann model of bremsstrahlung radiation losses. Furthermore, we show that the emission of low-energy photons, which have previously been neglected because theydo not contribute to net energy loss, can contribute significantly to the dynamics of electrons with an anisotropic distribution by enhancing the angular-deflection rate.
|
|
| 25. |
- Embréus, Ola, 1991, et al.
(author)
-
Effect of bremsstrahlung radiation emission on fast electrons in plasmas
- 2016
-
In: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 18:9, s. 093023-
-
Journal article (peer-reviewed)abstract
- Bremsstrahlung radiation emission is an important energy loss mechanism for energetic electrons in plasmas. In this paper we investigate the effect of spontaneous bremsstrahlung emission on the momentum-space structure of the electron distribution, fully accounting for the emission of finite-energy photons. We find that electrons accelerated by electric fields can reach significantly higher energies than what is expected from energy-loss considerations. Furthermore, we show that the emission of soft photons can contribute significantly to the dynamics of electrons with an anisotropic distribution.
|
|
| 26. |
- Embréus, Ola, 1991, et al.
(author)
-
On the relativistic large-angle electron collision operator for runaway avalanches in plasmas
- 2018
-
In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:1, s. 905840102-
-
Journal article (peer-reviewed)abstract
- Large-angle Coulomb collisions lead to an avalanching generation of runaway electrons in a plasma. We present the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator. The relation to previous models for large-angle collisions is investigated, and their validity assessed. We present a form of the generalized collision operator which is suitable for implementation in a numerical kinetic-equation solver, and demonstrate the effect on the runaway-electron growth rate. Finally we consider the reverse avalanche effect, where runaways are slowed down by large-angle collisions, and show that the choice of operator is important if the electric field is close to the avalanche threshold.
|
|
| 27. |
- Embréus, Ola, 1991, et al.
(author)
-
Relativistic Boltzmann collision operator for runaway-avalanche studies
- 2017
-
In: International Sherwood Fusion Theory Conference, Annapolis, USA.
-
Conference paper (other academic/artistic)abstract
- Avalanche runaway generation is a critical threat to large tokamaks such as ITER: according to the Rosenbluth-Putvinski theory[1], a small seed population of fast electrons will multiply through knock-on collisions by a factor of order R~exp(3 I[MA]), which for plasma currents of order I=10-15 MA means that a single fast electron can convert the entire ohmic current to runaway current.The exponential sensitivity of the avalanche multiplication factor R to the details of the runaway-generation dynamics shows a need for more accurate models of large-angle collisions.Existing models of large-angle collisions that have been used in magnetic-confinement fusion studies[1,2] have two main flaws: (i) they do not conserve electron momentum or energy, and (ii) they double count collisions with small-angle collisions, which are typically accounted for with a Fokker-Planck collision operator.We have developed a new large-angle collision operator based on the full relativistic Boltzmann equation which resolves these issues.We use kinetic simulations to show how the new improved collision operator modify the avalanche growth rates obtained with previous models. In particular, we compare results with the steady-state theory of Rosenbluth and Putvinski, as well as with theoretical predictions of a recent study[3] for avalanche generation in near-threshold electric fields E~E_c in the presence of synchrotron-radiation losses.References:[1] M. N. Rosenbluth and S. V. Putvinski, Nucl. Fusion 37, 1355 (1997).[2] S. C. Chiu, M. N. Rosenbluth, R. W. Harvey and V. S. Chan, Nucl. Fusion 38, 1711 (1998).[3] P. Aleynikov and B. N. Breizman, Phys. Rev. Lett. 114, 155001 (2015).
|
|
| 28. |
- Ficker, Ondrej, et al.
(author)
-
Long slide-away discharges in the COMPASS tokamak
- 2016
-
In: Proceedings of the 58th Annual Meeting of the APS Division of Plasma Physics. ; 61:18, s. GP10.00101-
-
Conference paper (other academic/artistic)abstract
- In this contribution, long runaway electron (RE)dominated discharges achieved in the COMPASS tokamak are presented. The extensivelength is possible due to a low consumption of available volt-seconds of thetokamak transformer in this type of discharge. Energetic electron losses in thisregime seems to be modulated mainly by small oscillations of a radial position (controllersetting) unlike in the RE discharges at higher electron density, where variousMHD phenomena affect the evolution of the losses. The behaviour of the slide-awayplasma is studied using magnetic coils, HXR detectors, ECE system and a pair of3He proportional counters of neutrons. The plasma scenario is also modelled usingFokker-Planck codes.
|
|
| 29. |
- Fülöp, Tünde, 1970, et al.
