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 휕퐸푧 휕퐸푥 - = 0 휕푥 휕푧 휕퐸푥 휕퐸푦 - = 0 휕푦 휕푥 휌퐸 휕퐸푥 휕퐸푦 휕퐸푧 훻 ∙ 퐸 = = 0 + + = 0 휀0 휕푥 휕푦 휕푧 휕퐵푥 휕퐵푦 휕퐵푧 훻 ∙ 퐵 = 0 + + = 0 휕푥 휕푦 휕푧 휕퐵 휕퐸푦 휕퐸푧 훻 × 퐸 = = 0 - = 0 휕푡 휕푧 휕푦 휕퐸푧 휕퐸푥 - = 0 휕푥 휕푧 휕퐸푥 휕퐸푦 - = 0 휕푦 휕푥 휌퐸 휕퐸푥 휕퐸푦 휕퐸푧 훻 ∙ 퐸 = = 0 + + = 0 휀0 휕푥 휕푦 휕푧 휕퐵푥 휕퐵푦 휕퐵푧 훻 ∙ 퐵 = 0 + + = 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 2 2 휌푉 훾푝 퐵 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 2 휌1 푉0 (훾+1)푀 훾+1 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 > Cs plasma flow of V < Cs plasma flow 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 . 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 (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 . 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 . 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