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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

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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]

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ICM Conference, MPA, Garching, 17 June 2015

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] clever undergraduate clever undergraduate

Magnetic Field Evolution, Plasma Heating and Microinstabilities in Weakly Collisional ICM

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Turbulence, Heating, Cooling (I. Zhuravleva)

“Inertial range,” consistent with Kolmogorov scaling

Zhuravleva, Churazov, AAS et al. 2014, Nature 515, 85 [arXiv:1410.6485]

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What Lurks Beneath

Kinetic ion heating Electron heating

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What Lurks Beneath

Kinetic ion heating Electron heating Parallel (“Braginskii”) viscous scale: – viscous ion heating – Alfvénic cascade peels off – no “dynamo” motions below this scale

(this could be within reach observationally!

  • cf. I. Zhuravleva’s

Chandra proposal)

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Magnetic Fields

Kinetic ion heating Electron heating Parallel (“Braginskii”) viscous scale: – viscous ion heating – Alfvénic cascade peels off – no “dynamo” motions below this scale

(this could be within reach observationally!

  • cf. I. Zhuravleva’s

Chandra proposal)

???

We don’t really understand field structure here: – saturated dynamo, – HBI/MTI – field dynamics subject to anisotropic pressure (see below) Very little observational info available, could do more? Kinetic turbulence: Alfvénic+compressive, like in solar wind? Well measured/understood (sort of) Motions

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Magnetic Fields ???

We don’t really understand field structure here: – saturated dynamo, – HBI/MTI – field dynamics subject to anisotropic pressure (see below) Very little observational info available, could do more? Kinetic turbulence: Alfvénic+compressive, like in solar wind? Well measured/understood (sort of) Motions

???

Firehose, mirror instabilities

???

Electron micro- instabilities Measured in SW, not well understood Changing magnetic fields cause microinstabilities, which adjust viscous stress and hence field dynamics

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Standard Turbulent MHD Dynamo

AAS et al., ApJ 612, 276 (2004) [astro-ph/0312046]

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Standard Turbulent MHD Dynamo

AAS et al., ApJ 612, 276 (2004) [astro-ph/0312046]

So, roughly, field in Lagrangian frame accumulates as random walk

(in fact, situation more complex because of need to combat resistivity)

This was the solution of

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Standard Turbulent MHD Dynamo

AAS et al., ApJ 612, 276 (2004) [astro-ph/0312046]

Key effect: a succession of random stretchings (and un-stretchings)

weaker field stronger field

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Weak Collisions Pressure Anisotropy

Changing magnetic field causes local pressure anisotropies:

conservation of conservation of weaker field stronger field

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Weak Collisions Pressure Anisotropy

Changing magnetic field causes local pressure anisotropies:

conservation of conservation of

Typical pressure anisotropy:

weaker field stronger field

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Pressure Anisotropy Microinstabilities

weaker field stronger field

Typical pressure anisotropy: mirror instability

destabilised Alfvén wave resonant instability

firehose instability Instabilities are fast, small scale. They are instantaneous compared to “fluid” dynamics. “Plasma beta”

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Pressure Anisotropy Microinstabilities

weaker field stronger field

mirror instability

resonant instability

firehose instability

Scott Melville: folding field goes firehose-unstable (in a 1D Braginskii model)

“Plasma beta”

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Marginal State At All Times?

weaker field stronger field

mirror instability firehose instability

Braginskii viscosity MIRROR FIRE HOSE [Bale et al., PRL 2009]

In the solar wind: How do you evolve the field from small to large while keeping everywhere within marginal stability boundaries? “Plasma beta”

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Effective Closure Dilemma

How do you evolve the field from small to large while keeping everywhere within marginal stability boundaries? Model I: Suppress stretching Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this Way to keep const rms B needed for this

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Dynamo under Model I (suppression of γ)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model I: Suppress stretching Suppose there is enough stirring to keep at the threshold:

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Dynamo under Model I (suppression of γ)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

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

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Dynamo under Model I (suppression of γ)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

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

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ICM heating under Model I

Viscous heating rate ( if we ignore energy cascade below )

Kunz, AAS et al., MNRAS 410, 2446 (2011) [arXiv:1003.2719]

Model I: Suppress stretching

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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]

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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]

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this

To stay at threshold, need effective collisionality

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this

To stay at threshold, need effective collisionality But collisionality determines viscosity

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this

To stay at threshold, need effective collisionality But collisionality determines viscosity And viscosity determines maximal rate of strain: is Kolmogorov’s energy flux

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this

To stay at threshold, need effective collisionality But collisionality determines viscosity And viscosity determines maximal rate of strain:

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

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:

  • ne large-scale

turnover rate

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Dynamo under Model II (enhancement of ν)

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Thus, secular growth, but gets to dynamical strength very quickly:

  • ne 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!)

