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Energetic ions from next generation
ultraintense ultrashort lasers:
scaling laws for TNSA
Matteo Passoni1,2,3,
Maurizio Lontano3, Luca Bertagna1, Alessandro Zani1
1 Dipartimento
di Energia, Politecnico di Milano
2 Istituto Nazionale di Fisica Nucleare (INFN) Milano
3 Istituto di Fisica del Plasma, CNR, Milano
2
Outline
- Introduction
• laser-driven ion acceleration physics
• TNSA mechanism
- Analytical models to describe TNSA
• plasma expansion vs particle acceleration in quasi-static field
- A 1D quasi-static analytical model based on “bound electrons”
• Comparisons with experimental results
• Predictions for future applications
- Conclusions
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Laser-driven ion acceleration
in solids targets
3
If an ultraintense and ultrashort laser pulse
hits the surface of a thin solid film, intense and
energetic (Multi-MeV) ion beams are effectively produced
The accelerated ions possess unique properties!
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Ion acceleration mechanism(s!):
general remarks
4
SOME CRUCIAL ISSUES:
solid
target
pre-plasma
(underdense)
1: laser pulse-front surface interaction
- generation of relativistic e- population
- role of pulse properties
Light ion
layer
(intensity, energy, prepulse, polarization)
- role of target properties
(density, profile, thickness, mass)
2: electron propagation in the target
- role of electron properties
relativistic ecurrent
Laser
pulse
return current
1
2
3
(max. energy, spectrum, temperature)
- role of target properties
- return current
main
pulse
3: effective charge separation
- generation of intense electric fields
- resulting ion acceleration
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
front
surface
pre-pulse
rear
surface
Ion acceleration mechanism(s!):
TNSA – RPA
5
IF THE e- POPULATION IS DOMINATED BY A THERMAL SPECTRUM…
(quite “natural” experimentally…)
…accelerating field due to strong charge separation
between hot electrons expanding in vacuum and the bulk target
Target Normal Sheath Acceleration mechanism
(TNSA)
IF THE THERMAL e- POPULATION IS “SUPPRESSED”…
(is it “feasible” experimentally…?)
…accelerating field due charge separation
induced by the balance between radiation pressure and electrostatic force
Radiation Pressure Acceleration mechanism
(RPA)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Ion acceleration mechanism(s!):
how to control their properties?
6
Various possibilities can be explored:
- Laser pulse
• different combinations of pulse energy, intensity, duration
• linear polarization to have a thermal component (TNSA)
• circular polarization + normal incidence to suppress it (RPA)
- Target
• ultrathin targets (with ultrahigh contrast!) can be used:
• “enhanced TNSA” (“hotter” electrons)
• “light sail” RPA (vs “hole boring” RPA with thick targets)
• “partially trasmitted pulse” regimes
• target density and structure can influence the process
• multilayers (control of the ion spectrum and species)
• mass limited (control of the accelerating field)
• nanostructured (e.g. to change the density parameter)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
TNSA: still a number of open issues!
7
- which are the most effective laser absorption process at
the target front surface? Dependence on pulse properties??
- role of pre-pulse/pre-plasma?
- differences between front and rear acceleration?
- role of target properties (thickness, density, structure…)?
How to describe the acceleration process theoretically?
- realization of suitable numerical simulations (Vlasov, PIC)
- development of analytical models
