Space Physics Seminar, Rice University, October 4, 2021

Alfvenic Turbulence and Switchbacks in the Solar Wind:New Perspectives with Parker Solar Probe.

Anna Tenerani Many thanks to:

C. González, C. Shi, N. Sioulas, O. Panasenco, L. Matteini, M. Velli

Outline

• Alfvénic fluctuations in the solar wind: an introduction

• Evolution of switchbacks: simulations and observations

• Beyond MHD: kinetic effects via extended MHD and hybrid simulations

• Conclusions

Outline

• Alfvénic fluctuations in the solar wind: an introduction

• Evolution of switchbacks: simulations and observations

• Beyond MHD: kinetic effects via extended MHD and hybrid simulations

• Conclusions

Two types of wind

Exploring the heliosphere out of the ecliptic: the Ulysses mission

Typical configuration (at solar minimum) of magnetic field structure and slow/fast wind

(Bruno & Carbone 2012)

Alfvénic turbulence from 0.3 AU to 1 AU

• |δB|/B0~1

• δ|B|/B0<<1

• δB/√ρμ0~∓δV

•mainly propagating outward

•Developed spectrum

• δρ/ρ<<1

��/����� ��/����� ��/����� ��/�����

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����

������� ����

��/����� ��/����� ��/����� ��/����� ��/�����-�-�-�����

��/����� ��/����� ��/����� ��/����� ��/�����-���

-��

�

��

���

����

V (km/

|B| (nT)BrBtBn

δVn (km/δBn

(from B. Tsurutani et al. PPCF 1997)

Alfvénic turbulence from 0.3 AU to 1 AU

PSP first perihelion overview

Magnetic field data from FIELDS,1 min res (see also Bale et al. Nature 2019)

Switchbacks seen by PSP

(Tenerani et al. ApJS 2020)

Switchbacks and jets explained (kinematically!)

(Matteini et al. GRL 2014)

• Switchbacks are the magnetic field manifestation of radial jets (or viceversa)

• Switchbacks are a consequence of the Alfvénic character of (3D) fluctuations and |B| =constant

Outline

• Alfvénic fluctuations in the solar wind: an introduction

• Evolution of switchbacks: simulations and observations

• Beyond MHD: kinetic effects via extended MHD and hybrid simulations

• Conclusions

Coronal origin or in-situ? (Are they proxy for coronal processes?)

Induced by velocity shears (Landi et al GRL 2006, Ruffolo et al ApJS 2020; Schwadron et

al 2020)

Induced by expansion (Squire et al, 2020; Mallet et al, 2021, Shoda et al 2021)

A product of reconnection (Drake et al 2021, Zank et al 2021)

(MacNeil et al. MNRAS 2020 )

How do switchbacks evolve?

(Landi, S. et al. Proc. of Solar Wind 11/ SOHO 2005)

Non-constant B Alfvénic kinks of magnetic field expand and “unfold” over a few dynamical time-scale

Understanding how such structures evolve can shed light on: • their origin • whether they might

contribute to turbulence and plasma heating

Alfvénic solutions to the MHD equations

Purely correlated or anti-correlated u and b fluctuations provide an exact solution (at arbitrary amplitude)

@u

@t+ u ·ru = �1

⇢r

✓p+

1

8⇡B2

◆+

1

4⇡⇢B ·rB

@B

@t+ u ·rB = B ·ru�B(r · u)

0

0

z± = u± bp4⇡⇢

@z±

@t+ (U0 ⌥Va) ·rz± + z⌥ ·rz± = 0

Model for switchbacks

B = B0x+r⇥ �(x, y)z+Bz(x, y)z<latexit sha1_base64="zH5PinOoXykBvVzvqJbdNWsVJpk=">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</latexit>

