Radiation Pressure Acceleration of Ions and the Role of

Radiation Pressure Acceleration ofIons and the Role of

Hydrodynamical BreakingAndrea Macchi

www.df.unipi.it/∼macchi

polyLAB, CNR-INFM, University of Pisa and INFN, Italy

PHELIX Theory Workshop, Darmstadt, October 15, 2007

A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.1/26

Coworkers


Coworkers

Alessandra Bigongiari, Francesco Ceccherini,Fulvio Cornolti,Tatiana V. Liseikina1,Domenico Prellino

Department of Physics, University of Pisa, Italy


Coworkers


Department of Physics, University of Pisa, Italy1On leave from Institute for ComputationalTechnologies, Novosibirsk, Russia


Coworkers


Department of Physics, University of Pisa, Italy1On leave from Institute for ComputationalTechnologies, Novosibirsk, Russia

Marco Borghesi and Satyabrata KarIRCEP and School of Mathematics and Physics,Queen’s University of Belfast, UK


OutlookWe consider two cases of ion acceleration driven by thesteady ponderomotive force (i.e. by radiation pressure):

1. Radial acceleration after self-channeling in underdenseplasma (ωp < ω)S. Kar, M. Borghesi, C. Cecchetti, F. Ceccherini, T. V. Liseikina, A. Macchi et al,arXiv:physics/0701332, New J. Phys. (in press)A.Macchi, F.Ceccherini, F.Cornolti, S.Kar, M.Borghesi, arXiv:physics/0701139

2. Longitudinal acceleration by circularly polarized pulsesin overdense plasma (ωp < ω)A. Macchi, F. Cattani, T. V. Liseikina, F. Cornolti, Phys. Rev. Lett. 94, 165003 (2005);T. V. Liseikina and A. Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).

We emphasize similiarities in the physical mechanismsof ion acceleration, in particular the role ofhydrodynamical “breaking” in the ion fluid.

















PART 1: RADIAL IONACCELERATION AFTER

SELF-CHANNELING IN ANUNDERDENSE PLASMA


Channeling in underdense plasma


Channeling in underdense plasmaThe interaction of a 1 ps, 1018

÷ 1019 W/cm2 pulse witha gas jet has been investigated at RAL using the protonimaging technique

3 mmOptical probe

CPA2

CPA1

Gas Jet

3 cm

(a)

Multilayer RCF stack

(d)

Proton probe

(b)ne

(1021

/cc)

(b)

S.Kar et al, NJP, in press [arxiv:physics/0701332]




Experimental data showthat a charge-displacementchannel is produced by thelaser pulse





Experimental data showthat a charge-displacementchannel is produced by thelaser pulseIn the trail of the channel areversal of the radial field isinferred



Simulations of the experiment


Simulations of the experimentParticle-in-Cell (PIC) simulations in 2D cartesian geometry



Laser amplitude aL = 1.7÷ 2.7duration τL = 150÷ 300TL (TL = λ/c)⇒ I = 1018

÷ 1019 W/cm2,τL = 0.5÷ 1 ps for λ = 1 µm.S-polarization (Ez)





Inhomogenous plasmaPeak density ne = 0.1nc

Size S = 500 λScalelength L = 400 λ





Inhomogenous plasmaPeak density ne = 0.1nc

Size S = 500 λScalelength L = 400 λ

� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � �

yx

x

0.1n c

pulselaser plasma

L S0


Self-channeling and radial field evolution


Self-channeling and radial field evolution2D PIC simulations show that the laser pulse drills a regularcharge-displacement channel in the low-density region





The profile of the“radial” space-chargefield (Ey) changes inthe trailing part of thepulse where fieldreversal occurs

S.Kar et al., NJP, in press [arXiv:physics/0702177]


Ponderomotive electrostatic 1D model

- 1D electrostatic PIC simulation, cylindrical geometry- Laser pulse action is included via the radial

ponderomotive force on electrons (as an “external”driver)

Fp = −mec2∇

√

1 + a2(r, t)/2

a2(r, t) = a2Le−(r/r0)

2−(t/τ)2

- Model equationsdpe

dt = −eEr + Fp,dpi

dt = ZeEr1r

∂∂r (rEr) = 4πρ = e(Zni − ne).

