SHOCKS, TURBULENCE, and PARTICLE ACCELERATION
MYKOLA GORDOVSKYY University of Manchester
STFC Introductory Solar System Plasma Physics Summer School, 12 September 2017 Outline . Basic phenomenology
. Shocks - Basic physics (conservation laws etc) - Shocks in the solar corona and collisionless SW plasma - Fermi I particle acceleration
. Turbulence - Basic physics in different regimes (collisionless, HD) - Existing misconceptions and non-existent controversies - Turbulence in the corona and SW - Fermi II particle acceleration
. Particle acceleration - Mechanisms of particle acceleration - Outstanding problems . Summary and open questions Outline . Basic phenomenology
. Shocks - Basic physics (conservation laws etc) - Shocks in the solar corona and collisionless SW plasma - Fermi I particle acceleration
. Turbulence - Basic physics in different regimes (collisionless, HD) - Existing misconceptions and non-existent controversies - Turbulence in the corona and SW - Fermi II particle acceleration
. Particle acceleration - Mechanisms of particle acceleration - Outstanding problems . Summary and open questions T&Cs, basic phenomenology etc
Thermal Non-thermal . Collisional . Collisionless
. Particle distribution . No reason for quickly becomes Maxwellian distribution Maxwellian . Behaves like a N-body . Behaves like a fluid system
. Magnetohydrodynamics . Kinetics
. Fluid lectures: . Kinetic lectures: - Philippa Browning: MHD; - David Tsiklauri: Plasma - Gunnar Hornig: kinetics; Magnetic reconnection; - Eduard Kontar: High- - Valery Nakariakov: energy solar/stellar Waves & instabilities atmospheres
T&Cs, basic phenomenology etc
Thermal Non-thermal
. Collisional . Non-collisional . Most interesting . Particle distribution thing happen. No reason for quickly becomes here Maxwellian distribution Maxwellian . Behaves like a N-body . Behaves like a fluid . Events in the solarsystem corona: Non- thermal plasma . Kinetics . Magnetohydrodynamics(energetic particles) in . Fluid lectures: thermal plasma. Kinetic lectures: - Philippa Browning: MHD ; - David Tsiklauri: Plasma - Gunnar Hornig: kinetics; Magnetic reconnection; - Eduard Kontar: High- - Valery Nakariakov: energy solar/stellar Waves & instabilities atmospheres
T&Cs, basic phenomenology etc
Heliosphere / Solar Wind: collisionless, magnetic pressuregas pressure
Corona: collisional/weakly collisional, magnetic field dominates
