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Experimental Studies of High‐Mach‐Number Collisionless Shocks in Laser Plasmas
Derek SchaefferPrinceton University/PPPL
2nd AAPPS DPP
Kanazawa, Japan
Nov. 15, 2018
Supported by: DOE and NNSA
Collaborators
• Will Fox (PPPL/PU)• Jack Matteucci (PU)• Amitava Bhattacharjee (PU/PPPL)• Gennady Fiksel (U. Michigan)• Kai Germaschewski (U. NH)• Chikang Li (MIT)• Russ Follett (LLE)• Dan Haberberger (LLE)• Daniel Barnak (LLE)• Suxing Hu (LLE)
Outline
• Introduction• Experimental generation of high‐MA collisionless shocks• Laboratory measurements of particle velocity distributions in developing shocks• Conclusion
Magnetized Collisionless Shocks are the Most Prevalent Shocks in Space and Astrophysical Systems
• Collisionless shocks convert the ram pressure of incoming supersonic flows to thermal pressure over length scales much shorter than the collisional mean free path• In systems with pre‐existing magnetic fields, the shocks are magnetized. These are known to be the source of very high‐energy particle acceleration, including cosmic rays• Despite decades of (mostly) spacecraft data, fundamental questions of shock physics remain, such as: How is energy partitioned between electrons and ions across a shock?• Laboratory experiments can complement spacecraft with controlled and reproducible plasma conditions
Solar Wind
Supernovae Remnants
Heliopause
Active Galactic Nuclei
Laboratory Platforms Allow Detailed Studies of Collisionless Shocks using Laser Plasmas
Piston
Upstream(Unshocked)Ambient
Downstream(Shocked)Ambient
B2 > B1n2 > n1T2 > T1
vshockvpiston
B1, n1, T1
Model for Piston‐Driven Shock Formation• Magnetized shocks can be generated by driving a supersonic piston plasma through a magnetized ambient plasma [Schaeffer+ PRL 2017, Niemann+ GRL 2014]
• Shocks form within ∼1 upstream 𝛚ci‐1 but
take several 𝛚ci‐1 to reach “steady state”.
Current experiments can access 1‐2 𝛚ci‐1.
• Important to distinguish between features of developing and fully‐formed shocks
• Spacecraft utilize particle analyzers to directly measure velocity distribution functions, which provide invaluable insight into shock physics• Analogous measurements can now be made with
Thomson scattering diagnostics, which will eventually allow direct comparisons between space and laboratory data
pistonplume
field and densitycompression
target
ambient plasma
B0 laser
Experimental Setup for High‐MA Shocks on Omega EP
TCC
PistonPlumes
CH PistonTarget
Current‐CarryingCu Wires
Drive Lasers
Precursor Laser
CH AmbientTarget
• Interaction probed with angular filter refractometry (AFR), shadowgraphy, and proton radiography (PR) diagnostics
• AFR probed along z• Measures contours of path‐
integrated density gradient• Shadowgraphy coincident with AFR
• Measures 2nd derivative of path‐integrated density
• PR probed the x‐z plane by sending protons along y• Protons deflected by magnetic
field, yielding a proton fluence map that can be inverted to get the path‐integrated magnetic field
Experimental Setup for High‐MA Shocks on Omega EP
MIFEDScoils
I MIFED
S
Main target
BG target
TCC
BMIFEDS BMIFEDS
4.5 mm
Ambientplasma
BG target
Pistonplasma
MIFEDS coils provide background magnetic field ~ 8T
Precursor beam ablates ambient plasma 12 ns before drive beams
Drive beams create supersonic piston plumes that expand into ambient plasma
Null Shots Show No Shock Features
1 mm
B0=0, n0=0
v0
PistonPlume
PistonTarget
Ambient Target
AFR Image
x=0
3.35 ns Ambient Target
PistonTarget
Null Shots Show No Shock Features
Without background magnetic field or ambient plasma, only piston plumes observed
1 mm
B0=0, n0=0
v0
PistonPlume
PistonTarget
Ambient Target
AFR Image
x=0
3.35 ns
B0=0, n0>0
v0
PistonPlume
PistonTarget
Ambient Target
AFR Image
1 mm
x=0
3.85 ns
Shock‐Like Gradients Observed with B0>0 and n0>0
T0 + 2.85 ns T0 + 3.85 nsT0 + 2.35 ns
Piston PlumeShock‐likegradient
v0 ≈ 700 km/s (MA ≈ 15)
v0
Shock‐Like Gradients Observed with B0>0 and n0>0
T0 + 2.85 ns T0 + 3.85 nsT0 + 2.35 ns
Piston PlumeShock‐likegradient
Compression width 𝚫 ∼ 0.5 c/𝝎pi ∼ 40 c/𝝎pe
shadowgraphy
2.35 ns
simulation
Shock‐Like Gradients Observed with B0>0 and n0>0
T0 + 3.85 nsT0 + 2.35 ns
Piston PlumeShock‐likegradient
T0 + 2.85 ns
Shock‐Like Gradients Observed with B0>0 and n0>0
T0 + 3.85 nsT0 + 2.35 ns
Piston PlumeShock‐likegradient
T0 + 2.85 ns
Density compression n/n0 ≈ 7
Magnetic Compressions Observed with Proton Radiography
Ambient Target
PistonTarget
MagneticCavity
MagneticCompression
T0 + 3.80 ns
1 mm
v0
PistonTarget
Ambient Target
x=0
MagneticCavity
MagneticCompression
T0 + 3.80 ns
1 mm
v0
PistonTarget
Ambient Target
x=0
Magnetic Compressions Observed with Proton Radiography
Magnetic compression B/B0 ≈ 3
Experimental System Simulated with Particle‐in‐Cell Code PSC
• 2D explicit PIC with Coulomb collision operator• Initialized with C+6, H+1 ambient plasma in uniform magnetic field• Heating operator to model laser ablation of CH piston plasma
Germaschewski, et al., JCP, 2016Fox, et al., PoP, 2018
PIC Simulations Indicate Formation of High‐MA Shock
