Flare Particle Acceleration in Large-scale Magnetic Fields

Peter Cargill Imperial College

With thanks toRim Turkmani, Loukas Vlahos, Heinz Isliker and

Klaus Galsgaard,

ISSI October 5, 2006

The context: solar flares

• Release of 1032 ergs in 1000 sec.Evidence from SMM, RHESSI is that:• Large fraction of energy (at least 20%, perhaps more) is in

energetic particles:• Electrons > 10 keV. Appears to be solid result.• Ions? Controversial in past (see 1996 EOS “debate”). Less

so now, but still measurement difficulties.To put in context…….• Acceleration in solar wind, substorm etc. low-efficiency

processes• Even SNR shocks few percent into particles

WHY ARE FLARES SPECIAL? A magnetic complexity not present elsewhere.

Particle acceleration and reconnection

Assume that reconnection process responsible for flare energy release.

3 possible processes:• Shock acceleration (fast and slow)• MHD turbulence• Direct electric fields (sub- and super-

Dreicer)

Need to accelerate:• Particles quickly (usually < 1 sec)• To relativistic energies• A lot of particles

Basic theory of acceleration processes in isolation quite well established.

Shock Acceleration (single shock)Needs: Prompt shock formation

Drift accn (quasi-perp shocks)• Energy limited by escape from

shock of particle.• Number of particles limited by short

interaction time.

Diffusive accn (quasi-par shocks)• Can give very high energies through

multiple interactions with shock• Limited energy gain due to loss of

particles.• Needs injection (ok for ions,

problem for electrons)

Decker and Vlahos (1986)

Direct Electric Fields Split into sub-Dreicer (V/m) or

super-Dreicer (reconnection: 103 V/m)

Sub-Dreicer• long potential drops to get

interesting energies• Serious problems with current

and charge neutrality (many oppositely-directed currents).

Super-Dreicer• Can readily attain high

energies.• No issues of neutrality• Readily attainable in

reconnection geometry Holman and Benka (1992)

MHD Turbulence

Alfvén and fast mode waves can interact strongly with ions and electrons respectively.

• Can produce very high particle energies quickly

• Injection required cascade to short wavelengths.

• Theory largely based on quasi-linear models.

Miller (1997)

Efficiency question at single siteConsider turbulent acceleration:• Fraction of coronal EM energy available for

dissipation (10 – 20%). Rest in potential field.• Fraction of energy in reconnection goes to jets

(50%)• Fraction of jet energy goes to turbulence (50%)• Fraction of turbulence goes to particles (20%)

End up with requirement for massive coronal field (Cargill, 1996), Miller et al. 1997)

WRONG! Flare involved a transition in physics.• Somehow (and rarely), things conspire for

massively efficient acceleration of particles.

Flare Energy Release: the Monolithic Current Sheet

• Originally due to Carmichael, Sturrock etc (1964, 1966).

• Kopp and Pneuman proposed for “post”-flare loops (1976).

• Numerous manifestations (see H. Hudson “cartoon” collection)

Cargill and Priest (1983) Shibata, (199X)

Perhaps a reasonable model for eruptive and long-lived flares (+ post-flare loops).

Extension to “all” flares in Yohkoh era• “Cartoon” physics.• No effort to assess viability on basis of physics

(particle acceleration, global electrodynamics)• Still needs a proper physics-based

assessment……

What is an alternative?

Distributed energy release.• Flare comprised of many

distributed energy sites.• Each one is current sheet (as

in previous model)Questions:

How does dissipation initiate?How does it spread?How are particles accelerated?Do particles interact with

multiple sites?

Approach. MHD or PIC codes?Vlahos (1994)

Distributed Energy Release: SOC models

Start from power law distribution of flares: N(E) = (E0/E)1.8

• Lu and Hamilton (1991) applied ideas of Self Organised Criticality (SOC: Bak et al., 1987) to coronal field.

• Used “rules” to link magnetic field at neighbouring points. • Drive magnetic field locally. Stressed fields then relaxed.

Energy release.• Obtained power law of N(E).• Very rarely, field relaxed at ALL points at same time……

this could be said to be a flare.Controversy!!!• What do the relaxation rules mean?• Is the forcing reasonable?• What about real coronal geometry?......... and• What about Maxwell (and Faraday!)? Much argument….

Synchronised Energy Release: SOC/CA models

•Distribution of current in CA model: zoom on right•Get many dissipation regions

Isliker et al., (2001)

Acceleration in CA modelExample: Super-Dreicer E-field.

(Arzner and Vlahos, 2004)

• Parameterise acceleration process

• Calculate distributed sites with CA model

• Ballistic particle motion between accelerators.

• Assume particle loss from system

• Particles gain (and lose) energy in jumps at multiple sites

• Systematic gain in time. Fast (<< 1 sec)

• Proof of principle of acceleration at many sites.

BUT…. What is relation to MHD description?

Acceleration in MHD models

3 kinds

(1) Simple current sheet, x-line etc.

(2) Spectral models of MHD turbulence

(3) 3-D models of coronal current sheet formation.

Acceleration in MHD TurbulenceEarly work, Matthaeus,

Goldstein, 1986. X- and o-points + superposed turbulence.

Energisation and trapping (o-points)

Dmitruk et al (2003, 2004) Full 3-D turbulence model Generate multiple current

sheets Track test particles in

model

Turbulent E and B fields

Particle trajectories

Energy vs. E (E)

Distributions

Acceleration in Stressed Magnetic Fields(Turkmani et al, ApJ Lett, 2005)

Step 1:

3-D Coronal MHD model (Galsgaard)

Drive corona by stressing footpoints

Develop a turbulent corona with multiple dissipation sites.

Step 2:

Freeze fields at an “interesting” time

Get global E-field:

E = -(u x B) + J

Inductive field plays no role……

Step 3

• Fully relativistic test particle code

• Inject distribution (T ~ 5 x 106)

• Track electrons and ions through multiple current sheets.

Sample Particles

Fast acceleration 0.1 (1) sec for e-(p+)

Encounters multiple acceleration sites.

• 74 % are accelerated (> 1 keV)– 40 % Leave from either

footpoint– 13 % Leave from the sides– 21 % Trapped

• 26 % Not accelerated

Sample electron

Energy

E-field

Time evolution and distribution functions

start end

Several phases.

Particles accelerated in multiple dissipation site MHD model

FastPlentifulAt many places

Effect of resistivity model?

Relation to CA modelsComputed Bremsstrahlung signature

Some questions

Can MHD ever describe a flare? Not if acceleration efficiency is as high as we believe. Transition from MHD to different plasma state In MHD sense particles require an “equation of state”. What is it?

What is influence of accelerated particles on reconnection? Can rapid acceleration change reconnection rates to very fast? Can these particles change character of diffusion regions?

Can production of large particle flux destabilise field over large area? “Dissipation spreading” (Papadopoulos, 1977)

Some may be answered by PIC codes.

Most require…….. conceptual thinking, not simulations (yet).

The observational future

“Son of RHESSI”Need for comprehensive payloadIons!Especially context measurements (plasma flows)

Solar-B/EISExpect to get measurements of mass flows and

turbulence in flares (synchronise with RHESSI)