Particle dynamics in a non-flaring solar active regionJ. Threlfall, T. Neukirch, C. E. Parnell, P.-A. Bourdin

School of Mathematics and Statistics, University of St Andrews, UKIWF, Austrian Academy of Sciences, AT

SH CK.SOLAR AND HELIOSPHERIC COLLISIONLESS KINETICS

Abstract

We present first results of test particle orbit calculations based on snapshots of an observationally drivenMHD model of a non-flaring slowly-evolving solar active region[1−2]. The test particle (electron andproton) orbits are calculated using the relativistic guiding centre approximation. Initial results suggestparticles can be accelerated to non-thermal energies due to local reconnection electric fields, despite thelack of flare-like behaviour. We discuss the implications of these results and highlight severalcharacteristic types of orbit behaviour within the simulated active region, in order to better understand theplasma response in such active region models at kinetic scales.

Introduction & motivation

Non-ideal MHD allows for reconnection; stored magneticenergy release. Early studies of reconnection often fo-cussed on X-point reconnection (with/without a guide field)for analytical simplicity. Test particles can be used to probethe diffusion region where MHD breaks down close to thenull and reveal underlying plasma behaviour[3−8]. Example X-point collapse/reconnection, credit: E. Priest

In 3D, there is no fundamental restriction on where reconnec-tion may occur, provided

∫E‖ds 6= 0[9−10]. Test particles also

reveal insights into reconnecting 3D structures. Typically thesecan either be single isolated topological structures (such as 3Dnulls[11−13] or magnetic separators[14−15]), or more complex con-figurations (e.g. current sheets[16−17], twisted coronal loops[18−19]

or collapsing magnetic traps[20−21]) which often contain (multiple)examples of simple topological features.

Example: test particle behaviour during 3D null reconnection[12]

Modern (MHD) models of solar/coronal structures now drivenby/reproduce observational data, and contain many topological struc-tures/features, often undergoing reconnection. Such models also oftenincorporate non-standard (solar-relevant) effects e.g. thermal conduc-tion, radiation, stratified atmospheres, etc.Ô How well does a modern, high resolution, observationally driven

MHD experiment model the physics on a kinetic level?Ô How do test-particles behave in such a complex environment?Ô Does this behaviour agree with observations?

Example: test particle behaviour during separator reconnection[15]

MHD active region model [Bourdin et al., A&A (2013)]

100 150 200 250

Solar-X [arcsec]

-18

0-1

30

-80

-30

So

lar-

Y [

arc

se

c]

a)

100 150 200 250

Solar-X [arcsec]

b)

SL1

SL2

SL3

CL1

100 150 200 250

Solar-X [arcsec]

c)

(L-R) Hinode/SOT magnetogram, Hinode/EIS Fe XV emission (at 1.5 MK) and simulated parallel electric field strength within AR core (+/− E||represented by pink/purple, strength decreases with opacity), observed on 14th Nov 2007. Green lines indicate connectivity of loops observed by

STEREO, circles indicate Doppler up/downflows. Threlfall et al. (sub.)

Use MHD simulations of a non-flaring active region[1], observed on 14th Nov. 2007 by Hinode andSTEREO. Simulations based on potential field extrapolation of magnetogram data (to determinemagnetic field structure in the corona) surrounded by MHD plasma in stratified atmosphere. Successivemagnetograms used to drive simulations at the photosphere, inducing currents (via braided field) whichare Ohmically dissipated. Experiment was designed to study coronal heating and includes gravity, heatconduction and optically thin radiation; simulations reproduce observed AR features[2], including locationsof heating and up/downflows. We use a single snapshot of MHD simulations as the environment intowhich we insert test particles using the relativistic guiding centre approach.

Test particle approach - relativistic guiding centre

Particle behaviour governed by the relativistic guiding centre approximation (GCA) equations[22]:du‖dt

=ddt(γv‖)

= γuE ·dbdt

+ Ωscle tsclE‖ −

µr

γ

∂B∂s,

R⊥ = uE +b

B??×

1Ωscl

e tscl

[µr

γ

(∇B? +

vscl2

c2 uE∂B?