Chromosphere, TR, lower corona: collisional, magnetic field dominates Photosphere, Chromosphere: collisional, gas pressure dominates Shock: basic physics
. Perturbation travels faster than the local phase speed wave is steepening, becomes non-linear Simple 1D (M)HD shock model UPSTREAM DOWNSTREAM V . B =B =0 -> Parallel shock T0 VT1 T0 T1 V N0 VN1 . B =B =0 -> ρ N0 N1 0 ρ1 Perpendicular shock p 0 p1
B T0 BT1 SHOCK
. Normal component Bn does not change!! (divB=0) . Normal mass flux is conserved (mass conservation) . Total energy density (I + K + M) is conserved . Momenta (separately, N and T) are conserved
. ET is conserved 휕퐵 휕퐸푦 휕퐸푧 훻 × 퐸 = = 0 - = 0 휕푡 휕푧 휕푦
휕퐸 휕퐸 푧 - 푥 = 0 휕푥 휕푧
휕퐸 휕퐸 푥 - 푦 = 0 휕푦 휕푥
휌 휕퐸 휕퐸푦 휕퐸 훻 ∙ 퐸 = 퐸 = 0 푥 + + 푧 = 0 휀0 휕푥 휕푦 휕푧
휕퐵 휕퐵푦 휕퐵 훻 ∙ 퐵 = 0 푥 + + 푧 = 0 휕푥 휕푦 휕푧 휕퐵 휕퐸푦 휕퐸푧 훻 × 퐸 = = 0 - = 0 휕푡 휕푧 휕푦
휕퐸 휕퐸 푧 - 푥 = 0 휕푥 휕푧
휕퐸 휕퐸 푥 - 푦 = 0 휕푦 휕푥
휌 휕퐸 휕퐸푦 휕퐸 훻 ∙ 퐸 = 퐸 = 0 푥 + + 푧 = 0 휀0 휕푥 휕푦 휕푧
휕퐵 휕퐵푦 휕퐵 훻 ∙ 퐵 = 0 푥 + + 푧 = 0 휕푥 휕푦 휕푧 Simple 1D (M)HD shock model UPSTREAM DOWNSTREAM V . B =B =0 -> Parallel shock T0 VT1 T0 T1 V N0 VN1 . B =B =0 -> ρ N0 N1 0 ρ1 Perpendicular shock p 0 p1
B T0 BT1 SHOCK
. Normal component Bn does not change!! (divB=0) . Normal mass flux is conserved (mass conservation) . Total energy density (I + K + M) is conserved . Momenta (separately, N and T) are conserved
. ET is conserved Rankine-Hugeniot relations
. MHD equations in conservative form
휕Й
= − 훻 ∙ 퐹푙푢푥Й + 푆표푢푟푐푒푠Й 휕푡
Rankine-Hugeniot relations . Mass conservation [퐴]≡ A1-A0 휌푉N = 0
. Parallel momentum conservation 2 2 퐵 휌푉N + 푝 + = 0 2휇0 . Perpendicular momentum conservation
퐵푁 휌푉T푉N + 퐵T = 0 휇0 . Total energy conservation 휌푉2 훾푝 퐵2 푉 ∙ 퐵 푉N + + 푉N − 퐵N = 0 2 훾 − 1 휇0 휇0 . ET conservation
푉N퐵T − 퐵N푉T = 0
. divB =0
퐵N = 0 Simplest case: 1D parallel shock
. 1D case, only normal component of B and V 휌1푉1 = 휌0푉0
2 2 휌1푉1 + 푝1 = 휌0푉0 + 푝0
휌 푉 3 훾푝 푉 휌 푉 3 훾푝 푉 1 1 + 1 1 = 0 0 + 0 0 2 훾 − 1 2 훾 − 1
. Solution - Shock compression ratio
휌 푉 (훾+1)푀2 훾+1 1 0 푟 = = = 2 ≈ ≈ 4 휌0 푉1 훾−1 푀 +2 훾−1 푉0 휌0 where 푀 = = 푉0 is the Mach number 퐶푠0 훾푝0 MHD shocks v. MHD waves [Valery Nakariakov: Waves and instabilities] Alfven Not compressive No shock; r=1 discontinuity
Fast magneto- B correlates with sonic ρ
Slow magneto- B anti-correlates sonic with ρ
Collisionless shocks
. Collisionless ≡ LR > m.f.p.
. Particles don’t thermalise due to collisions
. Particle scattering (velocity/pitch-angle change) is determined by magnetic field spatial scale (Turbulent magnetic field!!!)
