aapps dschaeffer 11-18 - PPPL

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


T0 + 2.85 ns T0 + 3.85 nsT0 + 2.35 ns


Compression width 𝚫 ∼ 0.5 c/𝝎pi ∼ 40 c/𝝎pe

shadowgraphy

2.35 ns

simulation


T0 + 3.85 nsT0 + 2.35 ns


T0 + 2.85 ns


T0 + 3.85 nsT0 + 2.35 ns


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


No ambient plasma Unmagnetized

ambient ions

x=3 mm x=4 mm

piston ions



ambient ions

Magnetized

deformation in ion flow

timing fiducials

x=3 mm x=4 mm x=3 mm

piston ions



ambient ions

Magnetized


piston ions

EPW

stray light block

EPW Lineouts w/ Best Fits



ambient ions

Magnetized

C ion phase space


piston ions

PIC Simulation

Ambient ions have not connected, so shock has not fully formed.



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


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)

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aapps dschaeffer 11-18 - PPPL