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Theoretical description of TNSA
8
How to develop analytical models
of the acceleration process in TNSA?
…generally speaking, two approaches are possible:
1) consider ions and hot electrons as an expanding plasma
described with fluid models
2) describe in detail the accelerating field as a
quasi-static electric field set up by the hot electrons
This is the approach of the present work!
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Hydrodynamic models for TNSA
9
These models (most popular from P. Mora)
have been found very useful and are widely
adopted to interpret experimental data.
[P. Mora, Phys. Rev. Lett. 90, 185002 (2003)
J. Fuchs, et al., Nature Phys. 2, 48 (2006)]
Limits of this kind of description:
- accelerated ions are a thin layer rather than a semi-infinite plasma
- empirical acceleration time t  1.3 pulse can be unphysical in
several regimes:
- too short for very short pulses (tens fs),
- too long for the most energetic part of the spectrum with long pulses (few ps)
- divergent maximum ion energy (see below!!)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Quasi-static theoretical models
for TNSA
10
The following physical picture can be assumed:
- hot electrons create a non-neutral region, source of an electric field
- light ions form a thin layer, the main target is made of heavier ions
- during the characteristic acceleration time of the light ions
hot electrons almost isothermal (cooling important at longer times),
heavier ions almost immobile
- until the number of accelerated light ions is much lower than the
number of hot electrons, the field is not heavly affected
the accelerating field can be assumed as quasy-static,
light ions treated as test particles
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Hot electrons description:
Boltzmann distribution/ infinite space
11
…i.e.: on the problem of maximum ion energy
Ni
N e  N 0e
e / Te
x
ne  0 as x  
   as x  
regardless the dimensionality, final ion energy diverges !!!
- isothermal models: introduce “truncation mechanisms”
Y. Kishimoto, et al., Phys. Fluids 26, 2308 (1983)
M.Passoni, M.Lontano, Laser Part. Beams 22, 171 (2004)
M. Lontano, M. Passoni, Phys.Plasmas, 13,042102 (2006)
M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Role of “bound” electrons – 1
12
How to build a more self-consistent description??
Kinetic approach
- consider the electron distribution function
f e  f e r, p, Te ,  
Ni
e-
 (x)
 r, p   mc2  e r 
only “trapped” ((r,p) < 0) e- are bound
from the potential to the target;
“passing” e- ((r,p) > 0) leave the system
x
e-
Y. Kishimoto, et al.,
Phys. Fluids 26, 2308 (1983)
lost at ∞
tot(x)
COULOMB 09, Senigallia, 16.06.2009
“E.S. field distribution at the sharp interface
between high density matter and vacuum”
M. Lontano, M. Passoni, Phys.Plasmas, 13, 042102 (2006)
Matteo Passoni
Role of “bound” electrons – 2
13
Any experimental evidence of “passing” vs “bound” electrons?
“Dynamic Control of Laser-Produced Proton Beams”
S. Kar et al., Phys. Rev, Lett., 100, 105004 (2008)
“… A small fraction of the hot
electron population escapes and
rapidly charges the target to a potential
of the order of Up preventing the bulk of
the hot electrons from escaping. …”
“… All targets were mounted on 3 mm
thick and 2 cm long plastic stalks in
order to provide a highly resistive
path to the current flowing from the
target to ground. …”
see also M. Borghesi’s talk!!
and K. Quinn et al. PRL (2009)
…then, in usual conditions
a globally neutral target with only “bound” electrons develops
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1D 1T trapped electron model – 1
14
  x , p  
n~
 

