Type III burst Dynamical spectrum:

1. 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. 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 (≈ ωpe and 2ωpe) scatter off thermal ions or couple to ion-acoustic waves and produce EM emission at ≈ ωpe & 2ωpe. Type III burst Dynamical spectrum: Good intro to mechanisms Malaspina et al. 2010 JGR, 115,A01101

3. 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. Model 1 is based on Vlasov code VALIS: Sircombe & Arber, 2009, JCP, 228, 4773; which solves full Vlasov equation for fe and fi with self-consistent E=(Ex,Ey,0) and B=(0,0,Bz) using Maxwell's Eqs. Simulation domain size (x,Vx,Vy)= (25000 λD ,80,80)= (103 c/ωpe ,80,80) each run: 32h 256 cores 1 TB data fe + fb = ne(x)exp[-(Vx2+Vy2)/2.0] + nb(x)exp[-((Vx - 0.2c)2+Vy2)/(2.0x9)] Vte=0.004c; Vb=0.2c; Tb=9Te x plasma β=0.17 In this geometry existence of kperp is crucial -- achieved by setting B0,z without it no EM waves are excited. ny=1 updates fluid-like equation of motion -- this prevents setting non zero pitch angle using the distribution function. z B0,z y

5. 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 nb/ne≈ 10-2 -- 10-3, results will be dominated by the Larmor Drift Instability…

6. Larmor drift-unstable case, inhomogeneous plasma without a beam

7. Larmor drift-unstable case, inhomogeneous plasma without a beam

8. Homogeneous plasma with low density beam nb/ne =5x10-6

9. Homogeneous plasma with low density beam nb/ne =5x10-6

10. Narrow-band emission lines 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

11. Larmor drift-unstable inhomogen. plasma + dense beam nb/ne =5x10-2

12. Larmor drift-unstable inhomogen. plasma + dense beam nb/ne =5x10-2

13. 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. Model 2 is based on EPOCH PIC code: EPSRC-funded CCPP consortium PI -- Arber. fully EM, relativistic PIC code. Updates E=(Ex,Ey, Ey) and B=(Bx, By,Bz) Simulation domain size = 65000 grids grid size 0.25-0.5 λD each run: 512 cores 28 h, 1.3x109 particles fe + fb = ne(x)exp[-(Px2+Py2+Pz2)/2.0] + nb(x)exp[-( (Px - Pxo)2+ (Py - Pyo)2 +Pz2)/(2.0x10)] Vte=0.007c; Pxo=Pyo=0.5c me/[1-0.52]1/2; Tb=10Te x strongly magnetized case β=6x10-5. kperp is non-zero by setting 45o beam pitch angle. Different pitch angles considered. z B0,x y

15. Time-distance plots, pitch angle 45o

18. 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 45o: ES standing wave excited, + escaping EM waves. Dynamical spectrum shows frequency decrease. 4) Homogeneous plasma, Case with beam, pitch angle 45o: ES standing wave excited, + escaping EM waves. No frequency decrease.

19. Thank you!

20. 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 20o; at 240 MHz 2.4o - i.e. FoV is not an issue for Solar Sci. (Rsun=0.5o). LOFAR vs other radio facilities

21. 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