[A. Macchi et al, arXiv:physics/0701139]



- 1D electrostatic PIC simulation, cylindrical geometry

- Laser pulse action is included via the radialponderomotive force on electrons (as an “external”driver)

Fp = −mec2∇

√

1 + a2(r, t)/2

a2(r, t) = a2Le−(r/r0)

2−(t/τ)2



dt = ZeEr1r







Fp = −mec2∇

√

1 + a2(r, t)/2

a2(r, t) = a2Le−(r/r0)

2−(t/τ)2



dt = ZeEr1r







Fp = −mec2∇

√

1 + a2(r, t)/2

a2(r, t) = a2Le−(r/r0)

2−(t/τ)2



dt = ZeEr1r







Fp = −mec2∇

√

1 + a2(r, t)/2

a2(r, t) = a2Le−(r/r0)

2−(t/τ)2



dt = ZeEr1r




Comparison with experimental results



The simple 1Dmodel has beenintegrated with aparticle tracing code(developed by A.Schiavi) to simulatethe proton projectionimages: very goodagreement is found







The model reproduces fairly experimental and numericalresults of radial ion acceleration in similar conditions[see e.g. Sarkisov et al, JETP 66, 828 (1997);Krushelnick et al, PRL 83, 737 (1999);Fritzler et al, PRL 89, 165004 (2002).]


Echo effect in the radial field


Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ



During the laserpulse the space-charge field Er

created by electrondepletion in thechannel exactlybalances the PMforce Fp



























After the laser pulseEr has almostvanished



After the laser pulseEr has almostvanished



Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions














Echo effect is due to “breaking”


Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones





















At breaking, strongelectron heatingoccurs

An ambipolarelectric field isgenerated aroundthe density spike


















Breaking time and place



Ions are accelerated byZeEr ' ZFr.For r > rmax ' r0,dFr/dr < 0 ⇒ ions tend topile up at the edge of thepulse profile

A. Macchi et al, arXiv:physics/0701139



If Fr was a linear function,all ions would get to asame point rb at the sametime tb.

ZFr ' −k(r − rb)




If Fr was a linear function,all ions would get to asame point rb at the sametime tb.

ZFr ' −k(r − rb)

By performing a linear approximation of Fr we obtain

rb = (3/2)3/2r0 tb =π

2

√

k

mi=

π

2e3/4

√

A

Z

mp

me

r0

a0c



Electric field generation after breaking


Electric field generation after breaking

A “hot” electron tail is gen-erated near the breakingpointThot ' 12.8 keV ' 6Tcold



Electric field generation after breakingHot electrons (density nh)generate an antisymmet-rical sheath field (exten-sion `s, peak field Es)around the density spike(thickness d)

Es = 2πenhd `s =8λ2

Dd



Electric field generation after breakingHot electrons (density nh)generate an antisymmet-rical sheath field (exten-sion `s, peak field Es)around the density spike(thickness d)

Es = 2πenhd `s =8λ2

Dd

Hot electron generation might be ascribed to non-adiabatic electron oscillations across the sharp densitygradient or to local two-stream-like instabilities



Ion dynamics after breaking


Ion dynamics after breaking


Ion dynamics after breakingAfter breaking theion spectrum “splits”:only faster ions areinjected outside thechannel







Low-energy ions are“reflected” from theinward field and re-turn towards the axis







A thin filament of plasma is generated on the axis at latetimesExperimental indication: see M. Borghesi et al, PRL 78, 879 (1997)




A thin filament of plasma is generated on the axis at latetimesExperimental indication: see M. Borghesi et al, PRL 78, 879 (1997)


Conclusions of Part 1

A “minimal” 1D electrostatic, ponderomotive, kineticmodel has been used to interpretate experimentalresults in the charge-displacement self-channelingregime of laser propagation in underdense plasmasSimulations gave an insight into ion dynamics andelectric field generationHydrodynamical breaking of the ion fluid leads tonon-trivial effects (electric field “echo”, ion reflection . . . )



A “minimal” 1D electrostatic, ponderomotive, kineticmodel has been used to interpretate experimentalresults in the charge-displacement self-channelingregime of laser propagation in underdense plasmas

Simulations gave an insight into ion dynamics andelectric field generationHydrodynamical breaking of the ion fluid leads tonon-trivial effects (electric field “echo”, ion reflection . . . )