∂t

)+ u‖

dbdt

+ γduE

dt

]+

vscl2

c2

u‖γ

E‖uE

,

dγdt

=vscl

2

c2

[Ωscl

e tscl

(R⊥ +

u‖γ

b)· E +

µr

γ

∂B?

∂t

], µr =

γ2v2⊥

B.

These normalised equations are solved using an RK4 scheme with adaptive step-size, subject to E&Bfield conditions given by AR model, for both electrons and protons, provided the spatial and temporalscales of the particle and MHD models are well separated (monitored for each simulated particle).

Particle initial conditions [Threlfall et al. (sub.)]

Initial particle distribution, Threlfall et al. (sub.)

Ô

2000 particles evenly distributedthroughout lower corona.

Ô

Uniform initial pitch angle (45)and kinetic energy (20 eV),simulated for 10 s. Resistivity (η = 100m2s−1) big to

resolve current sheet structures. Designed to study heating (ηj2),

but resulting E-fields (ηj) strongand extend into corona, capableof ’trapping’ particles. Extended E|| distribution, Threlfall et al. (sub.)

Global behaviour of particles [Threlfall et al. (sub.)]

Electron final positions, coloured by KEpeak, Threlfall et al. (sub.)

Electrons & protons both strongly acceler-ated by simulation E & B-fields. Both species can achieve same energy lev-

els, peaking at 0.4 GeV. Particles reaching peak energy levels typi-

cally accelerated to photosphere. Compact photospheric impact sites. Drift effects seen but negligible compared

to parallel motion - particles predominantlyfollow field lines. Approximately 1/4 of particles are ’trapped’

along field-lines within corona. Trapping at-tributed to strength and orientation of elec-tric field near the base of loops (single ex-ample shown in detail below).

Can also create energy spectra for all particles, byassessing energies of all particles in the domain atspecific times. Both electron and proton spectra rapidly conform

to power law distributions, with small power lawindices. Protons take longer to conform due to difference

in mass; both species ultimately reach same in-dex value over time. Power law indices recovered are extremely

’hard’; large numbers of particles achieve highlynon-thermal energies.

101 102 103 104 105 106 107 108

Kinetic Energy (eV)

10−6

10−4

10−2

100

102

Nu

mb

er

t= 0.08st= 0.16st= 0.64st= 2.56st= 9.50s

spectra

p=−1.10 (t= 9.50s)p=−1.10 (t= 2.56s)p=−1.10 (t= 0.64s)p=−1.12 (t= 0.16s)p=−1.14 (t= 0.08s)

fitted power law

Electron energy spectra over time with fitted power laws, Threlfall et al. (sub.)

These results imply that resistivity and current structures produce electric fields which are much higherand more extended than required to produce a purely thermal particle population.

Non-magnetic particle trapping [Threlfall et al. (sub.)]

0.001 0.010 0.100 1.000 10.000 100.000t (s)

100

101

102

103

104

105

KE

[e

V]

−0.02

−0.01

0.00

0.01

0.02

E|| [

Vm

−1]

0.001 0.010 0.100 1.000 10.000 100.000t (s)

−1.0

−0.5

0.0

0.5

1.0

v||/m

ax(v

||)

1.5•10−4

2.0•10−4

2.5•10−4

3.0•10−4

3.5•10−4

|B| [

T ]

Clockwise from left, path of a ’trapped’ electron compared tosurface of E|| = 0, with graphs showing kinetic energy & E|| and

normalised v|| & |B| over time, Threlfall et al. (sub.)

