Dissipation and Kinetic Physics of Astrophysical Plasma Turbulence - - PowerPoint PPT Presentation

Dissipation and Kinetic Physics of Astrophysical Plasma Turbulence

NSF PRAC project #1614664

Vadim Roytershteyn Space Science Institute

Blue Waters Symposium, Sunriver, OR, June 5, 2018

Stanislav Boldyrev, University of Wisconsin, Madsion Gian Luca Delzanno, LANL Yuri Omelchenko, Space Science Institute Nikolai Pogorelov, University of Alabama, Huntsville Heli Hietala, UCLA Chris Chen, Queen Mary University, London John Podesta, Space Science Institute Aaron Roberts, NASA Goddard William Matthaeus University of Delaware Homa Karimabadi, CureMetrix, Inc

Acknowledgements

Funding: NASA, NSF Collaborators:

The Problem(s)

Plasma Turbulence is a Ubiquitous Phenomenon

Fusion : magnetically confined, inertially confined, hybrid Solar corona Solar wind, planetary magnetospheres Heliosphere, interstellar Medium Jets, accretion disks, other astrophysical objects

Armstrong et al., 1995

Local Interstellar Medium

10

−6

10−5 10−4 10−3 10−2 10−1 1 10 10−6 10−4 10−2 1 102 104 106 spacecraft frequency (Hz) ACE MFI (58 days) ACE MFI (51 h) Cluster FGM + STAFF−SC (70 min) −1.00 ± 0.04 −2.73 ± 0.01 −1.65 ± 0.01 transition region inertial range sub-ion range f –1 range trace power spectral density (nT2Hz–1) lc~ 106 km re~ 1 km ri~102 km

Focus of This Project: Turbulence in Solar Wind & Magnetosphere

• Turbulence is of interest because of:
• Local energy input (e.g. to explain famously anomalous temperature profiles)
• Transport of energetic particles (solar energetic particles, cosmic rays, etc)
• Solar Wind is the best accessible example of astrophysical (=large scale) plasma

turbulence

Kiyani et al., 2015

Parker Solar Probe (NASA) Solar Orbiter (ESA)

Two Upcoming Missions Are Expected to Revolutionize Understanding of the Sun, the Solar Wind and the Solar Corona

PSP will provide in-situ measurements as close as 9.8 R

We need theory & numerical tools to make predictions and Internet the data

10-3 10-2 10-1 100 101 102 10-2 10-1 100 Scale Size (km) Heliospheric Distance (AU)

ρi di de ρe

Kinetic-Alfven regime Inertial kinetic-Alfven regime Rs Parker Solar Probe Solar Orbiter 1 AU

10-3 10-2 10-1 100 101 10-2 10-1 100 βs

Heliospheric Distance (AU) ratio of plasma pressure to magnetic pressure evolution of plasma microscales

The Nature of Kinetic Processes Is Expected to Change Closer to the Sun

ω2 = k2

zk2v2 Aρ2 i (1 + Te/Ti)

2 + βi(1 + Te/Ti) ≈ k2

zk2v2 Aρ2 i

2 + βi ,

ω2 = k2

zk2 ⊥d4 eΩ2 e

(1 + k2

⊥d2 e) (1 + 2/βi + k2 ⊥d2 e).

Chen & Boldyrev, 2017 Passot et al., 2017,18

βs = 8πnsTs/B2

• Short-wavelength turbulence at 1 AU is dominated by KAW
• KAW turbulence is relatively well studied
• as β↓, the nature of fluctuations changes (iKAW)
• iKAW is not well understood
• separation of scales increases as β↓

Methods

A Variety of Models & Approximations Are Used in Plasma Physics to Tackle Different Scales

smaller scales L: system size, energy injection scale, correlation scale ion kinetic scales electron kinetic scales debye length

collisional scale (collisional) collisional scale (c-less)

Magnetohydrodynamic approximation (MHD): incompressible, fully compressible, kinetic MHD.. Hall MHD multi-fluid multi-moments models hybrid kinetic … Landau Fluid Gyrokinetic Fully kinetic …

E + 1 c v × B = 0

∂tv + v · rv = 1 c j ⇥ B

∂tB = cr ⇥ E r ⇥ B = 4π c j

model complexity In many situations, cross-scale coupling play a role an important role global dynamics. Full understanding of global evolution may require multi-scale, multi-physics models

∂tfs + v · rfs + qs ms ✓ E + 1 c v ⇥ B ◆ · rvfs = C{fs, fs0, . . .}

+ Maxwell’s equations “First-Principle” description of weakly coupled plasmas:

