Feasibility of core collapse supernova experiments at the national ignition facility
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Feasibility of Core-Collapse Supernova Experiments at the National Ignition Facility. Timothy Handy. Euler Equations. H yperbolic system of conservation laws Requires an additional closure relation. de Laval Nozzle – A Basic Example. Assumptions: Ideal Gas

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Feasibility of Core-Collapse Supernova Experiments at the National Ignition Facility

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Feasibility of core collapse supernova experiments at the national ignition facility

Feasibility of Core-Collapse Supernova Experiments at the National Ignition Facility

Timothy Handy


Euler equations

Euler Equations

  • Hyperbolic system of conservation laws

  • Requires an additional closure relation


De laval nozzle a basic example

de Laval Nozzle – A Basic Example

  • Assumptions:

    • Ideal Gas

    • Isentropic (Reversible & Adiabatic)

    • One-dimensional flow

    • Compressible

  • Examples:

    • Rocket Engines

    • Astrophysical Jets


Stratified mediums atmospheres

Stratified Mediums (Atmospheres)

  • Layers of material

    • Density gradient

    • Generated due to gravity

  • Steady State vs. Static Equilibrium

    • Steady State – balanced state with change (dynamic processes)

    • Static Equilibrium – balanced state without change

  • Atmospheres are generally steady with dynamics

    • Pressure changes move flow

    • Heating and cooling processes trigger convection


Euler with sources

Euler with Sources

Gravity

Gravity + Heating


What counters gravity

What counters gravity?

  • What’s stopping us from falling?

  • This pressure term comes from the interaction between atoms (well, fermions…)

    • Two atoms can’t share the same space

  • What happens if the pressure disappears?

    • Our businessman is in trouble!


Core collapse supernovae

Core-Collapse Supernovae

Iron core grows

Mass is added from silicon burning

TOO BIG!

Bigger

Big

Okay

Gravity > Degeneracy Pressure

Electrons and Protons combine to form Neutrons and Neutrinos

+

+

=

+

-

Sudden loss of pressure at the core


Bounce

Bounce

  • Falling fluid parcels doesn’t know new equilibrium

    • Possible overshoot of equilibrium

    • Motion becomes supersonic at some point -> sonic point inside the flow

    • Compressed, high density plasma changes its properties (phase transition) and becomes nuclear matter

    • NM is much harder to compress and starts effectively acting as a solid boundary

    • This boundary acts as a reflector for the incoming flow

    • Reflected flow perturbations propagate upstream and evolve into a shock

  • String of springs


Bounce animation

Bounce Animation


State of affairs at this time

State of Affairs at this Time

  • The outer stellar envelope is infalling

  • Material passes through the shock

  • Advected downstream subsonically and settles down near the surface of the reflector (proto-neutron star)


Ohnishi design

Ohnishi Design

  • Ohnishi et al. (XXX) proposed an experimental design to study the shock

  • Drive material toward a central reflector using lasers

  • The material would then strike the reflector and produce a shock

  • Material would continue

    to move through the

    shock


Ohnishi design1

Ohnishi Design

  • Loss of gravity and heating/cooling

    • Can a laboratory shock be similar to a real shock?


Scaling law euler number and hedp

Scaling Law (Euler number) and HEDP

  • Characterization of the flow via Euler number [Ryutov et al. (XXX)]

  • HEDP diagram


State of affairs at this time1

State of Affairs at this Time

  • The outer stellar envelope is infalling

  • Material passes through the shock

  • Advected downstream subsonicallyand settles down near the surface of the reflector (proto-neutron star)

    The above are essential nozzle components

    Highlight difference with SN

    Settling

    Cooling by Neutrinos

    Gravity

    Convection

    Heating by Neutrinos

    The problem can now be reformulated as the composite of two problems

    Shock Stability Problem

    Settling Flow Problem

    Here our focus is on the first problem and initially without Heating


State of affairs at this time2

State of Affairs at this Time

  • The outer stellar envelope is infalling

  • Material passes through the shock

  • Advected downstream subsonicallyand settles down near the surface of the reflector (proto-neutron star)

  • The above are essential nozzle components

  • Supernova’s additional processes

    • Settling

      • Cooling by Neutrinos

      • Gravity

    • Convection

      • Heating by Neutrinos

  • The problem can now be reformulated as the composite of two problems

    • Shock Stability Problem

    • Settling Flow Problem

  • Our focus is on the shock stability problem (initially without heating)


Analytic

Analytic


Critical mach number ppre 0

Critical Mach number (Ppre>0)


Maximum aspect ratio

Maximum Aspect Ratio


Euler number vs mpre

Euler Number vs. Mpre


Initial bc constraints

Initial BC constraints


Semi analytic

Semi-Analytic


Latin hypercube sampling

Latin Hypercube Sampling


Semi analytic setup

Semi-analytic Setup


Semi analytic results

Semi-analytic Results


Semi analytic results1

Semi-analytic Results


One d

One-D


Setup

Setup


Coupling of shock to pert

Coupling of Shock to Pert


Stable advective times

Stable Advective Times


Two d

Two-D


Setup1

Setup


Qualitative results

Qualitative Results


Flux decomposition

Flux Decomposition


Conclusions parameter ranges

Conclusions – Parameter Ranges


Conclusions sasi recreation

Conclusions – SASI Recreation


Future work

Future Work


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