ICM Conference, MPA, Garching, 17 June 2015 Magnetic Field Evolution, Plasma Heating and Microinstabilities in Weakly Collisional ICM Alexander Schekochihin (Oxford) Steve Cowley (UKAEA) Matt Kunz (Princeton) Scott Melville (Oxford) Federico Mogavero (ENS Paris) Francois Rincon (Toulouse) Jim Stone (Princeton) Rincon, AAS & Cowley, MNRAS 447 , L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112 , 205003 (2014) [arXiv:1402.0010] Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672] AAS et al., PRL 100 , 081301 (2008) [arXiv:0709.3828]
ICM Conference, MPA, Garching, 17 June 2015 Magnetic Field Evolution, Plasma Heating and Microinstabilities in Weakly Collisional ICM Alexander Schekochihin (Oxford) Steve Cowley (UKAEA) Matt Kunz (Princeton) Scott Melville (Oxford) clever undergraduate clever undergraduate Federico Mogavero (ENS Paris) Francois Rincon (Toulouse) Jim Stone (Princeton) Rincon, AAS & Cowley, MNRAS 447 , L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112 , 205003 (2014) [arXiv:1402.0010] Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672] AAS et al., PRL 100 , 081301 (2008) [arXiv:0709.3828]
Turbulence, Heating, Cooling (I. Zhuravleva) “Inertial range,” consistent with Kolmogorov scaling Zhuravleva, Churazov , AAS et al. 2014, Nature 515, 85 [arXiv:1410.6485]
What Lurks Beneath Kinetic ion heating Electron heating
What Lurks Beneath Parallel (“Braginskii”) viscous scale: – viscous ion heating – Alfvénic cascade peels off – no “dynamo” motions below this scale (this could be within Kinetic reach observationally! ion heating cf. I. Zhuravleva’s Chandra proposal) Electron heating
Magnetic Fields Parallel (“Braginskii”) viscous scale: Motions – viscous ion heating – Alfvénic cascade peels off – no “dynamo” motions below this scale ??? (this could be within Kinetic reach observationally! We don’t really understand ion heating cf. I. Zhuravleva’s field structure here: Chandra proposal) Electron – saturated dynamo, heating – HBI/MTI Kinetic – field dynamics subject turbulence: to anisotropic pressure Alfvénic+compressive, (see below) Very little observational like in solar wind? info available, could do more? Well measured/understood (sort of)
Magnetic Fields ??? Firehose, Motions Measured mirror in SW, Changing magnetic fields instabilities not well cause microinstabilities, understood which adjust viscous stress ??? and hence field dynamics ??? We don’t really understand Electron field structure here: micro- – saturated dynamo, instabilities – HBI/MTI Kinetic – field dynamics subject turbulence: to anisotropic pressure Alfvénic+compressive, (see below) Very little observational like in solar wind? info available, could do more? Well measured/understood (sort of)
Standard Turbulent MHD Dynamo AAS et al., ApJ 612 , 276 (2004) [astro-ph/0312046]
Standard Turbulent MHD Dynamo This was the solution of So, roughly, field in Lagrangian frame accumulates as random walk (in fact, situation more complex because of need to combat resistivity) AAS et al., ApJ 612 , 276 (2004) [astro-ph/0312046]
Standard Turbulent MHD Dynamo weaker field stronger field Key effect: a succession of random stretchings (and un-stretchings) AAS et al., ApJ 612 , 276 (2004) [astro-ph/0312046]
Weak Collisions � Pressure Anisotropy Changing magnetic field causes local pressure anisotropies: conservation of weaker field conservation of stronger field
Weak Collisions � Pressure Anisotropy Changing magnetic field causes local pressure anisotropies: conservation of weaker field conservation of stronger field Typical pressure anisotropy:
Pressure Anisotropy � Microinstabilities Instabilities are fast, small scale. “Plasma beta” They are instantaneous compared to “fluid” dynamics. firehose instability weaker destabilised Alfvén wave field stronger field Typical pressure anisotropy: mirror instability resonant instability
Pressure Anisotropy � Microinstabilities “Plasma beta” Scott Melville: folding field goes firehose-unstable (in a 1D Braginskii model) firehose instability weaker field stronger field mirror instability resonant instability
Marginal State At All Times? In the solar wind : “Plasma beta” [Bale et al ., PRL 2009] Braginskii MIRROR viscosity firehose instability weaker FIRE field HOSE stronger field mirror instability How do you evolve the field from small to large while keeping everywhere within marginal stability boundaries?
Effective Closure Dilemma How do you evolve the field from small to large while keeping everywhere within marginal stability boundaries? Model I: Suppress stretching Way to keep const rms B needed for this Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this
Dynamo under Model I (suppression of γ ) Suppose there is enough stirring to keep at the threshold: Model I: Suppress stretching Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model I (suppression of γ ) Suppose there is enough stirring to keep at the threshold: Thus, explosive growth, but takes a long time to explode: for modeling details, caveats, complications, validity constraints, see Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model I (suppression of γ ) Suppose there is enough stirring to keep at the threshold: Thus, explosive growth, but takes a long time to explode: For typical ICM parameters, So this can efficiently restore fields from to current values , but for growth from a tiny seed, need a different mechanism Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
ICM heating under Model I Viscous heating rate ( if we ignore energy cascade below ) Model I: Suppress stretching Kunz, AAS et al., MNRAS 410 , 2446 (2011) [arXiv:1003.2719]
ICM heating under Model I Viscous heating rate ( if we ignore energy cascade below ) � Thermally stable ICM Kunz, AAS et al., MNRAS 410 , 2446 (2011) [arXiv:1003.2719]
ICM heating under Model I Viscous heating rate ( if we ignore energy cascade below ) � Thermally stable ICM � If , � If , Kunz, AAS et al., MNRAS 410 , 2446 (2011) [arXiv:1003.2719]
Dynamo under Model II (enhancement of ν ) To stay at threshold, need effective collisionality Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model II (enhancement of ν ) To stay at threshold, need effective collisionality But collisionality determines viscosity Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model II (enhancement of ν ) To stay at threshold, need effective collisionality But collisionality determines viscosity And viscosity determines maximal rate of strain: is Kolmogorov’s energy flux Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model II (enhancement of ν ) To stay at threshold, need effective collisionality But collisionality determines viscosity And viscosity determines maximal rate of strain: Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model II (enhancement of ν ) To stay at threshold, need effective collisionality But collisionality determines viscosity And viscosity determines maximal rate of strain: Thus, secular growth, but gets to dynamical strength very quickly: one large-scale turnover rate Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
Dynamo under Model II (enhancement of ν ) Thus, secular growth, but gets to dynamical strength very quickly: one large-scale turnover rate Modeling gives extremely intermittent, self-similar field distribution; see ( � intermittent viscosity, intermittent rate of strain, very hard to do right in “real” simulations with this effective closure!) Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
ICM heating under Model II Anomalous scattering of particles by Larmor scale fluctuations Model II: Enhance collisionality needed for this Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672] Mogavero & AAS, MNRAS 440 , 3226 (2014) [arXiv:1312.3672]
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