Our Go-To Model: Fully Kinetic and Hybrid PIC Simulations

∂fs ∂t + v · rfs + qs ms ✓ E + 1 c v ⇥ B ◆ · rvfs = X

s0

C{fs, fs0}

~up to 1010 cells ~up to 4x1012 particles ~120 TB of memory ~107 CPU-HRS (~103 CPU-YRS) Hybrid simulations kinetic ions + fluid electrons codes: H3D, HYPERES Fully kinetic simulations All species kinetic code: VPIC

r ⇥ B = 4π c j + 1 c ∂E ∂t 1 c ∂B ∂t = r ⇥ E r · E = 4πρ r · B = 0

~up to 1.7x1010 cells ~up to 2x1012 particles ~130 TB of memory Particle-In-Cell (PIC) is a very efficient, but relatively inaccurate method for solving full Vlasov-Maxwell system. Major limitations: noise and the need to resolve ALL kinetic spatial and temporal scales (in explicit methods) . Typical 3D simulation takes up a significant portion of a good modern supercomputer for ~10 days => BW

10

p

expensive sampling

p t=t1 x

efficient sampling

x v v

Goal : high-accuracy, implicit, fully kinetic simulation Problem : 6D! Sample phase space with 100 points in each direction=1012 unknowns per species Solution: Efficient (spectral) Discretization of the Velocity Space

11

We Investigate Several Related Problems on BW. Focus Today: SpectralPlasmaSolver: a Simulation Tool for Fluid-Kinetic Coupling

∂tfs + v · rfs + qs ms ✓ E + 1 c v ⇥ B ◆ · rvfs = C{fs, fs0, . . .}

fs =

Nn−1

X

n=0 Nm−1

X

m=0 Np−1

X

p=0

Cs

n,m,p(x, t)Ψn(ξs x)Ψm(ξs y)Ψp(ξs z)

Ψn(x) = (π2nn!)−1/2Hn(x)e−x2, w Maxweliian = 1 coefficient per direction; More coefficients = more complex distributions = more kinetic physics; Adaptivity = fluid-kinetic coupling Grant and Feix, 1967; Armstrong et al., 1970; Vencels et al., 2015; Loureiro et al., 2013; Camporeale et al. 2016; Delzanno et al., 2015; Vencels et al., 2016; Roytershteyn & Delzanno 2018;

An Implementation: FORTRAN90, PETSC + 2DECOMP&FFT + FFTW/MKL

dC dt = L1C + N (C, F) , dF dt = L2C + L3F,

( R1

• Cθ+1, Fθ+1

= Cθ+1 − Cθ − ∆t h L1Cθ+1/2 + N ⇣ Cθ+1/2, Fθ+1/2⌘i = 0 R2

• Cθ+1, Fθ+1

= Fθ+1 − Fθ − ∆tL2Cθ+1/2 − ∆tL3Fθ+1/2 = 0

10-2 10-1 100 101 102 103 104 105 time,s MPI ranks 101 102 102 103 104 time,s MPI ranks

single convolution complete cycle

communication starts dominating

The present version decomposes the solution space in 2/6 dimensions. There is more parallelism to explore!

(Some) Results on Turbulence

14

SPS: A Small Number of Hermite Modes Can Reproduce Collisionless Damping with Reasonable Accuracy.

• 10-7
• 10-6
• 10-5
• 10-4
• 10-3
• 10-2
• 10-1
• 100
• 101

10-2 10-1 100 101 γ/Ωci kde Vlasov, 1 Vlasov, 2 SPS, NH=4 SPS, NH=5 SPS, NH=6 10-3 10-2 10-1 100 101 10-2 10-1 100 101 ω/Ωci kde

θ = 89 βe = 0.04 Ti/Te = 10

• Collisionless damping is a very subtle physical phenomenon (2010 Fields Medal)
• For some parameters, the method can describe it with just a few modes

“exact” solution SPS simulations

10-10 10-8 10-6 10-4 SB k-3.8 0.4 0.8 C|| 100 102 10-1 100 101 Ce kde

New vs Old (SPS vs PIC): Decaying Turbulence Test

Roytershteyn & Delzanno, 2018

reference solution (ignore overall constant) SPS simulations spectrum of magnetic fluctuations magnetic compressibility - a “fingerprint” of the fluctuations compressibility - another quantity revealing the nature of fluctuations

SPS Simulations of Decaying Turbulence in Low-Beta Plasma

10-11 10-8 10-5 10-2 k-11/3 k-2.8 k-5/3 0.4 0.8 2 6 10 14 10-1 100 101

k⊥de Ce,i

Ck

Ce Ci Cave SE SB

S

Roytershteyn et al., 2018

17

x/de

y/de 251 251 251

x/de 251 x/de

|J| f✏ χv

Simulations Will Allow us to Address Key Questions, Such as Energy Dissipation, Structure Formation, etc

• 2D simulation with a traditional PIC method;
• the goal is to do this in 3D using new tools
• multiple scale ranges
• high-frequency fluctuations resembling iKAW
• particle acceleration at structures

2D PIC; βe=0.04, Ti/Te=10,mi/me=100; 25x25 c/ωpi; 4000 particles/cell/species

Summary

1.Understanding of plasma turbulence is a grand challenge problem. 2.We are using Blue Waters to study some aspects of this problem, namely kinetic effects associated with turbulence dissipation. 3.New methods are emerging for efficient solution of kinetic problems 4.18 Months on BW. Many exciting results. 1 paper published 2 under review 5 paper in various stage of preparation (from “submitting next week” to just starting) data for many more