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
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 (≈ ωpe and
2ωpe) scatter off thermal ions
or couple to ion-acoustic
waves and produce
EM emission at ≈ ωpe & 2ωpe.
Good intro to mechanisms Malaspina et al. 2010 JGR, 115,A01101
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 FokkerPlanck 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.
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
x
for fe and fi with self-consistent
plasma β=0.17
E=(Ex,Ey,0) and B=(0,0,Bz)
In this geometry
using Maxwell's Eqs. z
existence of kperp
B
Simulation domain
0,z
is crucial -- achieved
size (x,Vx,Vy)=
by setting B0,z without
(25000 λD ,80,80)=
it no EM waves are
(103 c/ωpe ,80,80)
y excited.
each run: 32h 256 cores
ny=1 updates fluid-like
1 TB data
equation of motion -fe + fb = ne(x)exp[-(Vx2+Vy2)/2.0] +
this prevents setting
nb(x)exp[-((Vx - 0.2c)2+Vy2)/(2.0x9)]
non zero pitch angle
Vte=0.004c; Vb=0.2c; Tb=9Te
using the distribution
function.
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

B0  p
2
J 

q
n
v
  th, /(c LIH )
2
B0
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…
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
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
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 nb/ne =5x10-6
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 nb/ne =5x10-6
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri
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
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 nb/ne =5x10-2
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 nb/ne =5x10-2
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
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=(Ex,Ey, Ey) and B=(Bx, By,Bz) x
strongly magnetized
case β=6x10-5.
z
Simulation domain
kperp is non-zero
size = 65000 grids
by setting 45o beam
grid size 0.25-0.5 λD
pitch angle.
B0,x
y
each run: 512 cores
Different pitch angles
28 h, 1.3x109 particles
considered.
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
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 45o
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri
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 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.
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri
Thank you!
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri
LOFAR vs other
radio facilities
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).
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
18 Nov 2010
Waves + Reconnection=?
U of Warwick
Astronomy Unit,
School of Mathematical Sciences
www.maths.qmul.ac.uk/~tsiklauri