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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
Alessandra Bigongiari, Francesco Ceccherini,Fulvio Cornolti,Tatiana V. Liseikina1,Domenico Prellino
Department of Physics, University of Pisa, Italy
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.2/26
Coworkers
Alessandra Bigongiari, Francesco Ceccherini,Fulvio Cornolti,Tatiana V. Liseikina1,Domenico Prellino
Department of Physics, University of Pisa, Italy1On leave from Institute for ComputationalTechnologies, Novosibirsk, Russia
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.2/26
Coworkers
Alessandra Bigongiari, Francesco Ceccherini,Fulvio Cornolti,Tatiana V. Liseikina1,Domenico Prellino
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.2/26
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.
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.3/26
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.
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.3/26
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.
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.3/26
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.
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.3/26
PART 1: RADIAL IONACCELERATION AFTER
SELF-CHANNELING IN ANUNDERDENSE PLASMA
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.4/26
Channeling in underdense plasma
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.5/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.5/26
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
Experimental data showthat a charge-displacementchannel is produced by thelaser pulse
S.Kar et al, NJP, in press [arxiv:physics/0701332]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.5/26
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
Experimental data showthat a charge-displacementchannel is produced by thelaser pulseIn the trail of the channel areversal of the radial field isinferred
S.Kar et al, NJP, in press [arxiv:physics/0701332]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.5/26
Simulations of the experiment
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.6/26
Simulations of the experimentParticle-in-Cell (PIC) simulations in 2D cartesian geometry
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.6/26
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)
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.6/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.6/26
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
� � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � �
yx
x
0.1n c
pulselaser plasma
L S0
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.6/26
Self-channeling and radial field evolution
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.7/26
Self-channeling and radial field evolution2D PIC simulations show that the laser pulse drills a regularcharge-displacement channel in the low-density region
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.7/26
Self-channeling and radial field evolution2D PIC simulations show that the laser pulse drills a regularcharge-displacement channel in the low-density region
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.7/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.7/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.8/26
Ponderomotive electrostatic 1D model
- 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
- Model equationsdpe
dt = −eEr + Fp,dpi
dt = ZeEr1r
∂∂r (rEr) = 4πρ = e(Zni − ne).
[A. Macchi et al, arXiv:physics/0701139]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.8/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.8/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.8/26
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]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.8/26
Comparison with experimental results
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.9/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.9/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.9/26
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).]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.9/26
Echo effect in the radial field
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
After the laser pulseEr has almostvanished
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
After the laser pulseEr has almostvanished
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect in the radial field1D electrostatic PIC simulationaL = 2.7, τL = 300TL, rL = 7.5λ
Er appears back(“echo”) where asharp spike of ni isproduced;the spike then“breaks” producinga fast bunch of ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.10/26
Echo effect is due to “breaking”
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
Echo effect is due to “breaking”Analysis of ion phase space show that hydrodynamicalbreaking occurs when faster ions overlap the slowest ones
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.11/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.12/26
Breaking time and place
If Fr was a linear function,all ions would get to asame point rb at the sametime tb.
ZFr ' −k(r − rb)
A. Macchi et al, arXiv:physics/0701139
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.12/26
Breaking time and place
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
A. Macchi et al, arXiv:physics/0701139
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.12/26
Electric field generation after breaking
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.13/26
Electric field generation after breaking
A “hot” electron tail is gen-erated near the breakingpointThot ' 12.8 keV ' 6Tcold
A. Macchi et al, arXiv:physics/0701139
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.13/26
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
A. Macchi et al, arXiv:physics/0701139
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.13/26
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
A. Macchi et al, arXiv:physics/0701139
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.13/26
Ion dynamics after breaking
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
Ion dynamics after breaking
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
Ion dynamics after breakingAfter breaking theion spectrum “splits”:only faster ions areinjected outside thechannel
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
Ion dynamics after breakingAfter breaking theion spectrum “splits”:only faster ions areinjected outside thechannel
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
Ion dynamics after breakingAfter breaking theion spectrum “splits”:only faster ions areinjected outside thechannel
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.14/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.15/26
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 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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.15/26
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 generation
Hydrodynamical breaking of the ion fluid leads tonon-trivial effects (electric field “echo”, ion reflection . . . )
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.15/26
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. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.15/26
PART 2: LONGITUDINAL IONACCELERATION BY CIRCULARLYPOLARIZED LASER PULSES IN
AN OVERDENSE PLASMA
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.16/26
1D simulation example of ion acceleration
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
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)]
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.17/26
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)
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.18/26
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
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)
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.18/26
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
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)
0ω
2ω
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.18/26
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
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)
0ω
2ω
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.18/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
Circular polarization1D PIC simulation, circular polarizationa = 11.3 ⇒ same energy of the linear polarization case;other parameters are the same
Only one group of MeV ionsaccelerated at the front side
T. V. Liseikina and A. Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
Circular polarization1D PIC simulation, circular polarizationa = 11.3 ⇒ same energy of the linear polarization case;other parameters are the same
Only one group of MeV ionsaccelerated at the front side
Electron energy isbelow 1 MeV;almost no “fast” electrons!
T. V. Liseikina and A. Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.19/26
Absorption efficiency: circular vs linear
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.20/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.20/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.20/26
Absorption efficiency: circular vs linear
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.20/26
Absorption efficiency: circular vs linear
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.20/26
Energy spectrum: circular vs linear
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.21/26
Energy spectrum: circular vs linearLinear polarization: higherpeak energies, but a thermal-like spectrum already in 1D.
T. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.21/26
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.
T. V. Liseikina and A.Macchi, arXiv:0705.4019, Appl. Phys. Lett. (in press).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.21/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.21/26
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).
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.21/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
accelerates ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
accelerates ions
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
accelerates ionsDensity spiking and breakingof the ion fluid
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
accelerates ionsDensity spiking and breakingof the ion fluidProduction of a single ionbunch with narrow energyspectrum
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
accelerates ionsDensity spiking and breakingof the ion fluidProduction of a single ionbunch with narrow energyspectrum
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
Ion bunch accelerationCircular polarization, but weaker (a = 2.0) and shorter(20 fs) pulse now: ne0/nc = 5
Electrostatic field Ex
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!
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.22/26
(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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
(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 when
all ions reach theevanescence point
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
(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 when
all ions reach theevanescence point
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
(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 when
all ions reach theevanescence point
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
(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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
(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 when
all ions reach theevanescence point
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.23/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.24/26
Conclusions of Part 2
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.25/26
Conclusions of Part 2
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)
Ion acceleration in this regime can be illustrated by asimple model, which accounts for ion “bunch” fomationvia hydrodynamical breaking
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.25/26
Conclusions of Part 2
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.25/26
Conclusions of Part 2
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.25/26
Conclusions of Part 2
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.25/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.26/26
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 interactions
This 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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.26/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.26/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.26/26
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
A. Macchi – PHELIX Theory Workshop, Darmstadt, October 15, 2007 – p.26/26