thermalization and plasma instabilities question: what is the (local) thermalization time for qgps...

Thermalization and Plasma Instabilities

Question: What is the (local) thermalization time for QGPs in heavy ion collisions?

A simpler question: What is it for arbitrarily high energy collisions, where s ¿1?

A much simpler question: How does that time depend on s?

In the saturation picture,

Aside: plasma physics is complicated

Image of solar coronal filament from NASA’s TRACE satellite

Why are QGP papers typically less complicated than

• Often study equilibrium QGP.

• In local equilibrium,

magnetic confinement » 1/(g2T)

expect no long-range color magnetic fields(HD instead of MHD).

• Study physics at scales where everything is weakly interacting.

?

Bottom-Up Thermalization(Baier, Mueller, Schiff, Son)

Starting pointt » 1/Qs

p » Qs ´ “hard” gluons in this talk

1/Qs

System expandsdensity decreasesmore perturbative

f(x,p) » 1/s initially non-perturbative

Bottom-Up Thermalization(Baier, Mueller, Schiff, Son)

Later, if interactions ignoredt ¿1/Qs

z » vz t

p » Qs ´ “hard” gluons in this talk

Bottom-Up Thermalization(Baier, Mueller, Schiff, Son)

Later, if interactions ignoredt ¿ 1/Qs

p » Qs

p

pz

Qs

Original bottom-up scenario:2-body collisions (with some LPM thrown in)

Stage I: 1 ¿ Qs t ¿ -5/2

small angle scattering:

soft Brem:

p

pz

“hard” gluons ´ p » Qs

“soft” gluons ´ p ¿ Qs

Qs

Stage II: -5/2 ¿ Qs t ¿ -13/5

• nsoft ¿ nhard

• Ehard À Esoft

• soft collisions soft gluons thermalize• hard particles lose energy by Brem + cascade

Local thermalization complete: Qs t » -13/5

Plasma instabilitiesMajor proponent that they are important for the QGP:

Stan Mrówczyński (`88, `93, `94, `97, `00, `03)

Application to bottom-up thermalization:Peter Arnold, Jonathan Lenaghan, Guy Moore

(`03)

But alsoHeinz (`84)Pokrovsky and Selikhov (`88, `90)Pavlenko (’92)Mrówczyński and Thoma (`00)Randrup and Mrówczyński (’03)Romatschke and Strickland (`03)Birse, Kao, Nayak (`03)

Anisotropic HTL self-energy

Calculate HTL self energy (,k)

or

negative eigenvalues of ij(0,k) instabilities at small k exponentially growing soft gauge fields

Anisotropic f(p)

[Note: I always assume f is parity symmetric, f(p) = f(–p).]

or linearized kinetic theory

Scalar Analogy

• Consider : Scalar theory at finite temperature.

Integrate out hard particles.massless

2 = (k2 + m02 +) ´ (k2 + meff

2)

k2+ < 0 = § i exponentially growing solutions

with » T2

• Effective potential :

• Linearized eq. :

Veff() = meff2 + 4 = 2 + 4

If < 0 (some multi-scalar models; Rochelle salts),

• =0 unstable• exponential growth of k < (- )1/2 modes• growth stops once is non-perturbative

A picture of theWeibel (or filamentation) instability

z

x

[adapted from Mrówczyński ’97]

A picture of theWeibel (or filamentation) instability

z

x

[adapted from Mrówczyński ’97]

J makes B grow

A contradictory picture

z

x

A contradictory picture

z

x

J makes B shrink

1st picture revisited 2nd picture

“trapped” trajectories focused

instability

“untrapped” trajectories

stability

For isotropic f(p), these effects cancel ij(0,k)=0.

p>

pz

k unstable

k stable

k>

kz

Note for later:Typical unstable modes have k pointing veryclose to the z direction

When does growth stop?

Answer: When fields become non-perturbatively large.

D » – igA A » / g

Possibility 1 (QED and QCD):

effects on hard particles non-perturbative

A » p / g

Possibility 2 (QCD only):self-interaction of soft modes non-perturbative

A » k / g

These are parametrically different scales: k ¿ p

Conjecture: Growing instabilities “abelianize” in QCD.

A » p / g (same as QED)

The complicated stuff that happens next is closely related to mainstream plasma physics of (collisionless) relativistic QED plasmas.

Suggestive arguments for abelianization[Arnold & Lenaghan, in preparation]

Start with (anisotropic) HTL effective action[adapted from Mrówczyński, Rebhan, Strickland ’04]

Find effective potential Veff by looking at Seff for time-independentconfigurations in A0 = 0 gauge.

Problem: too complicated!

pz kzInspired by

ignore kT and consider A = A(z) depending on z only.

A miracle [Iancu `98]:

is linear in A.

is quadratic in A.

pz kzInspired by

ignore kT and consider A = A(z) depending on z only.

A miracle [Iancu `98]:

is linear in A.

is quadratic in A.

pz kzInspired by

ignore kT and consider A = A(z) depending on z only.

A miracle [Iancu `98]:

is linear in A.

is quadratic in A.

Look at kz ! 0 limit:

System runs away in Abelian directions

e.g. or above.

Conjecture : Weibel instabilities “abelianize” as

SU2 gauge theory U1 plasma physics

SU3 gauge theory U1 £ U1 plasma physics

What happens next?

Does it stabilize as something that looks like this,requiring individual collisions to equilibrate further?

What happens next?

Does it stabilize as something that looks like this,requiring individual collisions to equilibrate further?

What happens next?

Does it stabilize as something that looks like this,requiring individual collisions to equilibrate further?

What happens next?

Current filaments attract

What happens next?

Current filaments attract magnetic tear instability

non-relativistic 2D+3D simulations by Califano et al.

[from Phys. Rev. Lett. 86 (2001) 5293]

But not all collisionless problems isotropize ...

Simulations by Honda et al. of uniform relativistic beamof electrons injected into a plasma:

[from Phys. Plasmas 7 (2000) 1302]

known as a Bennett self-pinch equilibrium (1934)

Original question : How does the thermalization time depend on s?

A lower bound :

• Near equilibrium, thermalization time

• After expansion time t, initial saturation energy density

is diluted to

• Setting and combing the above,

This is indeed smaller than the original bottom-up’s -13/5.And it might be the right answer for instability-driven thermalization.

A wish list

Full simulations of QCD kinetic theory to check the “abelianization” conjecture.

Simulations of QED and/or QCD kinetic theory to investigate isotropization of ultra-relativistic systems that start from

pz

What is parametric time scale for isotropization in each case?