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

Acknowledgements Collaborators: 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 Funding : NASA, NSF

The Problem(s)

Plasma Turbulence is a Ubiquitous Phenomenon Local Interstellar Medium Fusion : magnetically confined, inertially confined, hybrid Solar corona Solar wind, planetary magnetospheres Armstrong et al. , 1995 Heliosphere, interstellar Medium Jets, accretion disks, other astrophysical objects

Focus of This Project: Turbulence in Solar Wind & Magnetosphere l c ~ 10 6 km r i ~10 2 km r e ~ 1 km 10 6 − 1.00 ± 0.04 trace power spectral density (nT 2 Hz –1 ) 10 4 transition region − 1.65 ± 0.01 10 2 1 f –1 range inertial range sub-ion range 10 − 2 − 2.73 ± 0.01 10 − 4 ACE MFI (58 days) ACE MFI (51 h) 10 − 6 Cluster FGM + STAFF − SC (70 min) − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 1 10 spacecraft frequency (Hz) Kiyani et al. , 2015 • 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

Two Upcoming Missions Are Expected to Revolutionize Understanding of the Sun, the Solar Wind and the Solar Corona Solar Orbiter (ESA) Parker Solar Probe (NASA) PSP will provide in-situ measurements as close as 9.8 R � We need theory & numerical tools to make predictions and Internet the data

The Nature of Kinetic Processes Is Expected to Change Closer to the Sun ratio of plasma pressure to magnetic pressure evolution of plasma microscales 10 1 10 2 10 1 10 0 Kinetic-Alfven regime Scale Size (km) 10 0 d i 10 -1 β s Inertial kinetic-Alfven regime ρ i 10 -1 10 -2 d e 10 -2 β s = 8 π n s T s /B 2 Parker Solar Solar R s 1 AU ρ e Probe Orbiter 10 -3 10 -3 10 -2 10 -1 10 0 10 -2 10 -1 10 0 Heliospheric Distance (AU) Heliospheric Distance (AU) k 2 z k 2 ⊥ d 4 e Ω 2 ω 2 = k 2 z k 2 v 2 A ρ 2 ≈ k 2 z k 2 v 2 A ρ 2 i (1 + T e /T i ) ω 2 = e i e ) . , (1 + k 2 e ) (1 + 2 / β i + k 2 ⊥ d 2 ⊥ d 2 2 + β i (1 + T e /T i ) 2 + β i • 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 Chen & Boldyrev, 2017 • separation of scales increases as β ↓ Passot et al., 2017,18

Methods

A Variety of Models & Approximations Are Used in Plasma Physics to Tackle Different Scales ✓ ◆ ∂ t f s + v · r f s + q s E + 1 “First-Principle” description of · r v f s = C{ f s , f s 0 , . . . } c v ⇥ B m s weakly coupled plasmas: + Maxwell’s equations L: system size, energy electron ion kinetic debye injection scale, kinetic scales length correlation scale collisional scale scales collisional (collisional) scale (c-less) smaller scales Magnetohydrodynamic approximation (MHD): model complexity incompressible, fully compressible, kinetic MHD.. Hall MHD multi-fluid multi-moments models hybrid kinetic ∂ t v + v · r v = 1 Landau Fluid c j ⇥ B … Gyrokinetic r ⇥ B = 4 π ∂ t B = � c r ⇥ E c j Fully kinetic E + 1 c v × B = 0 … 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

Our Go-To Model: Fully Kinetic and Hybrid PIC Simulations Fully kinetic simulations Hybrid simulations All species kinetic kinetic ions + fluid electrons code: VPIC codes: H3D, HYPERES ✓ ◆ ∂ f s ∂ t + v · r f s + q s E + 1 X · r v f s = C{ f s , f s 0 } c v ⇥ B m s s 0 expensive efficient r ⇥ B = 4 π ∂ E c j + 1 sampling p ∂ t sampling c v p v ∂ B � 1 ∂ t = r ⇥ E c r · E = 4 πρ r · B = 0 ~up to 10 10 cells x t=t 1 x ~up to 4x10 12 particles ~up to 1.7x10 10 cells ~120 TB of memory ~up to 2x10 12 particles ~10 7 CPU-HRS (~10 3 CPU-YRS) ~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

