Type III burst Dynamical spectrum:

18 Nov 2010Waves + Reconnection=?U of Warwick

Astronomy Unit, School of Mathematical Scienceswww.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



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 (≈ ωpe and 2ωpe) scatter off thermal ions or couple to ion-acoustic waves and produceEM emission at ≈ ωpe & 2ωpe.

Good intro to mechanisms Malaspina et al. 2010 JGR, 115,A01101



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 theoryRobinson 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.



Model 1 is based on Vlasov code VALIS: Sircombe & Arber, 2009, JCP,228, 4773; which solves full Vlasov equationfor fe and fi with self-consistent E=(Ex,Ey,0) and B=(0,0,Bz)using Maxwell's Eqs.

Simulation domainsize (x,Vx,Vy)=(25000 λD ,80,80)=(103 c/ωpe ,80,80)

each run: 32h 256 cores1 TB data

fe + fb = ne(x)exp[-(Vx2+Vy

2)/2.0] +nb(x)exp[-((Vx - 0.2c)2+Vy

2)/(2.0x9)]Vte=0.004c; Vb=0.2c; Tb=9Te

x

y

z

plasma β=0.17

In this geometry existence of kperp

is crucial -- achieved by setting B0,z withoutit no EM waves areexcited.

ny=1 updates fluid-like equation of motion --this prevents setting non zero pitch angle using the distribution function.

B0,z



Larmor Drift Instability:

The variation of the particle Larmor radii (due to the inhomogeneity) generatestransverse to the both directions current

In the applicable regime of parameters,this leads to an unstable mode:

)/(2,2

0

0IHcth Lvnq

B

pBJ

Thus, unless the beam is dense nb/ne ≈ 10-2 -- 10-3, results will bedominated by the Larmor Drift Instability…



Larmor drift-unstable case, inhomogeneous plasma without a beam



Larmor drift-unstable case, inhomogeneous plasma without a beam



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



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



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



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



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



Conclusions -- part 1

1. New effect of excitation of standing ES waves in the beam injectionlocation. 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



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 domainsize = 65000 grids grid size 0.25-0.5 λD

each run: 512 cores28 h, 1.3x109 particles

fe + fb = ne(x)exp[-(Px2+Py

2+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

y

z

strongly magnetized case β=6x10-5.

kperp is non-zeroby setting 45o beampitch angle.

Different pitch anglesconsidered.

B0,x



Time-distanceplots, pitch angle 45o







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.



Thank you!



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) at30 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



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

Documents

Type III burst Dynamical spectrum: