Wakes and Shocksin Plasmas

Chan JoshiUCLA

Supported by DOE and NSFMIPSE Colloquium U. Michigan

Leonardo deVinci: Study of Wakes-1509

What is a Wake?

Structure of the displaced fluid behind an object causing disturbance

Neptune Laboratory

What is a Shock?

Subsonic Sonic Supersonic

A disturbance that travels at supersonic speeds through a medium

• At supersonic speeds, pressure will build at the front of a disturbance forming a shock

• Characterized by a rapid change in pressure (density and/or temperature) of the medium

In a plasma, a shock wave is characterized by a propagating electric field at speeds useful for ion acceleration (Vsh > 0.01c)

Object

Wake Bow Shock

Bullet at Mach 1.5 through air produces both a wake and a shock

Supersonic Disturbance in a Fluid can Produce both a wake and a shock

DensityCavitation Density Pile up

Wakes in Plasmas Excited byPassage of a Relativistic Electron Beam

C. Joshi Scientific American Feb 2006

Vg = Vph ~ c

Relativistic Electron Bunch

Decelerating

Accelerating

Wakes in Plasmas: Microscopic Capacitors Moving at Light Speed

A AcceleratingD Decelerating

Accelerating Field= 30GeV/m(1017/no)1/2

0.5

Chan

ge in

Den

sity

0

-0.5Position

Intense Laser Pulses can Excite both Wakes & Shocks in Plasmas

W. Lu, M. Tzoufras et al., UCLA

P =.2 PW, t =30fs

Rosenzweig et al. 1990 Pukhov and Meyer-te-vehn 2002

Dense Plasma vg,laser < c

2D PIC

3D PIC

Bow shockWakeTurbulent

Plasma

Dilute Plasma vg,laser ~ c

Vg=c(1-ne/2nc)

P=5 TW, τ=30 fs

Conventional Accelerator Plasma Accelerator

Copper Structure with irises Ionized GasPowered by microwaves Powered by a Laser or electron beam pulseEnergy Gain 20 MV/m Energy Gain 20 GV/mStructure Diameter 10cm Diameter 1mm Lifetime one picosecond

1 m.3 mm

N. Matlis et alNature Physics

Typical Laser-Wakefield Acceleration Experiment circa 2013

UCLA/UCSD/LLNL Collaboration

Injector-Accelerator Configuration Produces Narrow Energy Spread e- Beam (UCLA/LLNL/UCSD Collaboration)

High Quality Electron Beams Accelerated at 100 GeV/m in Laser Wakefield Accelerator

GeV class beams produced at U.T. AustinCourtesy M. Downer; unpublished results

GeV Electron Beams in just a cm-scale plasma accelerator!!!

Image plate for GeV e-

1T magnet

7 cm unifomgas cell

Beam dump

f/4095 – 125 J

150 fs

e-

laserpolarization

Laser pulse

Beam-Driven Wakefield Accelerators(Blowout Regime)

• Plasma ion channel exerts restoring force => space charge oscillations

• Linear focusing force on beams (F/r=2pne2/m)

• Space charge of the beam displaces plasma electrons

Rosenzweig et. 1990 Pukhov and Meyer-te-vehn 2002 (Bubble)

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--------- ----

--- -------------------- - --

---- - -- ---

------ -

- -- ---- - - - - - ------ - -

- - - - --- --

- -- - - - - -

---- - ----

-----

+ + + + + + + + + + ++ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + +

-

- --

--- --

Ez

drive beam

UCLA,USC,SLAC E 167 Collaboration

40 GeV Beam60 kA in 50 fs1 PW

Big-Wave Surfing on a Plasma Wake

Drive Beam

Accelerating Beam

Electric Field

Propagation Direction

Electron Beam Drivers Enable Meter-Scale Wakefield Acceleration

Initial Energy30-40 GeV

Final Energy10-100 GeV

Beam-Driven Wakefield Acceleration from 42 GeV-85 GeV in 85 cm.

I. Blumenfeld et al Nature 2007

Talk by T. Katsouleas Duke UV 445 p741 (2007)

SimulationsExperiment

10035 Energy (GeV)

UCLA/USC/SLAC Collaboration E167

Plasma Afterburner for a Linear Collider

C. Joshi and T. KatsouleasPhysics Today 2005

RAL

LBL Osaka

UCLA

E164X

ILC

ANL

Plasma Accelerator Progress“Accelerator Moore’s Law”

E167

LBNL

Working MachinesDoing physics

Max.Energy inExperiments

Electron beam driven

Laser beam driven

C. Joshi and T. KatsouleasPhysics Today 2005

Hot Cold

Shockacceleration

TNSAHigh-intensitylaser pulse

Shock acceleration

TargetNormalSheathAcceleration

Applications of Laser Accelerated Ions1) Medical isotopes2) Cancer therapy3) Proton radiography4) Fast ignition fusion

Fast electron travel through the target

e-

Mechanisms Leading to Shock And Target Normal Sheath Acceleration

L. Silva et al PRL

Laser Acceleration of Ions

Position

Mom

entu

m

Detached Supersonic shocks can be launched by a laser pulse in an over-dense plasma

SteepenedPlasma

ExtendedExponential Plasma

a0 = 2.5, τ = 2080/ωp

Shock continues to propagate long after laser piston is removed

Although laser beam filaments, Refluxing of heated electronsLaunches a planar shock

Laser Pulse (piston) stops near critical density and strongly heats electrons

In the frame of the shock we have interpenetrating plasmas

Plasma 1np1 = 2ncr

Te1

Cold IonsV1 →

Plasma 0np0

Te0

Cold Ions

• Interpenetrating plasmas with dissimilar densities (np1 > 3np0) form a shock

• Shock speed increases with :• Te

• Vdrift

• Te1/Te0 not important for Relativistic temperatures

• Vdrift > Vmax shock not formed

• Increasing Vdrift towards Vmax increases the % of reflected protons

UpstreamIons

DownstreamIons

Reflected Ions

• Downstream to upstream density ratio Γ• Downstream to upstream temperature ratio Θ• Relative drift velocity vdrift

• What determines the shock velocity? Vdrift and electron temperature ( Cs )

Linearly polarized light better than circular.Mechanism not to be confused with hole boring RPA

Collisionless if λmfp e-e, e-i, i-i << few λD

Excitation of Collisionless Shocks

Shock Excitation and Reflection of Ions

Motion of an ion in the potential well of an ion wave can be written in terms of the Sagdeev potential

Shocks excited in plasmas when the nonlinear Sagdeev (quasi) potential

Ψ(φ) = {Pi(φ, M) –Pe1(φ, Θ, Γ) – Pe0(φ, Θ, Γ)} < 0

Pi(φ, M) = ion pressure for cold ions & Maxwellian e-

Pe1(φ, Θ, Γ) =downstream e- pressure

Pe0(φ, Θ, Γ)= upstream e- pressure

M = Vsh/Cs with Cs = (kTe0/mi)1/2

Φ = eφ/kTe2 electrostatic potential energy difference

Φ plays role of space and ξ=x/λD plays role of time

Ions will be reflected when

eϕ > ½ miV2sh which gives eϕ crit = M2

crit/2

Critical Mach Number Needed for Ion Reflection as a Function of Γ and Θ

ExperimentalParameterRegime

Nonrelativistic

Relativistic

PIC simulations

F. Fiuza et al Submitted for publication

1 keV1 MeV1keV1MeV

EXPE

RIM

ENTS

Density Ratio Γ= nd/nu Threshold of Shocks(ion density evolution)

Γ=1 Γ=1.5

Γ=2 Γ=5

Expansion of a dense plasma into a rarefied exponential plasma E TNSA ~ 1/L

1D OSIRIS

Plasma1Constant Density

Plasma2Exponentialprofile

Density Ratio Γ Threshold of Shock Formation(ion momentum evolution)

Γ=1 Γ=1.5

Γ=2 Γ=5

V refl = 2V shock- V up

Drift Velocity Helps Shock Formation(ion density evolution)

Γ=1.5 vd=0 Γ=1.5 vd= 0.1Cs

Γ=1.5 vd= 0.5Cs Γ=1.5 vd= 0.75Cs

Drift Velocity Helps Shock Formation(ion momentum evolution)

Γ=1.5 vd=0 Γ=1.5 vd= 0.1Cs

Γ=1.5 vd= 0.5Cs Γ=1.5 vd= 0.75Cs

Te = 1MeVTi = 100 eV

Transition from Ion Acoustic Wave to Shock in Two Drifting Interpenetrating Plasmas

V r

e

f

l = 2V s

h

o

c

k

- V u

p

V drift too small : No Shock

V drift just right : Shock Onset

V drift too Large Plasmas pass through one another

Ion reflection Upstream and ion trapping downstream

Classic Ion Acoustic Wave

Nonlinear IAW onset of Ion Trapping

Shock

Strong Ion Trapping

Beam Loading damps IAW

High Efficiency Reflection from Shock

Formation of Collisionless shocks

• Two interpenetrating plasmas with dissimilar densities and in addition a relative drift expand through one another.

• The sheath field of the higher density plasma which expands with Cs seeds an ion acoustic wave behind it.

• When the conditions of density and drift velocity are right the Sagdeev potential becomes –ve and the nonlinear ion wave morphs into either a soliton (no dissipation) or a shock with ion reflection (upstream) and ion trapping (downstream) acting as the dissipation mechanisms.

