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Title: Full particle orbit effects in regular and stochastic magnetic fields

Abstract

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies themore » existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Authors:
 [1];  [2]; ; ;  [1];  [3]; ;  [4]
  1. Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France)
  2. (France)
  3. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States)
  4. CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France)
Publication Date:
OSTI Identifier:
22600020
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CHAOS THEORY; CHARGED PARTICLES; CHARGED-PARTICLE TRANSPORT; CYLINDRICAL CONFIGURATION; EQUATIONS OF MOTION; HAMILTONIANS; INTEGRAL CALCULUS; LORENTZ FORCE; MAGNETIC FIELDS; MAGNETIC MOMENTS; MAGNETIC SURFACES; NUMERICAL ANALYSIS; ORBITS; PARTICLES; PERTURBATION THEORY; PHASE SPACE; PITCHES; REVERSED SHEAR; STOCHASTIC PROCESSES; THERMAL BARRIERS

Citation Formats

Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr, CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex, Cambon, Benjamin, Leoncini, Xavier, Vittot, Michel, Castillo-Negrete, Diego del, Dif-Pradalier, Guilhem, and Garbet, Xavier. Full particle orbit effects in regular and stochastic magnetic fields. United States: N. p., 2016. Web. doi:10.1063/1.4958653.
Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr, CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex, Cambon, Benjamin, Leoncini, Xavier, Vittot, Michel, Castillo-Negrete, Diego del, Dif-Pradalier, Guilhem, & Garbet, Xavier. Full particle orbit effects in regular and stochastic magnetic fields. United States. doi:10.1063/1.4958653.
Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr, CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex, Cambon, Benjamin, Leoncini, Xavier, Vittot, Michel, Castillo-Negrete, Diego del, Dif-Pradalier, Guilhem, and Garbet, Xavier. 2016. "Full particle orbit effects in regular and stochastic magnetic fields". United States. doi:10.1063/1.4958653.
@article{osti_22600020,
title = {Full particle orbit effects in regular and stochastic magnetic fields},
author = {Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr and CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex and Cambon, Benjamin and Leoncini, Xavier and Vittot, Michel and Castillo-Negrete, Diego del and Dif-Pradalier, Guilhem and Garbet, Xavier},
abstractNote = {We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.},
doi = {10.1063/1.4958653},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = 2016,
month = 7
}
  • Cited by 1
  • Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less
  • The rf-SciDAC collaboration is developing computer simulations to predict the damping of radio frequency (rf) waves in fusion plasmas. Here we extend self-consistent quasi-linear calculations of ion cyclotron resonant heating to include the finite drift of ions from magnetic flux surfaces and rf induced spatial transport. The all-orders spectral wave solver AORSA is iteratively coupled with a particle based update of the plasma distribution function using a quasi-linear diffusion tensor representative of the k-vector spectrum. Initial results are presented for a high power minority heating scenario on the Alcator C-Mod tokamak and a high harmonic beam heating scenario on DIII-D.more » Finite orbit effects are shown to give a less peaked perpendicular energy profile and rf induced transport.« less
  • The study of collisional test particle diffusion in stochastic magnetic fields is extended to include the effects of the macroscopic flows of the plasma (drifts). We show that a substantial amplification of the diffusion coefficient can be obtained. This effect is produced by the combined action of the parallel collisional velocity and of the average drifts. The perpendicular collisional velocity influences the effective diffusion only in the limit of small average drifts. {copyright} {ital 1996 The American Physical Society.}
  • Collisional particle transport in stochastic magnetic fields is studied using a semi-analytical method. The aim is to determine the influence of the nonlinear effects that occur in the magnetic field line random walk on particle transport. We show that particle transport coefficients can be strongly influenced by the magnetic line trapping. The conditions that correspond to these nonlinear regimes are determined. We also analyze the effects produced by the space variation of the large-scale magnetic field. We show that an average drift is generated by the gradient of the magnetic field, which strongly increases and reverses its orientation in themore » nonlinear regime.« less