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ICM heating under Model II

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672] Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

Model II: Enhance collisionality

Anomalous scattering

  • f particles by Larmor

scale fluctuations needed for this

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ICM heating under Model II

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672] Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672]

So we learn nothing new: all the turbulent power input, whatever it is, gets viscously dissipated

(in Model I, as well, but it allows one to fix the temperature profile in terms of other parameters, while in Model II it is hard-wired)

This would mean that whatever determines the thermal stability of the ICM has, under Model II, to do with large-scale energy deposition processes, not with microphysics:

Rejoice all ye believers that microphysics should never matter!

(although you need microphysics to know whether Model II is right)

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Instabilities in a Box (M. Kunz)

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

decreasing field strength

to drive firehose

increasing field strength

to drive mirror

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Instabilities in a Box (M. Kunz)

Hybrid kinetic system solved by PEGASUS code:

Kunz, Stone & Bai, JCP 259, 154 (2014)

…in a shearing sheet

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability (M. Kunz)

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability (M. Kunz)

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

exponential growth

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

Firehose Instability: Linear

  • blique modes
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stability parameter perturbation energy

secular growth pinned at marginal level

Firehose Instability: Secular

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from firehose marginal stability

AAS et al., PRL 100, 081301 (2008) [arXiv:0709.3828] Rosin et al., MNRAS 413, 7 (2011) [arXiv:1002.4017] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from firehose marginal stability

AAS et al., PRL 100, 081301 (2008) [arXiv:0709.3828] Rosin et al., MNRAS 413, 7 (2011) [arXiv:1002.4017] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from firehose marginal stability

AAS et al., PRL 100, 081301 (2008) [arXiv:0709.3828] Rosin et al., MNRAS 413, 7 (2011) [arXiv:1002.4017] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from firehose marginal stability

AAS et al., PRL 100, 081301 (2008) [arXiv:0709.3828] Rosin et al., MNRAS 413, 7 (2011) [arXiv:1002.4017] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Firehose Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from firehose marginal stability secular growth

AAS et al., PRL 100, 081301 (2008) [arXiv:0709.3828] Rosin et al., MNRAS 413, 7 (2011) [arXiv:1002.4017] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

saturation pinned at marginal level

Firehose Instability: Saturated

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

firehose turbulence pinned at marginal level

Firehose Instability: Saturated

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Firehose Saturates at Small Amplitudes

small-amplitude Larmor-scale firehose turbulence

KAW?

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Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Saturated Firehose Scatters Particles

μconservation is broken at long times, firehose fluctuations scatter particles to maintain pressure anisotropy at marginal level

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effective collisionality required to maintain marginal stability measured scattering rate during the saturated phase

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Saturated Firehose Scatters Particles

measured scattering rate during the secular phase

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Mirror Instability (M. Kunz)

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010] Riquelme, Quataert & Verscharen, arXiv:1402.0014 (2014)

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Mirror Instability (M. Kunz)

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

exponential growth

long, oblique modes

Mirror Instability: Linear

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

secular growth asymptotes to marginal level

Mirror Instability: Secular

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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Mirror Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from marginal stability mirror-trapped particles in holes (fraction )

Rincon, AAS & Cowley, MNRAS 447, L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Mirror Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from marginal stability mirror-trapped particles in holes (fraction )

Rincon, AAS & Cowley, MNRAS 447, L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Mirror Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from marginal stability mirror-trapped particles in holes (fraction )

Rincon, AAS & Cowley, MNRAS 447, L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Mirror Instability: Secular

pressure anisotropy driven by shear pressure anisotropy from marginal stability mirror-trapped particles in holes (fraction )

Rincon, AAS & Cowley, MNRAS 447, L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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Mirror Instability: Secular

secular growth

Rincon, AAS & Cowley, MNRAS 447, L45 (2015) [arXiv:1407.4707] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

starting saturation asymptotes to marginal level

Mirror Instability: Secular

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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stability parameter perturbation energy

saturation asymptotes to marginal level

Mirror Instability: Saturated

Kunz et al., PRL 112, 205003 (2014) [arXiv:1402.0010]

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Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Mirror Saturates at Order-Unity Amplitudes

  • rder-unity-amplitude

(independent of S) long-parallel-scale mirror turbulence

KAW?

