1. Trans-Debye Scale Plasma Simulations
Jacob Trier Frederiksen
Niels Bohr Institute

2. Dept. Astronomy & Physics, Århus Univ.
Åke Nordlund
Niels Bohr Institute
Troels Haugbølle
Dept. Astronomy & Physics, Århus Univ.
Collaborators

3. Overview Trans-Debye Scale Modeling Example: GRB–CBM Interaction
Particle-in-cell codes
Random phase approximation, the hinge
Continuous collisional transfer
Challenges
Example: GRB–CBM Interaction
GRB-CBM model, setup
First light, results
’bold statements’
On-line Radiation Spectral Synthesis
Simple test, synchrotron, ω vs. log(ω)
Demonstration (2 minutes)
Challenges (if time leftover)
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

4. Trans-Debye Scale Modeling

5. Trans-Debye Scale Modeling Particle-in-cell; reminder
... ALSO EXPLAINED
YESTERDAY ...
PIC codes solve self-consistently
Maxwell’s equations (discretized space)
Lorentz forces on particles (continuous phase space)
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

6. Trans-Debye Scale Modeling Particle-in-cell codes
PIC codes are ideally collisionless, interaction only through mean fields:
Any collisionality must be explicitely implemented:
PIC codes should: 1) approximately resolve Debye length
2) have ”many” particles in Debye sphere
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

7. Trans-Debye Scale Modeling Random phase approximation (Pines & Bohm, ’52)
RPA splits dynamics at Debye length
Naturally achieve a split scheme for kinetic plasmas
Frederiksen et al., 2004
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

8. Trans-Debye Scale Modeling Continuous collisional transfer
Very detailed collision terms can be realized
Continuous weighting of particles
~ 10+ magn. resolution in physical particle number density
[P0,P1,P2,P3] 1 + [P0,P1,P2,P3] 2 conserved to ~10-6
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

9. Trans-Debye Scale Modeling Challenges, examples
Refined particle merging
Phase (search) space is multi-dimensional, Dtot ≈ Dr * Dp * Nsp * Ncollisions * Wpart * ... , at least Dtot ≈ 3*3*1*1*1... ~ !
Coupling grid photons with kinetic photons
Quantum description needed?
Delocalization of kinetic photons vs. localization of grid photons.
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

10. Example: GRB-CBM Interaction
ApJL, 680, L5-L8

11. Example: GRB–CBM Interaction Imagined scenery?
Rapid variation
Slow variation
...as also explained yesterday...
non-thermal
Wijers & Galama 1999
Felix Ryde & Milan Battelino, 2005
quasi-thermal / hybrid
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

12. Example: GRB–CBM Interaction Motivation and model
Preconditioning of circumburst medium prior to shocked ejecta arrival
Possible en-route burst lightcurve and spectral shaping
Internal vs. external shocks (variable CE?)
Model:
Take a ’good’ case from BATSE catalogue (GRB951102)
Make a quiescent cool CBM hydrogen plasma and inflict a burst of blackbody photons with Eγ ⊆ [50keV,1MeV]
Compton interact photons and electrons
Solve resulting plasma problem ....
GRB
Ryde & Battelino
KTH, Stockholm
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

13. Example: GRB–CBM Interaction First light, results
ApJL, 680, L5-L8,
PARTICLE ACCELERATION
PHOTON BOOSTING
QUASISTATIC MAGNETIC FIELD GENERATION
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

14. Example: GRB–CBM Interaction Conclusions/Discussion and speculation
Magnetic field generated in GRB front produces a solid back-scattering mechanism (propagating at ~light speed!) for UHECRs, i.e. naturally resolves Fermi-accel. escape problem.
Counter-streaming γ-photons are prone to pair produce ⇒ sub-shocks
Photon ‘spikes’ interesting; delayed HE emission? – waiting for GLAST results…!
Movie? --
arXiv: v1 [astro-ph]
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

15. Online Radiation Spectral Synthesis

16. Online Radiation Spectral Synthesis Motivation
Radiation diagnostics strong tool in discerning physics ‘behind’ observations.
Previous and very recent work; Hededal, & Nordlund (2005), Nishikawa et al. (2008) shows proofs of concept. – see for details.
Need to collect spectra runtime rather than through passive tracing – to correctly capture electromagnetic effects (Hededal, thesis, 2005)
PhotonPlasma code implements:
On-line spectral synthesis
Multiple observers
Active windowing
Sub-cycled tracing
Tunable radiation ensemble
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

17. Online Radiation Spectral Synthesis Simple test synchrotron, ω vs
Online Radiation Spectral Synthesis Simple test synchrotron, ω vs. log(ω)
Synchrotron, single particle, 3 obs, linear frequency scale,
γ=25, θobs,max=1/γ
Synchrotron, single particle, 3 obs, logarithmic frequency scale,
γ=25, θobs,max=1/γ
# bins =
Runtime ~ 500 secs
# bins = 100
Runtime ~ 0.8 sec
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

18. Synchrotron -- no distr. in pitch -- perfect p-decoherence
Online Radiation Spectral Synthesis Slope 2/3 or 1/3 – flatter?? ... steeper?? ...
Synchrotron no distr. in pitch perfect p-decoherence
Mono-energetic electrons
Perfectly de-phased
Homogeneous B-field
10 radiating particles
Gamma ~ 25
3 observers: perp – 1/Γ directions

19. Synchrotron -- distr. Pitch on [0 – ~ 2π/3] -- partial p-decoherence
Online Radiation Spectral Synthesis Slope 2/3 or 1/3 – flatter?? ... steeper?? ...
Synchrotron distr. Pitch on [0 – ~ 2π/3] partial p-decoherence
Mono-energetic electrons
Partially de-phased
Homogeneous B-field
10 radiating particles
Gamma ~ 25
3 observers: perp – 1/Γ directions
OK – how expensive? (demo)

20. Online Radiation Spectral Synthesis Challenges
Frequency interval for synthesis; howto, switch between intervals for high-res capture at varying gamma-factors (for individual particles)?
Synchrotron self-absorption; howto, do kinetic radiative transfer??
Parseval’s theorem; howto, trust power binning of modes in log-space vs. binning in lin-space??
Wavelets; howto, capture temporal development more fully in future??
Cooling; howto, cool particles realistically when PIC sims are normalized to plasma parameters?? – is it necessary..?
Several others...

21. Questions? NB: References next slide
Thanks a bunch
Questions?
NB: References next slide
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute

22. References Pines D & Bohm D – Phys. Rev. 85, 338 (1952)
Weibel E – PRL, 2, 83 (1959)
Hurley et al., Nature, 372, 652 (1994)
Medvedev M V & Loeb A – ApJ, 526, 697 (1999)
Thompson C & Madau P – ApJ, 538, 105 (2000)
Beloborodov A M -- ApJ, 565, 808 (2002)
Ryde F & Svensson R – ApJ, 566, 210 (2002)
Barbiellini, Celotti, Ghirlanda, Longo, Piro, Tavani -- MNRAS, 350, L5 (2004)
Haugbølle T – PhD Thesis, NBI, ArΧiv Astrophysics e-prints, astro-ph/ (2005)
Hededal C – PhD Thesis, NBI, ArΧiv Astrophysics e-prints, astro-ph/ (2005)
Frederiksen J T – PhD Thesis, Stockholm Observatory, ISBN (2008)
Hoshino M -- ApJ, 672, 940 (2008)
Guiliani, ArXiv Astrophysics e-prints, astro-ph/ v1 (in press, A&A Letters).
Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008
Jacob Trier Frederiksen, Niels Bohr Institute