particle-in-cell simulation of whistler heat flux
TRANSCRIPT
A. Micera | PSP SWG Telecon, February 5, 2021
Particle-In-Cell simulation of whistler heat flux instabilities:
Scattering of the strahl electrons into the halo and heat flux regulation in the near-Sun solar wind.
A. Micera 1,2, A. N. Zhukov 1,3, R. A. López 4, M.E. Innocenti 5, M. Lazar 2,5, E. Boella 6,7 and G. Lapenta 2
1 Solar-Terrestrial Centre of Excellence - SIDC, Royal Observatory of Belgium, Brussels, Belgium
2 Centre for mathematical Plasma Astrophysics, KU Leuven, Leuven, Belgium
3 Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia
4 Departamento de Física, Universidad de Santiago de Chile, Santiago, Chile
5 Institut für Theoretische Physik, Ruhr-Universität Bochum, Bochum, Germany
6 Physics Department, Lancaster University, Lancaster, UK
7 Cockcroft Institute, Daresbury Laboratory, Warrington, UK
2 A. Micera | PSP SWG Telecon, February 5, 2021
Electron VDFs in the solar wind often consist of three components: an almost isotropic core, a suprathermal halo population distributed at all pitch angles, a suprathermal field-aligned strahl.
Marsch (2006)
The electron VDF carries an important amount of heat flux in the solar wind
3 A. Micera | PSP SWG Telecon, February 5, 2021
Low halo fractional density. Strahl more pronounced.
Formation of the solar wind halo from the scattering of the strahl
Halekas et al. 2020 a
Štverak et al. 2009The halo fractional density increases with the heliocentric distance, while the strahl fractional density decreases.
Halekas et al. 2020 a
Better correlation of the strahl and halo fractional densities with the electron core , rather than with the collisional age.β
4 A. Micera | PSP SWG Telecon, February 5, 2021
Heat flux regulation and electron VDF shaping by wave-particle interactions
Halekas et al. 2020 b
The heat flux carried by the solar wind is suppressed below the values provided by collisional models.
Halekas et al. 2020 b
Kinetic instabilities are responsible for shaping the electron VDF and for regulating the solar wind heat flux.
Cattell et al. 2020
Parker Solar Probe data revealed the existence of whistler-mode waves with a direction of propagation that goes from quasi-parallel to highly oblique.
5 A. Micera | PSP SWG Telecon, February 5, 2021
Kinetic simulation to model near-Sun solar wind conditions
• 2D PIC simulation of whistler heat flux instabilities performed with iPIC3D code.
• Plasma and magnetic field parameters correspond to those measured by Parker Solar Probe during its first perihelion.
• The initial electron VDF is composed of core and strahl populations.
• The strahl is modelled as a drifting bi- Maxwellian distribution with . T∥/T⊥ = 2
f (v y
) [ar
b. u
n.]
103
102
101
100
10-1
10-2
10-3
vy [c]0.140.070.00-0.07-0.14
f (v x
) [ar
b. u
n.]
103
102
101
100
10-1
10-2
10-3
vx [c]0.140.070.00-0.07-0.14
core + strahl core strahl
B
6 A. Micera | PSP SWG Telecon, February 5, 2021
• The strahl undergoes pitch-angle scattering: reduction of its drift velocity and in the simultaneous broadening of its pitch angle distribution.
• Later on, secondary scattering processes: redistribution of the particles scattered in the perpendicular direction into a more symmetric halo.
Formation of a halo population at the expense of the strahl
7 A. Micera | PSP SWG Telecon, February 5, 2021
Formation of a halo population at the expense of the strahl
• The strahl undergoes pitch-angle scattering: reduction of its drift velocity and in the simultaneous broadening of its pitch angle distribution.
• Later on, secondary scattering processes: redistribution of the particles scattered in the perpendicular direction into a more symmetric halo.
8 A. Micera | PSP SWG Telecon, February 5, 2021
f (v)
[arb
. un.
]
102
100
10-2
10-4
vx [c]0.140.070.00-0.07-0.14
f (v)
[arb
. un.
]
102
100
10-2
10-4
vy [c]0.140.070.00-0.07-0.14
Halo formation and evolution towards a more symmetric distribution v y
[c]
0.14
0.07
0.00
-0.07
-0.14
(e)
v y [c
]
0.14
0.07
0.00
-0.07
-0.14
vx [c]0.140.070.00-0.07-0.14
vx[c]0.140.070.00-0.07-0.14
(d)
(f)
# pa
rticl
es [a
rb. u
n.]
60
40
20
0
-20
-40
-60
f e (t n
+1) /
f e (t
n)
102
101
100
10-1
10-2
vy [c]0.140.070.00-0.07-0.14
f (v)
[arb
. un.
]
104
103
102
101
100
10-1
10-2
vx [c]0.140.070.00-0.07-0.14
t2 = 0.94
t0 = 0t1 = 0.47t = 1.4t = 2.4tend =5.6
• Strahl component along the magnetic field direction and relaxation of its drift velocity.
• Appearance of the suprathermal halo which, at higher energies, deviates from the Maxwellian distribution.
