FR06 · Longitudinal expansion
Why does a plasma cool differently when it can push along its expansion? Longitudinal pressure does work as the matter expands, so its energy density falls faster. Collisions replenish that pressure; freely streaming particles instead lose longitudinal momentum and exert progressively less pressure along the expansion.
Compare an initially isotropic free-streaming gas, an ideal fluid and a relaxing shear stress at equal initial energy. Follow their cooling and their unequal longitudinal and transverse pressures.
Cyan: MIS relaxation. Amber: ideal fluid. Violet: initially isotropic free streaming. All begin at the same energy density; the initial shear control changes only MIS.
Time is in units of the initial proper time; energy density is in units of its initial value. Natural units are used. The pressure shape above encodes normalized tensor components and carries no physical length scale.
Physics tutorial
BackgroundAfter a heavy-ion collision, neighbouring slices of matter rush apart along the beam. In a boost-invariant description each slice has the same history when followed with its own clock.
Why it mattersDilution removes energy from a unit volume. Longitudinal pressure also does work, so the cooling rate tells us about the stress along the beam.
Start with the essentials
Proper time is the time measured along a comoving trajectory. Positive longitudinal pressure adds pressure work to dilution. The shear convention lowers longitudinal pressure when the shear variable is positive.
The expansion drives shear stress and a finite relaxation time delays its response. The last term follows the conformal MIS closure. The quadratic BRSSS term is set to zero.
Set shear stress to zero and integrate energy conservation. The ideal branch has equal pressures at every time. The temperature is defined by energy matching in every branch.
Typical misconceptionA hydrodynamic description requires equal pressures at every instant.
Better mental modelViscous hydrodynamics predicts unequal pressures. The residual measures agreement with a chosen constitutive approximation; the pressure ratio measures isotropy.
Choose Three cooling histories and leave the initial MIS shear at zero.
What to observe: All three start isotropic. Their subsequent longitudinal pressures differ, so their cooling histories separate.Compare Quickly relaxing shear and Long-lived anisotropy.
What to observe: Relaxation and expansion compete. A slow stress response preserves anisotropy for longer.Pause and drag the glowing time handle. Read the energy and pressure plots at the moving marker.
What to observe: The ideal branch follows the analytic power law. Free streaming starts with finite longitudinal pressure and approaches a slower late-time dilution law.Heavy-ion matter and hydrodynamics · Reading path
Articles on this path that use this experiment, followed by the other experiments they suggest.