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pressure anisotropy is regulated by trapped particles in magnetic mirrors, where field strength stays constant on average…

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Mirror Instability: Trapped Particles

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trapped passing Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Secular Mirror Doesn’t Scatter Particles

pressure anisotropy is regulated by trapped particles in magnetic mirrors, where field strength stays constant on average… no particle scattering until (late) saturation (off mirror edges)

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effective collisionality required to maintain marginal stability measured scattering rate during the saturated phase

Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

Secular Mirror Doesn’t Scatter Particles

measured scattering rate during the secular phase

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Conclusions So Far

Very different scenarios for plasma dynamo depending on whether nonlinear firehose and mirror fluctuations regulate pressure anisotropy by scattering particles or by adjusting rate of change of the magnetic field:

  • No scattering explosive growth, but long time to get going
  • Efficient scattering secular growth, but very fast

Driven firehose saturates at low amplitudes, scatters particles Driven mirror grows to without doing much scattering (marginal state achieved via trapped population in mirrors) [Both instabilities have a sub-Larmor tail, which appears to be KAW turbulence with the usual spectrum] Plasma Dynamo: the race is on

Mogavero & AAS, MNRAS 440, 3226 (2014) [arXiv:1312.3672] Kunz, AAS & Stone, PRL 112, 205003 (2014) [arXiv:1402.0010]

scales with collision time and initial field

  • ne large-scale

turnover time

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Conclusions So Far

Very different scenarios for plasma dynamo depending on whether nonlinear firehose and mirror fluctuations regulate pressure anisotropy by scattering particles or by adjusting rate of change of the magnetic field:

  • No scattering explosive growth, but long time to get going
  • Efficient scattering secular growth, but very fast

Driven firehose saturates at low amplitudes, scatters particles Driven mirror grows to without doing much scattering (marginal state achieved via trapped population in mirrors) [Both instabilities have a sub-Larmor tail, which appears to be KAW turbulence with the usual spectrum] Plasma Dynamo: the race is on

scales with collision time and initial field

  • ne large-scale

turnover time

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

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A 19th Century Programme…

What is the viscosity of a high-βplasma? What is the thermal conductivity of a high-βplasma?

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

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A 19th Century Programme…

What is the viscosity of a high-βplasma? What is the thermal conductivity of a high-βplasma?

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

When dining, I had often observed that some particular dishes retained their Heat much longer than others; and that apple-pies, and apples and almonds mixed, - (a dish in great repute in England) - remained hot a surprising length of

  • time. Much struck with this extraordinary

quality of retaining Heat, which apples appear to possess, it frequently recurred to my recollection; and I never burnt my mouth with them, or saw others meet with the same misfortune, without endeavouring, but in vain, to find out some way of accounting, in a satisfactory manner, for this surprising matter. Count Rumford, 1799

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The Place to Publish a Plasma (Astro)Physics Result You Are Proud Of:

No page limits or page charges Single-column format for beauty and e-reading LaTeX-based typesetting, UK-based copy editing (we will not screw up your LaTeX file or your grammar) Available through NASA ADS, arXiv-ing encouraged Free access to highest-cited papers and editors’ picks Interaction with a real editor, not a robot (protection against random stupid referees) EDITORS: Bill Dorland (Maryland) 2013- Alex Schekochihin (Oxford) 2013- EDITORIAL BOARD: Jon Arons (Berkeley) 2014- Antoine Bret (Castilla La Mancha) 2011- Francesco Califano (Pisa) 2014- Troy Carter (UCLA) 2014- Peter Catto (MIT) 2015- Bengt Eliasson (Strathclyde) 2012- Cary Forest (UW Madison) 2014- Frank Jenko (UCLA) 2014- Enzo Lazzaro (CNR Milan) 2012- Stuart Mangles (Imperial College) 2014- Thierry Passot (OCA Nice) 2014- Luis Silva (IST Lisbon) 2015- Ed Thomas Jr (Auburn) 2015- Dmitri Uzdensky (UC Boulder) 2015-

http://journals.cambridge.org/pla

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Discussion

What can plasma physics do for galaxy clusters?

  • Help with old questions:

subgrid models and all that (discussion of closures above) Mean field theory for high-beta (ICM) plasmas.

  • New questions: see below.

What can galaxy clusters do for plasma physics?

  • Microphysics frontier: the mean free path

(collisional to collisionless physics transition).

  • Dynamics of high-beta plasma (dynamo etc.).
  • Thermodynamics of high-beta plasma (heating, transport etc.).

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

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Effects of Magnetic Field

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

Initially parabolic magnetic field line subject to Braginskii viscosity (by Scott Melville)

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Effects of Magnetic Field

WE DON’T T RE REAL ALLY Y KN KNOW (YE YET) T) HOW MAGN GNETI TISED, HIGH GHβPL PLAS ASMA A MOVES

Initially parabolic magnetic field line subject to Braginskii viscosity (by Scott Melville)