particle-in-cell simulation of whistler heat flux

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


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


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.


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


• 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


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.


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


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


• 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


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


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


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


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.

https://iopscience.iop.org/article/10.3847/2041-8213/abc0e8

particle-in-cell simulation of whistler heat flux

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