• Magnetic cavity formed as magnetic flux is swept out by piston into thin, compressed region• Piston ions get trapped behind this magnetic compression• Ambient ions are reflected off magnetic compression, a hallmark of high‐MA shocks• A double “bump” in the density profile develops, corresponding to the separation of the shock from the trapped piston ions
Piston Ions
Ambient H Ions
Ambient C Ions
magnetic cavity shock
piston
downstream upstream
reflected ions
ni,tot/ni,0B/B0
Data Profiles Show Density Evolution that is Consistent with High‐MAShock Formation
shock
piston
pistonpileup
shock
Early time density compression mostly associated with pile‐up of piston ions
At late time clear double bump feature associated with shock and trapped piston ions
Schaeffer, et al., PRL, POP, 2017MA ∼ 15 magnetized collisionless shock observed
pistonpileup
Experimental Setup for Magnetized Collisionless Shocks on Omega
ambient CH target
piston CH targetbacklighter capsule for proton radiography
precursor beam
drive beam
drive beam copper coils2ω probe beam
scattered lightcollection
• Interaction probed with Thomson scattering (TS) and proton radiography (PR) diagnostics
• TS probed along expansion direction (x) at TCC• Light scattered from electron
plasma waves (EPW) and ion acoustic waves (IAW)
• EPW feature can yield electron density and temperature
• IAW feature can yield electron and ion temperatures and ion flow speed
• PR probed the x‐y plane by sending protons along z• Protons deflected by magnetic
field, yielding a proton fluence map that can be inverted to get the path‐integrated magnetic field
TCC
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma
• Scattered light from piston C ion population (H damped)
• Two streaks from forward and backward propagating ion acoustic waves
• Generally, will get two sets of waves per species per ion flow population
x=3 mm
piston ions
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma Unmagnetized
ambient ions
x=3 mm x=4 mm
piston ions
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma Unmagnetized
ambient ions
Magnetized
deformation in ion flow
timing fiducials
x=3 mm x=4 mm x=3 mm
piston ions
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma Unmagnetized
ambient ions
Magnetized
x=3 mm x=4 mm x=3 mm
piston ions
EPW
stray light block
EPW Lineouts w/ Best Fits
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma Unmagnetized
ambient ions
Magnetized
C ion phase space
x=3 mm x=4 mm x=3 mm
piston ions
PIC Simulation
Ambient ions have not connected, so shock has not fully formed.
IAW Spectra Show Ion Dynamics of Developing Shock
No ambient plasma Unmagnetized
piston ions
ambient ions
Magnetized PIC Simulation
C ion phase space
Directly observe the interaction between piston and ambient ions, which shows that the shock is in formation stage
x=3 mm x=4 mm x=3 mm
Plasma Parameters Exhibit Strong Dependence on Initial Conditions
Strong density compressions and heating observed even without fully formed shock!Necessary but not sufficient signature of shock formation.
magnetizedunmagnetized
Ion Flow Speed Electron Density Electron Temperature
strong density compression
piston
ambient
deformed piston flow
accelerated ambient ions
strong electron heating
Proton Radiography Indicates Strong Magnetic Field Compression
14.7 MeV Proton Radiography Image
• Piston plasma sweeps out background field By, forming magnetic cavity
• Transition from low fluence (black) to high fluence (white) regions indicate large proton deflections and magnetic compressions
• By can be re‐constructed by comparing data and synthetic fluence profiles
magnetic cavity
TS and PRAD Data Show Initial Shock Formation Process
• Magnetic field compressed by ambient plasma
• Piston plasma piles up behind magnetic field
• Electron temperature adiabatically heated by density compression
• Ambient ions accelerated by electron pressure gradient
• Piston flow also modified by pressure gradient
• In time, ambient ions will be accelerated to shock speed and begin to separate from piston
ByneTexvx,pistonvx,ambient
Profiles for Magnetized Plasma
Ex
Summary and Outlook
• We have observed for the first time the formation and evolution of a laser‐driven, high‐MA collisionless shock. The results agree well with PIC simulations.• We have measured for the first time particle velocity distributions in a developing magnetized collisionless shock using Thomson scattering.• Future experiments will build on our ability to measure velocity distributions to develop datasets that can be compared to spacecraft observations of collisionless shocks.• The development of this platform allows key questions of high‐MA shocks to be addressed:• Spatial and temporal scales of shock formation and reformation• Shock heating and energy partitioning• Particle injection and acceleration• Interplay between shocks, reconnection, and turbulence
AFR Diagnostic Measures Density Gradients
Haberberger, et al., PoP, 2014
dn/dx
x
opaque filter
transparent filter
0
1
signal
Plasma
ImagingOptics
AngularFilter
ImagePlane
ProbeBeam
Ambient Plasma Characterized with Thomson Scattering
BG target
kL (probe laser)
ks (collected light)
k = kL ‐ ks
Electron density ne0 = 1x1018 cm‐3
Electron temperature Te0 = 30 eV
EPW Spectra
Magnetic Field Reconstructed from Proton Fluence Data
Model By(x,z)
Measured proton fluenceSynthetic proton fluencePath‐integrated ByBy(x,0)
protons
(ellipse)