f e x , p  
exp
2
Te 
 mc 


2mcK1 

 T 
only the density of “trapped” e- enters
Poisson eq.; integrating over  < 0 we
get the trapped e- density ntr((r))
ntr r   
 r ,p 0
2  Ntr  

f e r ,p d 3 p
n
e
, N tr  ~tr
Te
n
 r ,p  0  p  pmaxr 
 x , p   mc2   1  e x   0
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
2

e

2e 


2
2
2 2
p  pm ax  m c  2   2 
 mc  mc 
1D 1T trapped electron model – 2
implicit analytical solution
15
Spatial extention of the electron cloud
 = x/D
(D from n~ )
0     0
[L. Bertagna, Master thesis, (2009)
Politecnico di Milano ]
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1D 1T trapped electron model – 3
16
[L. Romagnani, et al., P.R.L. 95, 195001 (2005)
M. Borghesi, et al., Fus. Sc. & Techn. 49, 412 (2005)]
proton imaging of rear field
LULI
interaction CPA1
I ≈ 3.51018 W/cm2
 ≈ 1.5 ps
1 - 40 m, Al, Au bent foils
experimental data best reproduced
by PIC simulations assuming a field
which becomes zero at a finite distance
h ≈ 20 m from the rear surface
t (ps)
Te ≈ 500 keV
int ≈ 6-7 MeV
E ≈ 3 1010 V/m
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1D 1T trapped electron model – 4
17
- determination of f from the knowledge of 0
- 0 related to the hot electron parameters inside the target
as far as the front side (- w = - w/D <  < 0)
- ions and cold electrons form provide a positively charged
background density ZNi - Ncold = NL
laser
0
*
in(x)
(x)
Thot
-w
0
xf
   e    0   *   e,max
max value of the
potential inside the target
COULOMB 09, Senigallia, 16.06.2009
=
Matteo Passoni
max value of
trapped electron energy
x
1D 1T trapped electron model – 5
18
Analytical solution in the ultra-relativistic limit
(appropriate near and inside the target for typical parameters)
 c p  e x  
c
UR
~

f e x, p   n
exp  

2Te
Te


p mc  1
0

 * 1e*  1


 Z 0Thot
i
max
e
*
ni  i  

1
 
0  0 

 e 
p 2  pm2 ax   2 
c 
“Theory of Light-Ion Acceleration
Driven by a Strong Charge Separation”
M. Passoni, M. Lontano,
Phys. Rev. Lett., 101, 115001 (2008)
maximum ion energy
H  i  0   H  i  0   
    
