# 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 »

- Authors:

- Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France)
- (France)
- Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States)
- 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. Fri .
"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 = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}