�(x, y) = A(e�r21 � e�r22 )<latexit sha1_base64="RbtXXjhAH/zBMJCr3GPcJd6PHDo=">AAACC3icbZDLSsNAFIYnXmu9RV26CS1CC7YkUdCNUHXjsoK9QJuGyXTSDp1MwsxEDKF7N76KGxeKuPUF3Pk2TtsstPWHgY//nMOZ83sRJUKa5re2tLyyurae28hvbm3v7Op7+00RxhzhBgppyNseFJgShhuSSIrbEccw8ChueaPrSb11j7kgIbuTSYSdAA4Y8QmCUlmuXuhGQ1J6OE7KF5cl3Esr3LV69rgyQ1th2dWLZtWcylgEK4MiyFR39a9uP0RxgJlEFArRscxIOinkkiCKx/luLHAE0QgOcEchgwEWTjq9ZWwcKadv+CFXj0lj6v6eSGEgRBJ4qjOAcijmaxPzv1onlv65kxIWxRIzNFvkx9SQoTEJxugTjpGkiQKIOFF/NdAQcoikii+vQrDmT16Epl21Tqr27WmxdpXFkQOHoABKwAJnoAZuQB00AAKP4Bm8gjftSXvR3rWPWeuSls0cgD/SPn8A0CKY/w==</latexit>

Bz(x, y)2 = B2 � (Bx(x, y)

2 +By(x, y)2)

<latexit sha1_base64="4B721oWzXVsJgBqx5sdsbuoZl5Y=">AAACD3icbZC7TsMwFIadcivlFmBkiahArYAqCUiwIFVhYSwSbZHaNHJcp7XqXGQ7qCHqG7DwKiwMIMTKysbb4LYZoOWXLH3+zzmyz+9GlHCh699KbmFxaXklv1pYW9/Y3FK3dxo8jBnCdRTSkN25kGNKAlwXRFB8FzEMfZfipju4Gteb95hxEga3Iomw7cNeQDyCoJCWox5azkNpeJyUO+al1TFPSpYzzO5HlpNkWHbUol7RJ9LmwcigCDLVHPWr3Q1R7ONAIAo5bxl6JOwUMkEQxaNCO+Y4gmgAe7glMYA+5nY62WekHUinq3khkycQ2sT9PZFCn/PEd2WnD0Wfz9bG5n+1Viy8CzslQRQLHKDpQ15MNRFq43C0LmEYCZpIgIgR+VcN9SGDSMgICzIEY3bleWiYFeO0Yt6cFatWFkce7IF9UAIGOAdVcA1qoA4QeATP4BW8KU/Ki/KufExbc0o2swv+SPn8AYLnmSs=</latexit>

u = �B/p⇢0

<latexit sha1_base64="K+tr75OdZbnKmnROhBqE75wB+fQ=">AAACB3icbZDLSsNAFIYn9VbrLepSkMEiuLEmVdCNUOrGZQV7gSaEyXTSDp1k4sxEKCE7N76KGxeKuPUV3Pk2TtMstPrDwMd/zuHM+f2YUaks68soLSwuLa+UVytr6xubW+b2TkfyRGDSxpxx0fORJIxGpK2oYqQXC4JCn5GuP76a1rv3REjKo1s1iYkbomFEA4qR0pZn7qeOH8AkuzzOoZmdOPJOqNQRI+5ZmWdWrZqVC/4Fu4AqKNTyzE9nwHESkkhhhqTs21as3BQJRTEjWcVJJIkRHqMh6WuMUEikm+Z3ZPBQOwMYcKFfpGDu/pxIUSjlJPR1Z4jUSM7XpuZ/tX6iggs3pVGcKBLh2aIgYVBxOA0FDqggWLGJBoQF1X+FeIQEwkpHV9Eh2PMn/4VOvWaf1uo3Z9VGs4ijDPbAATgCNjgHDXANWqANMHgAT+AFvBqPxrPxZrzPWktGMbMLfsn4+AZN6pj1</latexit>

r21,2 =(x� x1,2)2

�2x

+(y � y1,2)2

�2y

<latexit sha1_base64="ODHtA4Y/LtYWr9SH2d9XFcqvhFM=">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</latexit>

(Tenerani et al. ApJS 2020)

Switchback evolution

(Frame of reference moving with the kink)

Magnetic field lines (black) and density contours (color coded)

Factors affecting switchback evolution• If the background state is homogeneous, the process that eventually leads to a

breakdown of the initial state is the well known parametric decay instability, that provides an upper bound to the lifetime of switchbacks, with increasing lifetime for increasing system size.

• In our worst case scenario T_life~200 Ta, yielding ΔR~18 Rs. A larger distance is spanned for ‘unperturbed’ path, up to ΔR>43 Rs.