Ion Acceleration by Collisionless Shocks: Reduction to Practice

• Need two colliding plasmas with a density ratio of at least 1.5 and a relative drift velocity of < 0.5Cs

• Need strong electron heating to get a large corresponding shock velocity

• Longer pulses better: allow refluxing of electrons and homogenize any filamentation imprint left by the laser

• Need few times critical density and linear polarization for strong electron heating

Launch collisionless shock in a supercritical plasma by pushing on it to induce vdrift and strong heating to get a large cs .

Minimize TNSA fields by shock propagation in extended plasma

๏ λ0 = 10 μm๏ I0 = 1016 - 1018 Wcm-2

๏ τ0 = 3 ps/ 100 ps๏ W0 = 60 μm

๏Lg = 20 μm๏ ne0 =4x 1019

cm-3 (4 nc)๏ mi/me = 1836

Physical Parameters

Laser PlasmaGas jet

hybrid PIC

ni

Extended PlasmaSteepenedPlasma E TNSA ~ 1/L

NEPTUNE: Most Powerful CO2 Laser in the World

Neutralprofile

Plasma Profile

Plasma Density Profile at Peak of Laser Macropulse

Plasma Layer Heated and Pushed by the laser

Density Cavity

Neptune Laboratory

Experimental Arrangement

Time Structured Laser Pulse

Overdense Penetration and Radiation Pressure Lead to “Hole-Boring”

t= 33ps

t=131 ps

Measured Average Hole boring (shock propagation velocity) ~0.015c

Max ion energy ~ 100 keV

Radiation Pressure Induced Cavitation Leads toBoth density pile up and a drift

Theoretical Maximum Vhb = 0,041c for a0= 2.5 and n= 2ncr. Max Ion Energy = 800 keV

Neptune Laboratory

Energy spreads measured to be FWHM ΔE/E 1% :

Measured Proton spectra

Source Size : d = 120µmBeam Size (RMS) : σx 5.7mm : σy 2.2mm :Divergence : θx 37mrad : θy 14mrad :Emittance : εx = d.θx = 4.6mm.mrad εy = d.θy = 1.7mm.mradN ~ 106

Noise Floor

Energy Deposition : Ions & Photons

Bragg Peak for ions results in localized energy deposition

TUMOR

Multiple Beams Used to Irradiate Tumor

Radiation dose relative to peak (100%)

Simulations of Irradiating the Human Skull with Multiple Beams

Adapted from GSI Helmholtz Centre for Heavy Ion Research in Darmstadt

T

Tumor

Organ

Multiple X-Ray Beams

Eight X-ray Beams Two Carbon Ion beams

What is Needed for Tumor Therapy?

Treatment dose: 2 Gy/ 10min , Volume 1 Litre ~ 1-5 X109 particles/s

Energy requirements: 50 MeV (superficial tumors) > 200 MeV (deep tumors)

E/E ~5% ( Proven to be challenging to-date)

Dose Accuracy Isocentric DeliveryLow Cost

Laser-Based Ion Accelerator

Goal Cost : 10-20 million USDTable top laser system (developing)Transportation : MirrorsOnly has focusing magnet Gantry : small, protons generated in direction of patient

M. Murakami, et al., AIP Conf. Proc. 1024 (2008) 275, doi:10.1063/1.2958203

Scaling of Energy and Energy Spread with a0

OSIRIS 2D Simulations : F. Fiuza et al

2015

10

5

ao=2.5

Energy Spectrum Scaling with a0 Scaling of Maximum Energy with a0

Conclusions

• Shocks and wakes are produced by intense laser or particle beams in plasmas

• Strong electric fields are associated with these shocks and wakes.

• Wakes typically propagate at c and are useful for accelerating electrons to very high energies

• Collisionless shocks are detached from the disturbance that initially pushes and heats the plasma.

• Such shocks propagate at supersonic speeds and can accelerate ions to high energies.

ACKNOWLEDGEMENTS

• All my collaborators at LLNL including B.Pollock, J.Ralph, A. Pak, F. Albert, S. Glenzer, D.Froula (U. Rochester)

• C.Clayton, K. Marsh, D. Haberberger, S. Tochitsky, C.Gong

• F.Fiuza, L. Silva, W.Mori• All my collaborators on E167 experiment at

SLAC• And anyone I may have inadvertently missed.

Collisionless Shocks formed whenShock Thickness << Collisional mfp(s)

Pressure

Direction of Propagation

UpstreamDownstream

≈ few λD

Energy Dissipation through reflection of upstream ions

Gaining Kinetic Energy by Riding a Wave

Laird Hamilton:Hydrofoil Surfing in Hawaii