A “minimal” 1D electrostatic, ponderomotive, kineticmodel has been used to interpretate experimentalresults in the charge-displacement self-channelingregime of laser propagation in underdense plasmasSimulations gave an insight into ion dynamics andelectric field generation

Hydrodynamical breaking of the ion fluid leads tonon-trivial effects (electric field “echo”, ion reflection . . . )



A “minimal” 1D electrostatic, ponderomotive, kineticmodel has been used to interpretate experimentalresults in the charge-displacement self-channelingregime of laser propagation in underdense plasmasSimulations gave an insight into ion dynamics andelectric field generationHydrodynamical breaking of the ion fluid leads tonon-trivial effects (electric field “echo”, ion reflection . . . )


PART 2: LONGITUDINAL IONACCELERATION BY CIRCULARLYPOLARIZED LASER PULSES IN

AN OVERDENSE PLASMA


1D simulation example of ion acceleration


1D simulation example of ion acceleration1D PIC simulation, 26 cycles pulse, normal incidence,linear polarization, a = 16.0, ne0/nc = 10.(λ = 1µm → I = 3.5× 1020 W/cm2, τL = 86 fs,ne = 1022 cm−3.)

laser



laser



laser



laser



laser



laser



laser



laser

Three groups of MeV ions:two from “sheath” acceler-ation (from front and rearsides), one from the front –“shock” acceleration?[Silva et al, PRL 95, 195002 (2004)]



laser

Three groups of MeV ions:two from “sheath” acceler-ation (from front and rearsides), one from the front –“shock” acceleration?[Silva et al, PRL 95, 195002 (2004)]

Electrons are heated up toseveral tens of MeV


Switch fast electrons offFast electron generation at a steeplaser-plasma interface requires anoscillating force across the boundary.

For normal incidence, it is the 2ωL

component of the v ×B force.For circular polarization, the 2ωL

component vanishes; only thesecular (0ωL) component remains

⇒ The laser plasma interaction isdominated by radiation pressure(rather than by fast electron genera-tion and related effects)


Switch fast electrons off

Fast electron generation at a steeplaser-plasma interface requires anoscillating force across the boundary.For normal incidence, it is the 2ωL

component of the v ×B force.

For circular polarization, the 2ωL









0ω

2ω







0ω

2ω


Circular polarization


Circular polarization1D PIC simulation, circular polarizationa = 11.3 ⇒ same energy of the linear polarization case;other parameters are the same

T. V. Liseikina and A. Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).





















Only one group of MeV ionsaccelerated at the front side




Only one group of MeV ionsaccelerated at the front side

Electron energy isbelow 1 MeV;almost no “fast” electrons!



Absorption efficiency: circular vs linear



Ion acceleration with circularpolarization promises high ef-ficiency: 13.7% absorption forthe simulation shown.Absorption into electrons isnegligible

T. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).



Ion acceleration with circularpolarization promises high ef-ficiency: 13.7% absorption forthe simulation shown.Absorption into electrons isnegligible




Ion acceleration with circularpolarization promises high ef-ficiency: 13.7% absorption forthe simulation shown.Absorption into electrons isnegligibleThe simulation for same en-ergy, linear polarization showscomparable absorption, butreached later, dependent ontarget thickness, and intoseveral ion populationsT. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).



Ion acceleration with circularpolarization promises high ef-ficiency: 13.7% absorption forthe simulation shown.Absorption into electrons isnegligibleThe simulation for same en-ergy, linear polarization showscomparable absorption, butreached later, dependent ontarget thickness, and intoseveral ion populationsT. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).


Energy spectrum: circular vs linear


Energy spectrum: circular vs linearLinear polarization: higherpeak energies, but a thermal-like spectrum already in 1D.



Energy spectrum: circular vs linearLinear polarization: higherpeak energies, but a thermal-like spectrum already in 1D.Circular polarization: lowerpeak energies, but a peaked,highly non-thermal spectrum.




2D simulationsconfirm 1D resultsan show energy-dependent angularspread with lowdivergenceT. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).



2D simulationsconfirm 1D resultsan show energy-dependent angularspread with lowdivergenceT. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).


Ion bunch acceleration


Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5













Electrostatic field Ex

accelerates ions




accelerates ions




accelerates ionsDensity spiking and breakingof the ion fluid




accelerates ionsDensity spiking and breakingof the ion fluidProduction of a single ionbunch with narrow energyspectrum









Highly reminiscent of the ra-dial dynamics in theunderdense plasma case!