(author)
-
Kinetic modelling of runaways in fusion plasmas
- 2016
-
In: Proceedings of 26th IAEA Fusion Energy Conference, Kyoto, Japan. ; , s. TH/P4-1
-
Conference paper (other academic/artistic)abstract
- Mitigation of runaway electrons is one of the outstanding issues for a reliable operationof ITER and other large tokamaks. To achieve this, quantitatively accurate estimatesfor the expected runaway electron energies and current are needed. In this work we de-scribe an accurate theoretical framework for studying the effects of collisional nonlinear-ities, bremsstrahlung and synchrotron radiation emission, and knock-on collisions on therunaway electron distribution. We outline the identification of significant features of run-away electron behaviour enabled by this framework and their potential to affect the growthof a runaway population.
|
|
| 30. |
|
|
| 31. |
- Hoppe, Mathias, 1993, et al.
(author)
-
SOFT: A synthetic synchrotron diagnostic for runaway electrons
- 2018
-
In: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 58:2, s. 026032-
-
Journal article (peer-reviewed)abstract
- Improved understanding of the dynamics of runaway electrons can be obtained by measurement and interpretation of their synchrotron radiation emission. Models for synchrotron radiation emitted by relativistic electrons are well established, but the question of how various geometric effects -- such as magnetic field inhomogeneity and camera placement -- influence the synchrotron measurements and their interpretation remains open. In this paper we address this issue by simulating synchrotron images and spectra using the new synthetic synchrotron diagnostic tool SOFT (Synchrotron-detecting Orbit Following Toolkit). We identify the key parameters influencing the synchrotron radiation spot and present scans in those parameters. Using a runaway electron distribution function obtained by Fokker-Planck simulations for parameters from an Alcator C-Mod discharge, we demonstrate that the corresponding synchrotron image is well-reproduced by SOFT simulations, and we explain how it can be understood in terms of the parameter scans. Geometric effects are shown to significantly influence the synchrotron spectrum, and we show that inherent inconsistencies in a simple emission model (i.e. not modeling detection) can lead to incorrect interpretation of the images.
|
|
| 32. |
- Landreman, M., et al.
(author)
-
Numerical calculation of the runaway electron distribution function and associated synchrotron emission
- 2014
-
In: Computer Physics Communications. - : Elsevier BV. - 0010-4655. ; 185:3, s. 847-855
-
Journal article (peer-reviewed)abstract
- Synchrotron emission from runaway electrons may be used to diagnose plasma conditions during a tokamak disruption, but solving this inverse problem requires rapid simulation of the electron distribution function and associated synchrotron emission as a function of plasma parameters. Here we detail a framework for this forward calculation, beginning with an efficient numerical method for solving the Fokker-Planck equation in the presence of an electric field of arbitrary strength. The approach is continuum (Eulerian), and we employ a relativistic collision operator, valid for arbitrary energies. Both primary and secondary runaway electron generation are included. For cases in which primary generation dominates, a time-independent formulation of the problem is described, requiring only the solution of a single sparse linear system. In the limit of dominant secondary generation, we present the first numerical verification of an analytic model for the distribution function. The numerical electron distribution function in the presence of both primary and secondary generation is then used for calculating the synchrotron emission spectrum of the runaways. It is found that the average synchrotron spectra emitted from realistic distribution functions are not well approximated by the emission of a single electron at the maximum energy. © 2013 Elsevier B.V.
|
|
| 33. |
- Paz-Soldan, C, et al.
(author)
-
Synchrotron and collisional damping effects on runaway electron distributions
- 2016
-
In: 58th Annual Meeting of the APS Division of Plasma Physics. ; 61:18, s. CO4.00010 -
-
Conference paper (other academic/artistic)abstract
- Validated models of runaway electron (RE) dissipation are required to confidently approve safe ITER Q=10 operation. DIII-D experiments using quiescent REs are exploring the importance of synchrotron and collisional damping terms to RE dissipation. New time and energy-resolved measurements of RE bremsstrahlung hard X-ray (HXR) emission reveal stark differences between high and low energy REs as damping terms are varied. Previously reported anomalously high RE dissipation only applies to low energy REs. At high energy (where synchrotron effects are strongest) low synchrotron damping cases reach higher peak RE energy despite weaker particle confinement. Low-energy RE decay is observed concurrently with high-energy RE growth. RE dissipation models predict bump-on-tail distributions whose properties depend on the damping terms. Measured HXR spectra are very broad, as expected for bump-on-tail distributions.
|
|
| 34. |
- Stahl, Adam, 1985, et al.