. Collisionless shocks are more versatile and require more complicated math description Collisionless shocks
. Quasi-perpendicular shock Large angle
Ions escape / travel from the shock
. Quasi-parallel shock
Ions hang around / rotate Small angle into the shock Collisionless shocks: particle acceleration
V
P0
P0+2mV
. Type I Fermi acceleration: particle repeatedly reflected by “mirrors” moving towards each other
. Guarantied energy gain!! Collisionless shocks: particle acceleration
. Both HD and collisionless shocks accelerate particles but…
. …when m.f.p. is short, the energy gained by particles becomes “thermal” (particle distribution is Maxwellian)
. Therefore, particle acceleration on collisionless shocks is unavoidable, as plasma heating on HD shocks
Energy conversion on shocks
. MHD shocks
Kinetic energy Thermal energy of V > C plasma flow of V < C plasma flow s s
. Collisionless shocks
Kinetic energy Thermal energy
of V > Cs plasma flow of V < Cs plasma flow
Kinetic energy
of non-thermal particles Kinetic energy
of plasma waves Energy conversion on shocks UPSTREAM DOWNSTREAM . MHD shocks
Kinetic energy Thermal energy of V > C plasma flow of V < C plasma flow s s
. Collisionless shocks
Kinetic energy Thermal energy
of V > Cs plasma flow of V < Cs plasma flow
Kinetic energy
of non-thermal particles Kinetic energy
of plasma waves Energy conversion on shocks UPSTREAM DOWNSTREAM . MHD shocks
Kinetic energy Thermal energy of V > C plasma flow of V < C plasma flow s s
. Collisionless shocks
Kinetic energy Thermal energy
of V > Cs plasma flow of V < Cs plasma flow
Kinetic energy
of non-thermal particles Kinetic energy
of plasma waves Shocks in the corona . Shocks in the reconnection regions
Petschek 1964
Forced reconnection in non-neutral Harris current sheet (Gordovskyy et al, 2011) Shocks in the corona . Upward-propagating waves becoming non-linear (can contribute to the coronal heating)
Footpoint-driven magneto-acoustic wave propagation in a localized solar flux tube Fedun et al. 2011 Shocks in the SW / Heliosphere
. Coronal Mass Ejections
NASA / SOHO / LASCO S White / U Mariland
Karpen et al. 2012 Corona-Romero & Gonzalez-Esparza 2012 Shocks in the SW / Heliosphere
. Planetary magnetospheres
Belmont / Tsyganenko / 2008
Magnetic field, nT
Density, 1/cm3 Temperature, eV Shocks outside Solar System
Shock generated star formation / AstroBEAR code Cygnus A DRAGN
Tiho supernova remnant Veil nebula supernova remnant Summary: shocks
. Creates structures in the solar/space plasmas
. Fast flow kinetic energy is converted into heat, non- thermal particles, waves Kinetic energy Thermal energy of V > Cs plasma flow of V < Cs plasma flow
Kinetic energy Thermal energy of V > C plasma flow of V < C plasma flow s s Kinetic energy of non-thermal particles Kinetic energy of plasma waves . Occurs during magnetic reconnection and eruptions in the corona, ubiquitous in the solar wind, Earth/planetary magnetospheres etc
What is turbulence?
Stanford
New Mexico New
Uni
Uni
, ,
K Hayashi, Hayashi, K
Vladimirova N N
. Essentially non-linear, fluid phenomenon
. Occurs when inertial forces in fluid dominate over viscosity
. Results in energy transfer from larger to smaller spatial scales Turbulence: basic physics (Kinetic)
ENERGY IN
L0
eddie
Turbulent cascade cascade Turbulent (aka Richardson (aka cascade)
l0 (Thermal +) ENERGY OUT Turbulence: theory
. Results in energy transfer from larger to smaller spatial scales
. Steady energy input results in a steady state solution: Kolmogorov spectrum with the inertial range
Energy IN
Energy OUT
Inertia > Viscosity High viscosity Waves v. Turbulence
. “Waves or turbulence?!” – Turbulence can always be represented by waves with a wide spectrum
. Therefore, Acoustic / Alfven / Magneto-sonic / etc turbulence MHD v. HD Turbulence . Magnetic field adds a preferred direction, making turbulence anisotropic, with more interesting effects
Turbulent cascade cascade Turbulent
. Advection is stronger ||B, dissipation is stronger ┴B, - similar to other transport effects in plasma Turbulence in collisionless plasma
. Its possible to have wide spectrum kinetic waves with the cascade and dissipation at high k
. Collisionless plasma may have viscosity due to wave- particle interaction
