Flow Vorticity and Rotation - PowerPoint Presentation

Slide1

Flow Vorticity and Rotation in Peripheral HIC

Dujuan Wang

1

2014 CBCOS, Wuhan, 11/05/2014

University

of Bergen,

NorwaySlide2

IntroductionVorticity for LHC, FAIR & NICARotation in an exact hydro modelSummary

Outline2Slide3

Introduction

Pre-equilibrium stage  Initial state Quark Gluon Plasma  FD/hydrodynamics  Particle In Cell (PIC) code Freeze out, and simultaneously “hadronization” 

Phase transition

on hyper-surface  Partons/hadrons3Slide4

Relativistic Fluid dynamics modelRelativistic fluid dynamics (FD) is based on the conservation laws and the assumption of local equilibrium (

 EoS)4-flow:energy-momentum tensor:

In Local

Rest (LR) frame = (e, P, P, P);For perfect fluid

:

4Slide5

tilted initial state, big initial angular momentum Structure and asymmetries of I.S. are

maintained in nearly perfect expansion.[L.P.Csernai, V.K.Magas,H.Stoecker,D.D.Strottman, PRC 84,024914(2011)]Flow velocity

Pressure gradient

5Slide6

The rotation and Kelvin Helmholtz Instability (KHI)[L.P.Csernai, D.D.Strottman, Cs.Anderlik

, PRC 85, 054901(2012)]6More details in Laszlo’ talk Straight line 

Sinusoidal wave for peripheral collisionsSlide7

Classical flow:

Relativistic flow:2. Vorticity

The

vorticity in [x,z]plane is considered.Definitions: [L.P.

Csernai

, V.K.

Magas

, D.J. Wang,

PRC

87

, 034906(2013)]

7Slide8

Weights:

+00++++-In [

x,z] plane:

Etot: total energy in a y layerNcell: total num. ptcls. In this y layerCorner cellsMore details:8Slide9

In Reaction Plane t=0.17 fm/c

Vorticity @ LHC energy:9Slide10

In Reaction Plane t=3.56 fm/c

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In Reaction Plane t=6.94 fm/c

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All y layer added up at t=0.17 fm/c

b512Slide13

All y layer added up

at t=3.56 fm/cb513Slide14

Average Vorticity in summaryDecrease with timeBigger for more peripheral collisionViscosity damps the vorticity

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Circulation:

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Vorticity @ NICA , 9.3GeV:

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Vorticity @ FAIR, 8 GeV

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3, Rotation in an exact hydro model

Hydrodynamic basic equations

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The variables:

Csorgo, arxiv: 1309.4390[nucl.-th]Scaling variable:

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cylindrical coordinates:

rhs:More details:

y

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lhs:

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Expansion energy at the surface Expansion energy at the longitudinal directionRotational energy at the surface

For infinity case:

Kinetic energy:

(α and β are independent of time)sρM & syM:Boundary of spatial integral22Slide23

Internal energy:

23Slide24

The solution:

Runge-Kutta

method: Solve first order DE

initial condition for R and Y is needed, and the constants Q and WSolutions:24Slide25

Table 1 : data extracted fromL.P. Csernai, D.D Strottman and Cs Anderlik, PRC 85, 054901 (2012)

R : average transverse radius Y: the length of the system in the direction of the rotation axis θ : polar angle of rotation ω : anglar velocity 25Slide26

Energy time dependence:Energy conserved !decreasing internal energy and rotational energy leads the increasing of kinetic energy .

26Slide27

Smaller initial radius parameteroverestimates the radial expansion velocitydue to the lack of dissipationSpatial expanding:

27Slide28

In both cases the expansion in the radial direction is large.Radial expansion increases faster, due to the centrifugal force from the rotation. It increases by near to 10 percent due to the rotation.the expansion in the direction of the axis ofrotation is less.

Expansion Velocity:28Slide29

SummaryThank you for your attention!

High initial angular momentum exist for peripheral collisions and the presence of KHI is essential to generate rotation.Vorticity is significant even for NICA and FAIR energy. The exact model can be well realized with parameters extracted from our PICR FD model29Slide30

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Table 2 : Time dependence of characteristic parameters ofthe exact fuid dynamical model. Large extension in the beam direction is neglected. 31Slide32

α and β

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