| 1. |
- Embréus, Ola, 1991, et al.
(författare)
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Conservative large-angle collision operator for runaway avalanches
- 2015
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Ingår i: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. PP12.00107-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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.
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| 2. |
- Embréus, Ola, 1991, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: 42nd European Physical Society Conference on Plasma Physics, EPS 2015.
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Konferensbidrag (refereegranskat)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.
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| 3. |
- Embréus, Ola, 1991, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 22:5, s. 052122-
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Tidskriftsartikel (refereegranskat)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.
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| 4. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Gaussian radial basis functions for plasma physics: Numerical aspects
- 2015
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Ingår i: 42nd European Physical Society Conference on Plasma Physics, EPS 2015, Lisbon, Portugal, 22-26 June 2015.
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Konferensbidrag (refereegranskat)abstract
- A magnetized plasma is described by the Vlasov equation and the non-linear Fokker-Planck collision operator [1]. The Vlasov part describes phase-space advection and the collision operator adds dissipation due to collisional energy and momentum exchange. Numerical discretization of the collision operator, however, is far from trivial. Recently, we have developed a new approach [2] to address this issue. The new approach is based on an expansion in Gaussian Radial Basis Functions (RBFs), a method widely used in neural network calculations [3]. In this paper, we discusss useful details regarding the numerical implementation of the RBF method.
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| 5. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Guiding-center transformation of the radiation-reaction force in a nonuniform magnetic field
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:5, s. 475810504-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present the guiding-center transformation of the radiation-reaction force of a classical point charge traveling in a nonuniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field nonuniformity length scale, so that the guiding-center Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation-reaction force is obtained with the Poisson bracket formalism originally introduced by [A. J. Brizard, Phys. Plasmas 11 4429 (2004)], where it was used to eliminate the fast gyromotion from the Fokker-Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-center radiation-reaction force include tracing of charged particle orbits in complex magnetic fields as well as kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g., for runaway electron dynamics in tokamaks.
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| 6. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Radiation reaction induced non-monotonic features in runaway electron distributions
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:5, s. 475810502-
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Tidskriftsartikel (refereegranskat)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.
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| 7. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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The Gaussian Radial Basis Function Method for Plasma Kinetic Theory
- 2015
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Ingår i: Physics Letters, Section A: General, Atomic and Solid State Physics. - : Elsevier BV. - 0375-9601. ; 379:42, s. 2735-2739
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Tidskriftsartikel (refereegranskat)abstract
- Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas.
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| 8. |
- Newton, Sarah, 1981, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. CP12.00118-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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.
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| 9. |
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| 10. |
- Stahl, Adam, 1985, et al.
(författare)
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Effective Critical Electric Field for Runaway-Electron Generation
- 2015
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 114:11, s. 115002-
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Tidskriftsartikel (refereegranskat)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.
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