2Z exp     1
 Z Z 
COULOMB 09, Senigallia, 16.06.2009
12
Matteo Passoni
2
ion energy spectrum
1D 1T trapped electron model – 6
19
The maximum electron energy e,max = *
as a scaling law
How to obtain e,max = * ?
Difficult both theoretically and experimentally…
- Make use of proper numerical simulations of laser-target interaction
- From the analysis of several published results
(starting with observed proton energies and using the model to infer * )
we get the fitting (valid for the “ordinary” TNSA regime…)
 e,max 
K e,max
Te
 A  B ln EL J    *
A=4.8, B=0.8, where EL is the laser energy
i
 max
 Z0 ( * )Thot ( I )  f ( Z , EL , I )
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Pulse energy – intensity plane:
present day experiments
[23]
[1]
[24]
[25]
[27]
[27]
[26]
[28]
[30]
[29]
…agreement within 10 %
M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
20
Dependence on intensity:
present day experiments
21
[ From M. Borghesi et al.,
Plasma Phys. Contr. Fus. 50, 024140 (2008)]
There is a combined variation
of pulse energy & intensity!
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1T trapped electron model
Comparison with experimental data
22
Experimental data from T. Ceccotti, Ph. Martin (CEA Saclay):
fixed pulse duration (25 fs) and focal spot with UHC: BWD TNSA!
BWD H+
[M. Passoni et al.,
AIP Conf. Proc. (in press)]
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Experiments with reduced
wavelength and different spot size
23
Wavelength: 528 nm (2w)
Pulse width: 400 fs
Max intensity (I2):
~4.8*1018 Wcm-2m²
Temporal contrast: >1010
1/5 spot
3m
Spot size (FWHM)
~ 4.4m
COULOMB 09, Senigallia, 16.06.2009
3m
Spot size (FWHM)
~ 0.9m
Matteo Passoni
From J. Fuchs
presentation at ULIS ’09
(2 weeks ago),
and here yesterday!
Experiments with reduced
wavelength and different spot size
[MeV]
energy
maximum
Proton
Proton
maximum
energy
[MeV]
12
24
Need only ~ 1/10 energy to
accelerate the protons.
EPM
10
∝ILaser
8
6
5.5 MeV protons
Direct
4
Au 2m thick
Al 2m thick
Al 0.5m thick
2
0
0
Only 0.8 J
2
4
6
8
Energy on~target
[J]
7J
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
10
12
From J. Fuchs
presentation
Experiments with reduced
wavelength and different spot size
25
Preliminary theoretical interpretation
of these experiments…
- General trend well reproduced
- Underling physics seems
to be nicely captured
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1T trapped electron model
Comparison with experimental data
Quasi-monoenergetic MeV carbon beams
- our model
26
[B. M. Hegelich et al.,
Nature 439, 441 (2006)]
EL  20 J
I L  1019 W cm2
wt  20 μm
 L  0.8 ps
C5+ ions
estimated layer
thickness: < 5 nm
Use of Ultrahigh-Contrast Laser Pulses and thin targets
- our model
electron energy
distribution (PIC)
[T. Ceccotti et al,
Phys. Rev. Lett.
99, 185002 (2007)]
EL  0.65 J
I L  5 1018 W cm 2
contrast  1010
wt  0.4 μm
 L  0.065 ps
No fitting parameters
used!
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
TNSA:
dependence on laser parameters
27
Pulses with fixed duration (25 fs) and focal spot:
prediction of max. ion energy vs. intensity
In these conditions,
combined variation
of pulse energy & intensity
Effective dependence
on intensity changes
with the “decades”
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Pulse energy – intensity plane:
TNSA beyond 1021 W/cm2: ?
28
Example :
100 MeV protons with
Ti:Sa (=800 nm);
I = 4x1021 W/cm2;
EL = 5 J
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Predictions for applications:
hadrontherapy with TNSA?
29
Possible path to reach 250 MeV
protons and 10 nA current with
“usual” TNSA:
Ti:Sa (=800 nm);
I = 1x1022 W/cm2;
EL = 50 J;  = 15 fs (focal=4 µm)
(3 PW system);
Rep. rate 5 Hz
(with 1010 protons/pulse in the
selected energy interval)