(Another) simple model

- We take simple profiles . . .. . . which crudely approximate“realistic” ones

- ion profile is compressed- “breaking” at the time when

all ions reach theevanescence point


(Another) simple modelAssumption: quasi-equilibrium between electrostatic fieldand ponderomotive force (both Lagrangian constants).Ions are accelerated by the electrostatic field until breaking.






- We take simple profiles . . .

. . . which crudely approximate“realistic” ones











- ion profile is compressed

- “breaking” at the time whenall ions reach theevanescence point







Model predictions

Input parameters d, E0, np0 are related by the Poissonequation and the constraints of charge conservationand total radiation pressure Prad ' 2IL/c:E0 = 4πen0d , n0(d+ ls) = np0ls ,

12eE0np0ls '

2cIL

Equations of motion are easily solved to yield maximumion velocity and breaking time, assuming ls ' c/ωp:

vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.

The average ion front velocity vf = vm/2 is the “holeboring” speed.Similar predictions, but different physics with respect tothe “shock” acceleration picture


Model predictions

Input parameters d, E0, np0 are related by the Poissonequation and the constraints of charge conservationand total radiation pressure Prad ' 2IL/c:

E0 = 4πen0d , n0(d+ ls) = np0ls ,12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.



Model predictions


12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.



Model predictions


12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.



Model predictions


12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.



Model predictions


12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.

The average ion front velocity vf = vm/2 is the “holeboring” speed.

Similar predictions, but different physics with respect tothe “shock” acceleration picture


Model predictions


12eE0np0ls '

2cIL


vm = 2c√

ZA

me

mp

nc

neaL τi ' TL

12πaL

√

AZ

mp

me.




The use of circular polarization leads to a new regime of“radiation-pressure-dominated” ion accelerationIon acceleration features may be interesting for specificapplications (creation of warm dense matter?)Other recent works suggest that using very thin targetsextremely high energies may be produced(see Zhang et al, Phys. Plasmas 14, 073101 (2007); Robinson et al, arXiv:0708.2050)

Ion acceleration in this regime can be illustrated by asimple model, which accounts for ion “bunch” fomationvia hydrodynamical breaking



The use of circular polarization leads to a new regime of“radiation-pressure-dominated” ion acceleration

Ion acceleration features may be interesting for specificapplications (creation of warm dense matter?)Other recent works suggest that using very thin targetsextremely high energies may be produced(see Zhang et al, Phys. Plasmas 14, 073101 (2007); Robinson et al, arXiv:0708.2050)




The use of circular polarization leads to a new regime of“radiation-pressure-dominated” ion accelerationIon acceleration features may be interesting for specificapplications (creation of warm dense matter?)

Other recent works suggest that using very thin targetsextremely high energies may be produced(see Zhang et al, Phys. Plasmas 14, 073101 (2007); Robinson et al, arXiv:0708.2050)











A general conclusion . . .

During a stay in Darmstadt (end of1999), Prof. Peter Mulser suggestedme to work on a problem of breakingof (electron) plasma waves driven bylaser-plasma interactionsThis work has never been finalized :-(

It was my destiny to eventually re-alize that hydrodynamical breakingis a very basic and important phe-nomenon in laser-plasma interaction,although in a different context



During a stay in Darmstadt (end of1999), Prof. Peter Mulser suggestedme to work on a problem of breakingof (electron) plasma waves driven bylaser-plasma interactions

This work has never been finalized :-(




During a stay in Darmstadt (end of1999), Prof. Peter Mulser suggestedme to work on a problem of breakingof (electron) plasma waves driven bylaser-plasma interactionsThis work has never been finalized :-(




During a stay in Darmstadt (end of1999), Prof. Peter Mulser suggestedme to work on a problem of breakingof (electron) plasma waves driven bylaser-plasma interactionsThis work has never been finalized :-(It was my destiny to eventually re-alize that hydrodynamical breakingis a very basic and important phe-nomenon in laser-plasma interaction,although in a different context



During a stay in Darmstadt (end of1999), Prof. Peter Mulser suggestedme to work on a problem of breakingof (electron) plasma waves driven bylaser-plasma interactionsThis work has never been finalized :-(It was my destiny to eventually re-alize that hydrodynamical breakingis a very basic and important phe-nomenon in laser-plasma interaction,although in a different context


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