(author)
-
Eddington capture sphere around luminous stars
- 2012
-
In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 546:10
-
Journal article (peer-reviewed)abstract
- Test particles infalling from infinity onto a compact spherical star with a mildly super-Eddington luminosity at its surface are typically trapped on the “Eddington capture sphere” and do not reach the surface of the star. The presence of a sphere on which radiation pressure balances gravity for static particles was first discovered some twenty five years ago. Subsequently, it was shown to be a capture sphere for particles in radial motion, and more recently also for particles in non-radial motion, in which the Poynting-Robertson radiation drag efficiently removes the orbital angular momentum of the particles, reducing it to zero. Here we develop this idea further, showing that “levitation” on the Eddington sphere (above the stellar surface) is a state of stable equilibrium, and discuss its implications for Hoyle-Lyttleton accretion onto a luminous star. When the Eddington sphere is present, the cross-section of a compact star for actual accretion is typically less than the geometrical cross-section πR2, direct infall onto the stellar surface only being possible for relativistic particles, with the required minimum particle velocity at infinity typically about half the speed of light. We further show that particles on typical trajectories in the vicinity of the stellar surface will also be trapped on the Eddington capture sphere.
|
|
| 35. |
- Stahl, Adam, 1985, et al.
(author)
-
Escape, capture, and levitation of matter in Eddington outbursts
- 2013
-
In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 555
-
Journal article (peer-reviewed)abstract
- Context: An impulsive increase in luminosity by one half or more of the Eddington value will lead to ejection of all optically thin plasma from Keplerian orbits around the radiating star, if gravity is Newtonian and the Poynting-Robertson drag is neglected. Radiation drag may bring some particles down to the stellar surface. On the other hand, general relativistic calculations show that gravity may be balanced by a sufficiently intense radiation field at a certain distance from the star. Aims: We investigate the motion of test particles around highly luminous stars to determine conditions under which plasma may be ejected from the system. Results: In Einstein's gravity, if the outburst is close to the Eddington luminosity, all test particles orbiting outside an "escape sphere" will be ejected from the system, while all others will be captured from their orbits onto the surface of another sphere, which is well above the stellar surface, and may even be outside the escape sphere, depending on the value of luminosity. Radiation drag will bring all the captured particles to rest on this "Eddington capture sphere," where they will remain suspended in an equilibrium state as long as the local flux of radiation does not change and remains at the effective Eddington value.
|
|
| 36. |
- Stahl, Adam, 1985
(author)
-
Momentum-space dynamics of runaway electrons in plasmas
- 2017
-
Doctoral thesis (other academic/artistic)abstract
- Fast electrons in a plasma experience a friction force that decreases with increasing particle speed, and may therefore be continuously accelerated by sufficiently strong electric fields. These so-called runaway electrons may quickly reach relativistic speeds. This is problematic in tokamaks – devices aimed at producing sustainable energy through the use of thermonuclear fusion reactions – where runaway-electron beams carrying strong currents may form. If the runaway electrons deposit their kinetic energy in the plasma-facing components, these may be seriously damaged, leading to long and costly device shutdowns.Crucial to the runaway phenomenon is the behavior of the runaway electrons in two-dimensional momentum space. The interplay between electric-field acceleration, collisional momentum-space transport, and radiation reaction determines the dynamics and the growth or decay of the runaway-electron population. In this thesis, several aspects of this interplay are investigated, including avalanche multiplication rates, synchrotron radiation reaction, modifications to the critical electric field for runaway generation, rapidly changing plasma parameters, and electron slide-away. Two numerical tools for studying electron momentum-space dynamics, based on an efficient solution of the kinetic equation, are presented and used throughout the thesis. The spectrum of the synchrotron radiation emitted by the runaway electrons – a useful diagnostic for their properties – is also studied.It is found that taking the electron distribution into account properly is crucial for the interpretation of synchrotron spectra; that a commonly used numerical avalanche operator may either overestimate or underestimate the runaway-electron growth rate, depending on the scenario; that radiation reaction modifies the critical electric field, but that this modification often is small compared to other effects; that electron slide-away can occur at significantly weaker electric fields than expected; and that collisional nonlinearities may be significant for the evolution of runaway-electron populations in disruption scenarios.
|
|
| 37. |
- Stahl, Adam, 1985, et al.