…these requirements could be even less demanding
if “improved” schemes of TNSA
can be adopted at these laser parameters
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Conclusions
30
- Quasi-static models give simple expressions for
the TNSA maximum ion energy and for the energy spectrum
others exist…
B.J. Albright, et al., Phys. Rev. Lett. 97, 115002 (2006)
J. Schreiber, et al. Phys. Rev. Lett. 97, 045005 (2006)
M. Nishiuchi, et al., Phys. Lett. A 357, 339 (2006)
A.P. Robinson, et al., Phys. Rev. Lett. 96, 035005 (2006)
- hold for short time (in this sense, complementary to fluid models)
- A 1D quasi-static model of TNSA has been developed:
• experimental results in good agreement with the expectations
• predictions for future applications are easily feasible
- Further improvements in several directions are possible:
magnetic fields, max e- energy, 2T, 3D, space charge effects, expanding target..
Work in progress…
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
31
THANK YOU FOR YOUR ATTENTION!
And thanks to the co-workers!
Maurizio Lontano, Luca Bertagna, Alessandro Zani
for more details…
[email protected]
www.nanolab.polimi.it
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Experimental Results (Fuchs J.)
32
In following tables there are predictions using (1) nominal pulse energy in φ* scaling
lawCOULOMB
or (2) effective
pulse
energy:
09, Senigallia,
16.06.2009
Matteo Passoni
Comparison between experimental point and UR model predictions
(1)
33
Experiment
al point
I
[1020
W/cm2]
EL
[J]
Iλ2
[I/10 m2]
fS
[m]
Emax,TEO
[MeV]
Emax,EXP
[MeV]
1
2.50
2.45
6.85
0.9 (T.F.)
14.23
10.5
2
1.75
1.72
4.8
0.9 (T.F.)
10.9
9.5
3
3.25
3.2
8.9
0.9 (T.F.)
17.25
9.5
4
1.75
1.72
4.8
0.9 (T.F.)
10.9
9
5
0.8
0.8
2.2
0.9 (T.F.)
5.8
5.7
6
0.8
0.8
2.2
0.9 (T.F.)
5.8
5.9
7
0.8
0.8
2.2
0.9 (T.F.)
5.8
5.2
8
2.5
0.1
0.3
4.4 (Direct)
1.75
2
9
4.8
0.2
0.5
4.4 (Direct)
3.2
4
10
5.5
0.23
0.63
4.4 (Direct)
3.6
2
11
9
0.37
1
4.4 (Direct)
5.4
7
12
8.5
0.35
0.9
4.4 (Direct)
5.1
6
13
9.5
0.4
1
4.4 (Direct)
5.7
10
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Comparison between experimental point and UR model predictions
(2)
34
Experimenta
l point
I
[1020
W/cm2]
EL
[J]
Iλ2
[I/10 m2]
fS
[m]
Emax,TEO
[MeV]
Emax,EXP
[MeV]
1
2.50
2.45
6.85
0.9 (T.F.)
10.9
10.5
2
1.75
1.72
4.8
0.9 (T.F.)
8.15
9.5
3
3.25
3.2
8.9
0.9 (T.F.)
13.34
9.5
4
1.75
1.72
4.8
0.9 (T.F.)
8.15
9
5
0.8
0.8
2.2
0.9 (T.F.)
4.2
5.7
6
0.8
0.8
2.2
0.9 (T.F.)
4.2
5.9
7
0.8
0.8
2.2
0.9 (T.F.)
4.2
5.2
8
2.5
0.1
0.3
4.4 (Direct)
1.3
2
9
4.8
0.2
0.5
4.4 (Direct)
2.5
4
10
5.5
0.23
0.63
4.4 (Direct)
2.8
2
11
9
0.37
1
4.4 (Direct)
4.4
7
12
8.5
0.35
0.9
4.4 (Direct)
4.2
6
13
9.5
0.4
1
4.4 (Direct)
4.6
10
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
35pulse energy)
Expected results from UR model (scaling law for φ* with NOMINAL
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Comparison theoretical vs. experimental results (scaling law for φ* 36
with NOMINAL pulse
energy)
2.3
COULOMB 09, Senigallia, 16.06.2009
6.9
Matteo Passoni
11
37
Expected results from UR model (scaling law for φ* with EFFECTIVE
pulse energy)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Comparison theoretical vs. experimental results (scaling law for φ* with EFFECTIVE
38
pulse energy)
2.3
COULOMB 09, Senigallia, 16.06.2009
6.9
Matteo Passoni
11
From Ph. Martin’s talk….
39
Linear scaling law
Next decade ?
Max proton Energy (MeV)
BWD H+
7
6
5
4
3
2
1
0
Wanna get 100 MeV ?
Just build up a 1PW laser (but clean !)
theory
0
5 10 15 20 25 30 35
Laser Power (TW)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1T trapped electron model – 7
Comparison with experimental data
40
Proton spectra with different laser parameters
D  2 R  f L  wt tan 
- model
R=14m
R=0,7m
R=0,7m
R=14m
0,05m
0,05m
n  3 x10 cm 3
22
n  1,5 x10 22 cm 3
0,05m
