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

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

Timothy Handy


Euler equations
Euler Equations National Ignition Facility

  • Hyperbolic system of conservation laws

  • Requires an additional closure relation


De laval nozzle a basic example
de Laval Nozzle – A Basic Example National Ignition Facility

  • Assumptions:

    • Ideal Gas

    • Isentropic (Reversible & Adiabatic)

    • One-dimensional flow

    • Compressible

  • Examples:

    • Rocket Engines

    • Astrophysical Jets


Stratified mediums atmospheres
Stratified Mediums (Atmospheres) National Ignition Facility

  • 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 National Ignition Facility

Gravity

Gravity + Heating


What counters gravity
What counters gravity? National Ignition Facility

  • 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 National Ignition Facility

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 National Ignition Facility

  • 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 National Ignition Facility


State of affairs at this time
State of Affairs at this Time National Ignition Facility

  • 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 National Ignition Facility

  • 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 National Ignition Facility

  • 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 National Ignition Facility

  • 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 National Ignition Facility

  • 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 National Ignition Facility

  • 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 National Ignition Facility


Critical mach number ppre 0
Critical Mach number ( National Ignition FacilityPpre>0)


Maximum aspect ratio
Maximum Aspect Ratio National Ignition Facility


Euler number vs mpre
Euler Number vs. National Ignition FacilityMpre


Initial bc constraints
Initial BC constraints National Ignition Facility


Semi analytic
Semi-Analytic National Ignition Facility


Latin hypercube sampling
Latin Hypercube Sampling National Ignition Facility


Semi analytic setup
Semi-analytic Setup National Ignition Facility


Semi analytic results
Semi-analytic Results National Ignition Facility


Semi analytic results1
Semi-analytic Results National Ignition Facility


One d
One-D National Ignition Facility


Setup
Setup National Ignition Facility


Coupling of shock to pert
Coupling of Shock to Pert National Ignition Facility


Stable advective times
Stable National Ignition FacilityAdvective Times


Two d
Two-D National Ignition Facility


Setup1
Setup National Ignition Facility


Qualitative results
Qualitative Results National Ignition Facility


Flux decomposition
Flux Decomposition National Ignition Facility


Conclusions parameter ranges
Conclusions – Parameter Ranges National Ignition Facility


Conclusions sasi recreation
Conclusions – SASI Recreation National Ignition Facility


Future work
Future Work National Ignition Facility


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