. Same 5/3 spectrum is observed in SW turbulence, the inertial range spanning 6 orders of magnitude – SW turbulent spectrum seems to be universal from MHD to
electron scales
et al 2009 2009 PRL al et
. Particle acceleration Alexandrova
Turbulence: particle acceleration
Gurion
Ben
Uni
/ /
Keshet U U . Type II Fermi acceleration: particle repeatedly scattered by moving waves, its momentum & energy changing stochastically
. May gain or lose energy depending on the wave spectrum Turbulence in the solar corona
. Turbulisation of plasma during magnetic reconnection
Temperature and density in twisted coronal loop (Pinto et a. 2016)
Temperature evolution in kink-unstable twisted magnetic fluxtube (Hood et al. 2009) Turbulence in the solar corona . Non-thermal line broadening indicates strong turbulence in flares
Thermal broadening Turbulent line broadening in flares, correlates with the Non-thermal broadening temperature (Doschek et al. 2008)
Turbulence spatially correlates with the temperature and energy release (Gordovskyy et al. 2016) Turbulence in the solar corona
. Turbulence accounts for ~1% of the energy released in solar flares, but can be extremely important for non-thermal particle scattering
Kontar et al. 2016 PRL Turbulence in solar wind
Belcher & Davis 1971 Leamon et al. 1996
Cluster mission observed the turbulent eddies in SW in-situ / NASA / Derelli 2013 Summary: turbulence
. Occurs when inertial forces dominate over collisions
. Transfers energy from large-scale plasma flows to small-scale flows, then dissipates, converting energy into heat. Energy IN
Energy OUT
Inertia > Viscosity High viscosity . Destroys large-scale structures Particle acceleration and transport
. Different types of particle acceleration: stationary electric field, waves & turbulence, shocks, betatron (collapsing magnetic traps) [Eduard Kontar’s lecture on Monday]
Kinetic energy
of V > Cs plasma flow
Kinetic energy Magnetic energy of non-thermal particles
Kinetic energy
of plasma waves Particle acceleration in the corona and SW
[Sarah Matthews: Solar & Stellar flares] Particle acceleration in the corona and SW
DC acceleration in RCS Particle acceleration in the corona and SW
Gordovskyy et al. 2011 Particle acceleration in the corona and SW
DC acceleration in RCS
Fermi I acceleration on shocks Particle acceleration in the corona and SW
DC acceleration in RCS
Fermi II acceleration on waves
Fermi I acceleration on shocks Particle acceleration in the corona and SW
Gordovskyy et al. 2014 Outstanding problems
. How, where and when particles are accelerated?
. Do coronal and IPS particles come from the same source of acceleration?
. Are the same mechanisms responsible for electrons and ions?
. How on Earth you can transport a huge amount of charged particles from the upper corona to the chromosphere? Precipitating electrons # Footpoint area ~1-10 Mm2 # Electron flux density is about 1023-24 m-2 s-1, current ~104-5A/m2, corresponding to B~104T
Compensation in the corona
23-24 # fdown = fup = 10 for n=1016m-3,
Summary: shocks
. Creates structures in the solar/space plasmas
. Fast flow kinetic energy is converted into heat, non- thermal particles, waves Kinetic energy Thermal energy of V > Cs plasma flow of V < Cs plasma flow
Kinetic energy Thermal energy of V > C plasma flow of V < C plasma flow s s Kinetic energy of non-thermal particles Kinetic energy of plasma waves . Occurs during magnetic reconnection and eruptions in the corona, ubiquitous in the solar wind, Earth/planetary magnetospheres etc Summary: turbulence
. Occurs when inertial forces dominate over collisions
. Transfers energy from large-scale plasma flows to small-scale flows, then dissipates, converting energy into heat. Energy IN
Energy OUT
Inertia > Viscosity High viscosity . Destroys large-scale structures Particle acceleration and transport
. Different types of particle acceleration: stationary electric field, waves & turbulence, shocks, betatron (collapsing magnetic traps) [Eduard Kontar’s lecture on Monday]
Kinetic energy
of V > Cs plasma flow
Kinetic energy Magnetic energy of non-thermal particles
Kinetic energy
of plasma waves . Still no clear, comprehensive picture of particle acceleration and transport in the corona and heliosphere