(author)
-
NORSE: A solver for the relativistic non-linear Fokker-Planck equation for electrons in a homogeneous plasma
- 2017
-
In: Computer Physics Communications. - : Elsevier BV. - 0010-4655. ; 212, s. 269-279
-
Journal article (peer-reviewed)abstract
- Energetic electrons are of interest in many types of plasmas, howe ver previous modelling of their properties have been restricted to the use of linear Fokker-Planck collision ope rators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modelling of the momentum- space dynamics of the electrons in cases where strong departure s from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than pre viously predicted.
|
|
| 38. |
- Stahl, Adam, 1985
(author)
-
Synchrotron radiation from runaway electrons in plasmas
- 2015
-
Licentiate thesis (other academic/artistic)abstract
- Highly relativistic runaway electrons are of great concern in the area of fusion energy research, since their presence in tokamak plasmas have the potential to hinder the successful and stable operation of the device, and potentially cause severe structural damage. In this thesis, runaway electron generation dynamics is investigated using the newly developed efficient computational tool CODE. A particular emphasis is given to the synchrotron radiation emitted by the runaways, as this is an important source of information about their properties. The synchrotron emission spectrum is studied, as well as the effects of radiation back-reaction on the electron distribution and the runaway electron dynamics. Synchrotron emission back-reaction is found to have a significant impact on the runaway distribution, leading to an increase in the critical electric field for runaway generation, as well as the appearance of non-monotonic features in the runaway tail for electric-field strengths above a certain threshold, potentially acting as a source of bump-on-tail instabilities. Both of these effects may contribute to reduce the severity of the runaway problem, although their importance is largest at high temperatures and low densities, likely making the impact in a tokamak disruption scenario limited. It is also found that the previously used approximation of considering only the emission from the most strongly emitting particles when modeling the synchrotron spectrum from runaway distributions can produce highly inaccurate results, and that the use of the full runaway distribution in this context is necessary.
|
|
| 39. |
- Tinguely, Alex, et al.
(author)
-
Analysis of Runaway Electron Synchrotron Emission in Alcator C-Mod
- 2016
-
In: Proceedings of the 58th Annual Meeting of the APS Division of Plasma Physics. ; 61:18, s. TO4.00007-
-
Conference paper (other academic/artistic)abstract
- Alcator C-Mod’s high magnetic field allows relativistic “runaway” electron (RE) synchrotron radiation (SR) to beobserved in the visible wavelength range. Our aim is to determine the evolution of the RE energy distribution function, current, and density from measured SR spectra, providing insight into basic plasma physics as well as mitigation for fusion devices. Recent theoretical studies predict that the SR reaction force and collisional friction will balance the electric force, forming a “bump” on the tail of the energy distribution. However, both mono-energetic and monotonically-decreasing distributions fit the experimental data equally well. The COllisonal Distribution of Electrons code is applied to C-Mod RE discharges and compared to experiment.In addition, a scan in magnetic field from 2.7 -- 8 T explores the importance of SR as a power loss mechanism and limit on the maximum RE energy.
|
|
| 40. |
- Tinguely, RA, et al.
(author)
-
Synchrotron emission in Alcator C-Mod: spectra at three magnetic fields, visible camera images, and polarization data
- 2017
-
In: 59th Annual Meeting of the APS Division of Plasma Physics. ; , s. JP11.00096-
-
Conference paper (other academic/artistic)abstract
- Alcator C-Mod's high magnetic field allows runaway electron synchrotron emission to be observed in the visible wavelength range. Visible spectrometers were used to measure synchrotron spectra at three magnetic fields: 2.7, 5.4, and 7.8 T. Both a test-particle model and kinetic solver CODE (COllisional Distribution of Electrons) explore the energy evolution of the runaway population and the impact of magnetic-field-dependent synchrotron radiation as a power loss mechanism. Additionally, distortion-corrected visible camera images capture the spatial distribution and evolution of synchrotron emission in C-Mod. Initial results show good agreement between experiment and the new synthetic diagnostic SOFT (Synchrotron-detecting Orbit-Following Toolkit). Finally, a first look at synchrotron polarization data is presented.
|
|
| 41. |
- Wielgus, Maciej, et al.
(author)
-
Oscillations of the Eddington capture sphere
- 2012
-
In: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 545:9
-
Journal article (peer-reviewed)abstract
- We present a toy model of mildly super-Eddington, optically thin accretion onto a compact star in the Schwarzschild metric, which predicts periodic variations of luminosity when matter is supplied to the system at a constant accretion rate. These are related to the periodic appearance and disappearance of the Eddington capture sphere. In the model the frequency is found to vary inversely with the luminosity. If the input accretion rate varies (strictly) periodically, the luminosity variation is quasi-periodic, and the quality factor is inversely proportional to the relative amplitude of mass accretion fluctuations, with its largest value Q ≈ 1/(10|δṀ/Ṁ|) attained in oscillations at about 1 to 2 kHz frequencies for a 2 M⊙ star.
|
|
