# Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos

## Abstract

Using a full orbit test particle approach, we analyse the motion of a single proton in the vicinity of magnetic null point configurations which are solutions to the kinematic, steady state, resistive magnetohydrodynamics equations. We consider two magnetic configurations, namely, the sheared and torsional spine reconnection regimes [E. R. Priest and D. I. Pontin, Phys. Plasmas 16, 122101 (2009); P. Wyper and R. Jain, Phys. Plasmas 17, 092902 (2010)]; each produce an associated electric field and thus the possibility of accelerating charged particles to high energy levels, i.e., > MeV, as observed in solar flares [R. P. Lin, Space Sci. Rev. 124, 233 (2006)]. The particle's energy gain is strongly dependent on the location of injection and is characterised by the angle of approach β, with optimum angle of approach β{sub opt} as the value of β which produces the maximum energy gain. We examine the topological features of each regime and analyse the effect on the energy gain of the proton. We also calculate the complete Lyapunov spectrum for the considered dynamical systems in order to correctly quantify the chaotic nature of the particle orbits. We find that the sheared model is a good candidate for the acceleration of particles, andmore »

- Authors:

- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22408229

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; CHAOS THEORY; CHARGED PARTICLES; ELECTRIC FIELDS; ENERGY LEVELS; LYAPUNOV METHOD; MAGNETIC FIELD CONFIGURATIONS; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; MEV RANGE; ORBITS; PROTONS; SHEAR; SOLAR FLARES; SPECTRA; STEADY-STATE CONDITIONS; TEST PARTICLES; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY

### Citation Formats

```
Gascoyne, Andrew, E-mail: a.d.gascoyne@sheffield.ac.uk.
```*Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos*. United States: N. p., 2015.
Web. doi:10.1063/1.4916402.

```
Gascoyne, Andrew, E-mail: a.d.gascoyne@sheffield.ac.uk.
```*Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos*. United States. doi:10.1063/1.4916402.

```
Gascoyne, Andrew, E-mail: a.d.gascoyne@sheffield.ac.uk. Sun .
"Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos". United States.
doi:10.1063/1.4916402.
```

```
@article{osti_22408229,
```

title = {Dynamics of charged particle motion in the vicinity of three dimensional magnetic null points: Energization and chaos},

author = {Gascoyne, Andrew, E-mail: a.d.gascoyne@sheffield.ac.uk},

abstractNote = {Using a full orbit test particle approach, we analyse the motion of a single proton in the vicinity of magnetic null point configurations which are solutions to the kinematic, steady state, resistive magnetohydrodynamics equations. We consider two magnetic configurations, namely, the sheared and torsional spine reconnection regimes [E. R. Priest and D. I. Pontin, Phys. Plasmas 16, 122101 (2009); P. Wyper and R. Jain, Phys. Plasmas 17, 092902 (2010)]; each produce an associated electric field and thus the possibility of accelerating charged particles to high energy levels, i.e., > MeV, as observed in solar flares [R. P. Lin, Space Sci. Rev. 124, 233 (2006)]. The particle's energy gain is strongly dependent on the location of injection and is characterised by the angle of approach β, with optimum angle of approach β{sub opt} as the value of β which produces the maximum energy gain. We examine the topological features of each regime and analyse the effect on the energy gain of the proton. We also calculate the complete Lyapunov spectrum for the considered dynamical systems in order to correctly quantify the chaotic nature of the particle orbits. We find that the sheared model is a good candidate for the acceleration of particles, and for increased shear, we expect a larger population to be accelerated to higher energy levels. In the strong electric field regime (E{sub 0}=1500 V/m), the torsional model produces chaotic particle orbits quantified by the calculation of multiple positive Lyapunov exponents in the spectrum, whereas the sheared model produces chaotic orbits only in the neighbourhood of the null point.},

doi = {10.1063/1.4916402},

journal = {Physics of Plasmas},

number = 3,

volume = 22,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}