0,05m
n  1,5 x10 22 cm 3
n  3 x10 22 cm 3
[R.A. Snavely, et al.,
Phys. Rev. Lett., 85, 2945 (2000)]
[M. Nishiuchi, et al.,
Phys. Lett. A, 357, 339 (2006)]
EL  500 J
EL  0.25 J
I L  3 1020 W cm 2
I L  3 1018 W cm 2
wt  100 μm
wt  3 μm
 L  0.5 ps
 L  70 fs
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Other quasi-static models…
41
“Theory of Laser Acceleration of Light-Ion Beams
from Interaction of Ultrahigh-Intensity Lasers with Layered Targets ”
B.J. Albright, et al., Phys. Rev. Lett. 97, 115002 (2006)
- extention of the 2T model to describe layered targets
“Analytical Model for Ion Acceleration by High-Intensity Laser Pulses “
J. Schreiber, et al. Phys. Rev. Lett. 97, 045005 (2006)
- surface charge model exploiting radial symmetry for the electric field
“The laser proton acceleration in the strong charge separation regime ”
M. Nishiuchi, et al., Phys. Lett. A 357, 339 (2006)
- approach analogous to the 1T model to interpret experiments
“ Effect of Target Composition on Proton Energy Spectra in
Ultraintense Laser-Solid Interactions “
A.P. Robinson, et al., Phys. Rev. Lett. 96, 035005 (2006)
- study of the effects of a non negligible proton density in the target
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Further theoretical references…
42
…not exaustive list…
“Ion acceleration in expanding multi-species plasmas”
V. Yu. Bychenkov et al., Phys. Plasmas, 11, 3242 (2004)
“Ion acceleration in short-laser-pulse interaction with solid foils “
V. T. Tikhonchuk, et al., Plasma Phys. Controlled Fusion 47, B869 2005.
“Collisionless expansion of a Gaussian plasma into a vacuum”
P. Mora, Phys. Plasmas 12, 112102 (2005)
“Thin-foil expansion into a vacuum”
P. Mora, Phys. Rev. E 72, 056401 (2005)
“Test ion acceleration in a dynamic planar electron sheath ”
M.M. Basko, Eur. Phys. J. D, 41, 641 (2007)
“Nanocluster explosions and quasimonoenergetic spectra by homogeneously
distributed impurity ions”
M. Murakami & M. Tanaka, Phys. Plasmas 15, 082702 (2008)
V. F. Kovalev, et al., JETP, 95, 226 (2002)
S. Betti, et al., Pl. Phys. Contr. Fus. 47, 521 (2005)
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
Arguments for discussion
43
The field of laser-based ion acceleration
is extraordinary active…some examples:
- elimination of the pre-pulse to allow:
- efficient TNSA front acceleration
- more efficient electron heating
- use of ultrathin targets (promising to increase ion properties)
- production and control of a “true ion beam”
- Achievement of monoenergetic collimated low-emittance ion beams
- investigation of new accelation schemes
(e.g. Radiation Pressure Acceleration, RPA, other kinds of targets)
- construction of satisfactory theoretical descriptions of these issues
- development of the possible applications
COULOMB 09, Senigallia, 16.06.2009
Matteo Passoni
1T trapped electron model – 7
Comparison with experimental data
44
Proton spectra with different laser parameters
D  2 R  f L  wt tan 
- model
R=14m
R=8m
R=0,7m
R=8m
R=14m
0,05m
0,05m
n  3 x10 cm 3
0,05m
22
n  1,5 x10 cm
22
3
0,05m
0,05m
n  1,5 x10 22 cm 3
n  3 x10 22 cm 3
[R.A. Snavely, et al.,
Phys. Rev. Lett., 85, 2945 (2000)]
neest,L  4.4 10 21 cm 3
EL  500 J
I L  3 10
20
wt  100 μm
 L  0.5 ps
W cm
2
Te  7 MeV
K e ,m ax  61 MeV
Eim,meaax
 58 MeV
Eim,modax
 58.4 MeV
[P. McKenna, et al.,
Phys. Rev. E, 70, 036405 (2004)]
neest,L  3.6 10 21 cm 3
EL  400 J
I L  2 10 W cm
20
2
wt  100 μm
 L  0.7 ps
Te  5.7 MeV
K e ,m ax  46.7 MeV
Eim,meaax
 44 MeV
Eim,modax
 45.9 MeV
M. Passoni, M. Lontano, Phys. Rev, Lett., 101, 115001 (2008)
COULOMB 09, Senigallia, 16.06.2009
n  1,5 x10 22 cm 3
Matteo Passoni
[M. Nishiuchi, et al.,
Phys. Lett. A, 357, 339 (2006)]
EL  0.25 J
Te  0.26 MeV
K e ,m2 ax  1 MeV
I L  3 10 W cm
18
wt  3 μm
 L  70 fs
Eim,meaax  0.88 MeV
Eim,modax  0.92 MeV