• Generation of a tail-like structure in the distribution function at and hence of a more symmetric halo.
vx < 0
t0 = 0t1 = 0.94 Ω−1
ci
tend = 5.6 Ω−1ci
v y [c
]
0.14
0.07
0.00
-0.07
-0.14
vx [c]0.140.070.00-0.07-0.14
v y [c
]
0.14
0.07
0.00
-0.07
-0.14
vx [c]0.140.070.00-0.07-0.14
9 A. Micera | PSP SWG Telecon, February 5, 2021
Scattering due to whistler modes
k y [t
pi /
c]
25
20
15
10
5
0
kx [tpi / c]14121086420
t = 0.47 [1ci-1](c)
k y [t
pi /
c]
25
20
15
10
5
0
a [1
ci]
101
100
10-1
tr [1
ci]
160
120
80
40
0
(b)(a)
kx [tpi / c]14121086420
t = 5.6 [1ci-1]
|FFT
(bB z
/ B 0
)|
10-3
10-4
10-5
10-6
x [c / tpi]86420
t = 5.6 [1ci-1]
(d)
(f)
y [c
/ t
pi]
8
6
4
2
0
x [c / tpi]86420
t = 0.47 [1ci-1](e)
B z [m
i c t
pi /
e]
3 10-5
2 10-5
1 10-5
0
-1 10-5
-2 10-5
-3 10-5
• The strongest instability is the Oblique Whistler Heat Flux Instability, with at .
• The FFT of the simulated clearly exhibits evidence of this instability.
• When the O-WHFI is already saturated, modes parallel to are noticeable.
γmax θ ≈ 65∘
δBz /B0
B0
10 A. Micera | PSP SWG Telecon, February 5, 2021
• Fastest oblique mode, at and exponentially grows and saturates at .
• The theoretical growth rate of the fastest growing mode shows remarkable agreement with the numerical growth rate.
• Parallel and quasi-parallel whistler modes are manifested at later times and become dominant after .
kx = 6.5 ωpi/cky = 13.5 ωpi/c
t ≈ 0.6 Ω−1ci
t ≈ 2 Ω−1ci
|FFT
(bB z
/ B 0
)|
10-3
10-4
t [1ci-1]
6543210
fastest oblique mode
parallel mode at =12 γth,max
kx ωpi /c
Whistler-mode waves shift towards smaller angles of propagation
11 A. Micera | PSP SWG Telecon, February 5, 2021
The parallel strahl momentum is converted to perpendicular momentumw
s [c]
0.020
0.018
0.016
0.014
t [1ci-1]
6543210
wth,∥,strahlwth,⊥,strahl
T � /
T ||
1.2
1.0
0.8
0.6
t [1ci-1]
6543210
corestrahl
12 A. Micera | PSP SWG Telecon, February 5, 2021
Cyclotron and Landau resonances shape the electron VDFv y
[c]
0.14
0.07
0.00
-0.07
-0.14
t = 0.0 [ ci-1]1 t = 0.47 [ ci
-1]
v y [c
]
0.14
0.07
0.00
-0.07
-0.14
t = 0.94 [ ci-1] t = 1.4 [ ci
-1]
v y [c
]
0.14
0.07
0.00
-0.07
-0.14
vx [c]0.140.070.00-0.07-0.14
t = 2.4 [ ci-1]
vx [c]0.140.070.00-0.07-0.14
t = 5.6 [ ci-1]
# pa
rticl
es [a
rb. u
n.]
104
102
100
10-2
10-4
1(a) (b)
(c) (d)
(e) (f)
11
1 1
• First, cyclotron resonance scattered electrons towards high values of .
• Later on cyclotron resonant interaction with parallel whistler waves.
n = 1v⊥
n = − 1
v∥ = (n Ωce + ωr)/k∥
n = 0 n = 1n= -1
13 A. Micera | PSP SWG Telecon, February 5, 2021
Heat flux reduction as a consequence of the instability
• The decrease of the heat flux is % .
• The strongest heat flux decrease is simultaneous with the O-WHFI.
• The heat flux is mostly carried by (Feldman et al. 1975).
• The regulation of is essentially produced by the relaxation of (Innocenti et al. 2020).
≈ 46
Qenth,s
Qsus
Qs,
x /
q max
0.7
0.6
0.5
0.4
0.3
0.2
0.1
t [1ci-1]
6543210
Qs,
x /
Qs,
x(t=
0)
1.0
0.9
0.8
0.7
0.6
0.5
t [1ci-1]
6543210
u s [c
]
0.032
0.028
0.024
0.020
0.016
t [1ci-1]
6543210
Qs = Qenth,s + Qbulk,s + qs
Qs =ms
2 ∫ v∥v2fsd3v
Qenth,s = 32 nsmsusw2
s
Qbulk,s = 12 msnsu3
s
qs =ms
2 ∫ (v∥ − us)(v − us)2 fsd3v
14 A. Micera | PSP SWG Telecon, February 5, 2021
Summary
These simulations were performed on the supercomputers SuperMUC (LRZ) and Marconi (CINECA) under PRACE allocations.
Micera A., Zhukov A. N., López, R. A., Innocenti, M. E., et al. 2020, ApJL, 903, L23
• 2D fully kinetic simulation has been performed to investigate the role of the oblique and parallel branches of whistler heat flux instability in shaping the electron VDFs in the solar wind.
• In a plasma consisting of a drifting core and strahl electrons, as recently observed by Parker Solar Probe in the near-Sun solar wind, whistler waves, propagating at oblique angles with respect to the background magnetic field, can be excited.
• The oblique whistler waves drive a significant pitch-angle scattering of the strahl, which results in the formation of a suprathermal electron halo population.
• The excited whistler-mode waves shift towards smaller angles of propagation as the bulk velocity of the strahl decreases.
• The electron system experiences secondary effects due to the resonant interaction with parallel whistler waves, which lead to a further relaxation of the suprathermal electrons and hence to a more symmetric halo.
• The process leads to a significant decrease of the heat flux carried by the strahl population.