We observe a large number of examples of test particles, both electron and proton, which continue tooscillate between loop footpoints for the duration of the particle simulation. In the above test case, we ruleout the magnetic mirror effect as the cause of this trapping, and instead identify orbit encounters withstrong (and oppositely oriented) electric fields along the same field line (often near the photosphere)which cause the particle to remain ’trapped’ in the same region. To our knowledge such a type of trap hasnever before been encountered in test-particle simulations. Whether such a trap may produce anobservational signature is unknown; such a signature might allow for further insights into electric fieldstructures within the solar atmosphere.

Summary

Conclusions:H Combined test particles with MHD simulations of a non-flaring active region[1−2].H Orbits commonly achieve high energies, due to strength and extent of E-field in simulations.H Uncover a form of non-magnetic trapping (due to regions of oppositely oriented E||).H Can use results to further constrain future MHD simulation parameters modelling active region heatingand reconnection.

Extensions and future work:MHD model: ’realistic’ resistivity and currents? Accompanying X-ray data? Other obs. (e.g. NuSTAR)?. Test-particle model: Need a way to slow accelerated particles (e.g. include collisions/wave-particle

interaction effects?). More ’realistic’ initial conditions? Beyond test-particle approach?

References[1] Bourdin, P.-A., Bingert, S., & Peter, H. 2013, A&A, 555, AA123[2] Bourdin, P.-A., Bingert, S., & Peter, H. 2014, PASJ, 66, 1[3] Bruhwiler, D. L. & Zweibel E. G. 1992 JGR, 97, 10825[4] Browning, P. K. & Vekstein, G. E. 2001 JGR, 106, 18677–18692[5] Hamilton et al., 2003 SolP, 214, 339–352[6] Zharkova, V. V., & Gordovskyy, M. 2004, ApJ, 604, 884[7] Wood, P. & Neukirch, T. 2005, SolP, 226, 73[8] Hamilton et al., 2005 ApJ, 625, 496–505[9] Schindler, K., Hesse, M., & Birn, J. 1988 JGR, 93, 5547–5557

[10] Hesse, M. & Schindler, K. 1988, JGR, 93, 5559–5567[11] Dalla, S. & Browning, P. K. 2005 A&A, 436, 1103–1111

[12] Dalla, S. & Browning, P. K. 2008 A&A, 491, 289–295[13] Stanier, A., Browning, P., & Dalla, S. 2012, A&A, 542, A47[14] Threlfall et al., 2015, A&A, 574, A7[15] Threlfall, J., Stevenson, J. E. H., Parnell, C. E., & Neukirch T. , in prep.[16] Turkmani et al., 2005, ApJl, 620, L59–L62[17] Onofri, M., Isliker, H., & Vlahos, L. 2006 PRL, 96 (15), 151102[18] Gordovskyy, M. & Browning, P. K. 2011 ApJ, 729, 101[19] Gordovskyy et al., 2014 A&A, 561, A72[20] Grady, K. J., Neukirch, T., and Giuliani, P. 2012 A&A, 546, A85[21] Eradat Oskoui, S., Neukirch, T., & Grady, K. J. 2014 A&A, 563, A73[22] Northrop, T. 1963, The adiabatic motion of charged particles

This project has received funding from the European Union’s Seventh Framework Programme for research, technological development anddemonstration under grant agreement no 284515 (SHOCK). Website: project-shock.eu/home/. This work was supported by the InternationalMax-Planck Research School (IMPRS) on Solar System Physics. The results of this research have been achieved using the PRACE ResearchInfrastructure resource Curie based in France at TGCC, as well as JuRoPA hosted by the Julich Supercomputing Centre in Germany. Preparatory workhas been executed at the Kiepenheuer-Institut fur Sonnenphysik in Freiburg, as well as on the bwGRiD facility located at the Universitat Freiburg,Germany. We thank Suguru Kamio for his help finding active region observations. Hinode is a Japanese mission developed, launched, and operated byISAS/JAXA, in partnership with NAOJ, NASA, and STFC (UK). Additional operational support is provided by ESA and NSC (Norway).

http://www-solar.mcs.st-andrews.ac.uk/˜jamest/ jwt9@st-andrews.ac.uk