We Investigate Several Related Problems on BW. Focus Today: SpectralPlasmaSolver: a Simulation Tool for Fluid-Kinetic Coupling Goal : high-accuracy, implicit, fully kinetic simulation Problem : 6D! Sample phase space with 100 points in each direction=10 12 unknowns per species Solution: Efficient (spectral) Discretization of the Velocity Space ✓ ◆ ∂ t f s + v · r f s + q s E + 1 · r v f s = C{ f s , f s 0 , . . . } c v ⇥ B m s N p − 1 N n − 1 N m − 1 X X X C s n,m,p ( x , t ) Ψ n ( ξ s x ) Ψ m ( ξ s y ) Ψ p ( ξ s f s = z ) n =0 m =0 p =0 Ψ n ( x ) = ( π 2 n n !) − 1 / 2 H n ( x ) e − x 2 , 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; 11

An Implementation: FORTRAN90, PETSC + 2DECOMP&FFT + FFTW/MKL d C dt = L 1 C + N ( C , F ) , = C θ +1 − C θ − ∆ t h ⇣ C θ +1 / 2 , F θ +1 / 2 ⌘i ( L 1 C θ +1 / 2 + N C θ +1 , F θ +1 � � = 0 R 1 = F θ +1 − F θ − ∆ t L 2 C θ +1 / 2 − ∆ t L 3 F θ +1 / 2 = 0 d F C θ +1 , F θ +1 � � R 2 dt = L 2 C + L 3 F , 10 1 single convolution complete cycle 10 0 10 2 time,s time,s 10 -1 communication starts dominating 10 -2 10 1 10 2 10 3 10 4 10 5 10 2 10 3 10 4 MPI ranks MPI ranks The present version decomposes the solution space in 2/6 dimensions. There is more parallelism to explore!

(Some) Results on Turbulence

SPS: A Small Number of Hermite Modes Can Reproduce Collisionless Damping with Reasonable Accuracy. θ = 89 � β e = 0 . 04 T i /T e = 10 10 1 -10 -7 -10 -6 10 0 -10 -5 Vlasov, 1 -10 -4 Vlasov, 2 “exact” ω / Ω ci γ / Ω ci 10 -1 -10 -3 SPS, N H =4 solution SPS, N H =5 -10 -2 SPS SPS, N H =6 10 -2 simulations -10 -1 -10 0 10 -3 -10 1 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 kd e kd e • Collisionless damping is a very subtle physical phenomenon (2010 Fields Medal) • For some parameters, the method can describe it with just a few modes 14

New vs Old (SPS vs PIC): Decaying Turbulence Test k -3.8 SPS simulations 10 -4 reference solution S B 10 -6 (ignore overall constant) 10 -8 spectrum of magnetic fluctuations 10 -10 magnetic compressibility - a 0.8 “fingerprint” of the fluctuations C || 0.4 0 compressibility - another quantity 10 2 revealing the nature of fluctuations C e 10 0 10 -1 10 0 10 1 kd e Roytershteyn & Delzanno, 2018

SPS Simulations of Decaying Turbulence in Low-Beta Plasma 10 -2 k -5/3 10 -5 k -2.8 S S B S E 10 -8 k -11/3 10 -11 0.8 C k 0.4 0 14 C e C ave 10 C e,i 6 C i 2 10 -1 10 0 10 1 k ⊥ d e Roytershteyn et al. , 2018

Simulations Will Allow us to Address Key Questions, Such as Energy Dissipation, Structure Formation, etc 251 | J | f ✏ χ v y/d e 0 x/d e x/d e x/d e 0 251 0 251 0 251 • 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; β e= 0.04, T i /T e =10,m i /m e =100; 25x25 c/ ω pi ; 4000 particles/cell/species 17

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