1. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Vlasov-Maxwell and PIC, self-consistent electromagnetic wave emission simulations in the solar corona David Tsiklauri Queen Mary University of London November 18, 2010 Tentative title for the workshop: Waves + Reconnection=? University of Warwick

2. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Type III burst Dynamical spectrum: Basic physics of the radio emission mechanism (plasma emission): *solar flares (reconnection) induce an electron beam; *This generates Langmuir waves via bump-on-tail instability; *Lamgmuir waves (≈ ω pe and 2ω pe ) scatter off thermal ions or couple to ion-acoustic waves and produce EM emission at ≈ ω pe & 2ω pe. Good intro to mechanisms Malaspina et al. 2010 JGR, 115,A01101

3. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Previous theoretical efforts to reproduce the observed features of the type III bursts: (i) General picture of EM wave generation by coalescence of two Langmuir waves has been proposed by Ginzburg & Zheleznyakov 1958, followed by quasi-linear beam relaxation Vedenov et al 1961 (ii) large, 1 AU-scale, phenomenological models based on Fokker- Planck equation describing the time evolution of the probability distribution of plasma frequency radiation; Stochastic growth theory Robinson 1992; Cairns & Robinson 1998 (iii) (attempt of) small-scale, 1000 Debye length = 10 -10 AU, fully kinetic, Particle-In-Cell (PIC) simulation with self-consistent EM fields: Sakai et al (2005)+others. However, the previous PIC simulations of type III solar radio bursts have never attempted to reproduce the dynamic spectra.

4. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Model 1 is based on Vlasov code VALIS: Sircombe & Arber, 2009, JCP, 228, 4773; which solves full Vlasov equation for f e and f i with self-consistent E=(E x,E y,0) and B=(0,0,B z ) using Maxwell's Eqs. Simulation domain size (x,V x,V y )= (25000 λ D,80,80)= (103 c/ω pe,80,80) each run: 32h 256 cores 1 TB data f e + f b = n e (x)exp[-(V x 2 +V y 2 )/2.0] + n b (x)exp[-((V x - 0.2c) 2 +V y 2 )/(2.0x9)] V te =0.004c; V b =0.2c; T b =9T e x y z plasma β=0.17 In this geometry existence of k perp is crucial -- achieved by setting B 0,z without it no EM waves are excited. n y =1 updates fluid-like equation of motion -- this prevents setting non zero pitch angle using the distribution function. B 0,z

5. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Larmor Drift Instability: The variation of the particle Larmor radii (due to the inhomogeneity) generates transverse to the both directions current In the applicable regime of parameters, this leads to an unstable mode: Thus, unless the beam is dense n b /n e ≈ 10 -2 -- 10 -3, results will be dominated by the Larmor Drift Instability…

6. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Larmor drift-unstable case, inhomogeneous plasma without a beam

7. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Larmor drift-unstable case, inhomogeneous plasma without a beam

8. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Homogeneous plasma with low density beam n b /n e =5x10 -6

9. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Homogeneous plasma with low density beam n b /n e =5x10 -6

10. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Aurass, et al A&A 515 (2010): interpret this as gyroresonance line emission at 314 MHz. Homogeneous plasma with low density beam offers an alternative interpretation. (i) fluxes (ii) transient intensity Narrow-band emission lines

11. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Larmor drift-unstable inhomogen. plasma + dense beam n b /n e =5x10 -2

12. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Larmor drift-unstable inhomogen. plasma + dense beam n b /n e =5x10 -2

13. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Conclusions -- part 1 1. New effect of excitation of standing ES waves in the beam injection location. In turn, ES waves are producing escaping EM radiation. 2. Homogeneous case with low density beam offers an alternative interpretation for narrow-band lines in the radio dynamic spectrum. 3. Low density electron beam case confirms quasi-linear theory predictions [(i) free streaming and (ii) long relaxation time]. 4. High density electron beam case shows deviations from the quasi-linear theory which manifests itself by (i) fast quasi-linear relaxation, (ii) disintegration of the beam, and (iii) generation of significant electron return current and ion heating. Tsiklauri, D. Solar Phys. Dec. 2010 issue preprint - arXiv:1008.2290v2

14. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Model 2 is based on EPOCH PIC code: EPSRC-funded CCPP consortium PI -- Arber. fully EM, relativistic PIC code. Updates E=(E x,E y, E y ) and B=(B x, B y,B z ) Simulation domain size = 65000 grids grid size 0.25-0.5 λ D each run: 512 cores 28 h, 1.3x10 9 particles f e + f b = n e (x)exp[-(P x 2 +P y 2 +P z 2 )/2.0] + n b (x)exp[-( (P x - P xo ) 2 + (P y - P yo ) 2 +P z 2 )/(2.0x10)] V te =0.007c; P xo =P yo =0.5c m e /[1-0.5 2 ] 1/2 ; T b =10T e x y z strongly magnetized case β=6x10 -5. k perp is non-zero by setting 45 o beam pitch angle. Different pitch angles considered. B 0,x

15. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Time-distance plots, pitch angle 45 o

16. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri

17. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri

18. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Conclusions -- part 2 For the setup commensurate to type III bursts we find: Inhomogeneous plasma: 1) Case with no beam: no ES wave excited, + low level drift EM wave noise. 2) Case with beam, pitch angle 0: ES standing wave excited, + low level drift EM wave noise. 3) Case with beam, pitch angle 45 o : ES standing wave excited, + escaping EM waves. Dynamical spectrum shows frequency decrease. 4) Homogeneous plasma, Case with beam, pitch angle 45 o : ES standing wave excited, + escaping EM waves. No frequency decrease.

19. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Thank you!

20. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Nancay Radioheliograph: * Single frequency observations * range 150 - 432 MHz * resolution 1' LOFAR (Chilbolton, UK): *Multiple frequency observations (corresponding to different heights) * range 30 - 240 MHz * resolution 10" (in imaging mode) * Imaging, monitoring and spectroscopic modes. * beam size (single station) at 30 MHz 20 o ; at 240 MHz 2.4 o - i.e. FoV is not an issue for Solar Sci. (R sun =0.5 o ). LOFAR vs other radio facilities

21. 18 Nov 2010 Waves + Reconnection=? U of Warwick Astronomy Unit, School of Mathematical Sciences www.maths.qmul.ac.uk/~tsiklauri Plans for use of Chilbolton (single LOFAR station) data: to guide/ constrain our 1.5D Vlasov -- main novelty: forward modelling (e.g. density) by obtaining synthetic dynamical spectra. Dynamic spectra of the radio flux from the whole Sun can be recorded continuously, and imaging is not needed. This mode enables monitoring of the solar activity even when solar observations are not in the LOFAR schedule, and make best use of the available resources