• What may affect the above estimates:• Expansion and related large scale underlying gradients may affect the above

estimates

• Non-periodicity (random scattering rather than coherent interactions with density fluctuations)

• Other inhomogeneities

• Parametric instabilities are a plague that seems to be unavoidable also in the solar wind. This suggests that in the absence of some dynamical driver the occurrence of s/b should decrease with radial distance. Otherwise, their occurrence rate could be stationary or increasing.

Radial evolution of fluctuations Previous work using Helios during Alfvénic periods

Log

P (n

T2/H

z)

Log R (AU)0

2

4Slope-3.2

-4.1

-4.2

-4.2

f=2.8. 10-4-2.5 10-3 Hzf=2.5. 10-3- 10-2

f= 10-2- 3 10-2

f= 3 10-2- 8.3 10-2 (τ-1≈10-5-10-6 Hz) [Adapted from Bavassano et al., JGR (1982).]

Radial evolution of fluctuations in the inner heliosphere from 0.1 to 3 AU

(Tenerani et al. in prep)

Switchbacks counts/km as a function of radial distance and pdf

Where do switchbacks come from? How do they evolve?

★ Radial amplitudes of switchbacks decrease faster than the overall turbulent fluctuations. Specifically, their amplitude square scales approximately as at all scales, a result that we interpret in terms of saturated amplitudes

★ The occurrence of switchbacks in the solar wind depends on the duration of the switchbacks and both in-situ formation and decay are at play in the solar wind

★ in-situ drivers like the expansion are more efficient in generating switchbacks at the larger scales, however, beyond 1 au we observe a net decrease of the cumulative counts per km of switchbacks, regardless of their duration

★ We conclude that it is possible that switchbacks of two or more type can coexist: those generated close to the sun and that decay as they propagate away, and those that are reformed or maintained alive in the inner heliosphere by a balance of expansion (or other in-situ drivers) and decay processes.

★ How can such a peculiar nonlinear state can be achieved? There has to be some process that comes into play that turns the field back to its highly Alfvénic state

δB2 ∼ R−4

Outline

• Alfvénic fluctuations in the solar wind: an introduction

• Evolution of switchbacks: simulations and observations

• Beyond MHD: kinetic effects via extended MHD and hybrid simulations

• Conclusions

ion-cyclotron/mirror

parallel and oblique firehose

(Matteini et al. 2013)]

Nonthermal features in the expanding solar wind

• Evolving temperature anisotropies

• Field-aligned beam at the local Alfvén speed

• Perpendicular heating (non-adiabatic expansion)

Revisiting the traditional firehose instability

*Rosenbluth 1956 LANL Report 3030 Parker 1958 PRL 109, 1874 Chandrasekhar et al. 1958 , Proc. Roy. Soc.

Nonlinear evolution of firehose instability from initial incoherent noise seeded in both transverse directions

• Linear instability of shear Alfvén waves in an anisotropy plasma*:

• Purely growing modes when

�k

2

✓p?pk

� 1

◆< �1

Bz

By

Magnetic field hodogram

! = k cos ✓Va

s

1 +�k

2

✓p?pk

� 1

◆

pk

pk

(Tenerani & Velli ApJL 2018)

kz

kzB2k

|B|2(z)

Numerical results of firehose instability

Alfvén wave steepening & collapse

n

Alfvén wave steepening & collapsen

• An initial Alfvénic fluctuation steepens due to a combination of dispersion and nonlinearities

• At the steepened from a field aligned electric field forms that accelerates the particles (protons) to form a beam

• As a result, the field-aligned electric field and compressible fluctuations are damped nonlinearly

(González, Tenerani, Matteini et al. ApJL 2021)

Top: fields and distribution function contour as a function of time in one point in space

Right: evolution of the averaged distribution function

Summary and conclusionWe observe 2 populations of Alfvénic fluctuations.

A population roughly following the predicted WKB at the larger scales

The switchbacks corresponding to ‘saturated’ fluctuations

Switchbacks both decay and reform

Expansion can drive switchbacks in the inner heliosphere, but other types of switchbacks cannot be ruled out

Open question: what is the physical mechanism that enforces the constant-B constraint (i.e. incompressibiltiy) on expanding fluctuations!?

Parametric decay and wave collapse may prevent uncontrolled growth of fluctuations at several tens of solar radii, and may also cause s/b decay. But where are compressible effects?

Kinetic simulations of large amplitude fluctuations provide a possible route to the understanding of the evolution of Alfvénic fluctuations towards a incompressible nonlinear state