Prediction of Hot Electron Production
by Ultraintense KrF Laser-Plasma Interactions
on Solid-Density Targets
Susumu KATO*, Eiichi TAKAHASHF, Eisuke MIURA*,
Tatsufumi NAKAMURA*, Tomokazu KATOf and Yoshiro OWADANO*
* National Institute of Advanced Industrial Science and Technology (AIST),
Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
^Department of Applied Physics, Waseda University,
3-4-1 Ohkubo, Shinjuku, Tokyo, 169-8555, Japan
Abstract The scaling of hot electron temperature and the spectrum of electron energy by intense
laser plasma interactions are reexamined from a viewpoint of the difference in laser wavelength.
Laser plasma interaction such as parametric instabilities is usually determined by the IX2 scaling,
where / and A is the laser intensity and wavelength, respectively. However, the hot electron temperature is proportional to (ncr/neo)1^ [(14-ao)1/2 -1] rather than [(1 + «o)1/2 -1] at the interaction
with overdense plasmas, where neo is a electron density of overdense plasmas and ao is a normalized
laser intensity.
INTRODUCTION
High energy electron production by an intense ultrashort laser pulse has attracted much
interest for the fast ignitor concept in inertial fusion energy (IFE) [1]. The main requirements of the fast ignitor are hole boring through the coronal plasma, penetration to high density, and generation of high energy particles. The ultra-intense irradiation experiments with infrared subpicosecond laser, e.g., Nd:glass (A = 1053 nm) or
Tirsapphire (A = 800 nm) lasers, the powers and focused intensities of which are exceeding 100 TW and 1020 W/cm2 are possible by chirped pulse amplification (CPA) techniques [2,3]. Namely, the classical normalized momentum of electrons ao = Posc/rac =
(/A 2 /1.37 x 1018)1/2 > i, where m is the electron mass, c is the speed of light, / is the
laser intensity in W/cm2, and AM is the laser wavelength in microns. On the other hand,
KrF laser (A = 248 nm) has the advantage for the fast ignitor concept that the critical
density is close to core and hot electron energies are suitable since the critical density of
KrF laser is ten times greater than one of infrared laser [4]. However, KrF laser irradiance intensities have been only the order of 1018 W/cm2, namely ao < 1 [5, 6]. Several
TW KrF laser [7] will provide irradiances exceeding 1019 W/cm2 by focusing to about
two times diffraction limited spot size using full vacuum propagation system.
The absorption, electron spectrum, and hot electron temperature have been usually
investigated and scaled by the parameters /A2, ne/ncr, and L/A [8, 9], where ne, ncr,
and L are the electron density, critical density, and density scale length, respectively.
CP634, Science of Super strong Field Inter actions, edited by K. Nakajima and M. Deguchi
© 2002 American Institute of Physics 0-7354-0089-X/02/$ 19.00
290
Critical density absorption of the laser light converts laser energy into hot electrons with
a suprathermal temperature Th0t approximately proportional to \//A2 for ao > 1, and
Thot ~ [(1 + ao)1//2 - l]rac2 at moderate density [10], where me2 = 511 keV is a electron
rest mass, Thot = 160 keV, 0.92 MeV, and 3.88 MeV for 1X^ = 1 x 1018, 1 x 1019,
and 1 x 1020 W/cm2//m2, respectively. The scaling of the hot electron temperature is
supported by experiments of Ndrglass and Ti:sapphire lasers [11, 12]. On the other
hand, the results from one dimensional simulation for normal incidence have shown
that T^t ~ f?(^cr/'fteo)Q! [(1 + ao)1^2 — l]^c2 in the density region 10 < neQ/ncr < 100
and the normalized intensity 4 < 0% < 30, where 77 = 1.2 ~ 1.9 and a = 1/2, which
weekly depend on /A 2 and ne/ncr [9], When ao > 1, Th0t oc ^(//neo) 1 , namely the
hot electron temperature is almost independent of the wavelength.
In this paper, the scaling of the hot electron temperature and the electron energy
spectrum are reexamined from a viewpoint of the difference in laser wavelength using a
particle-in-cell (PIC) simulation code. The difference in hot electron spectrum and flux
between KrF laser and Infrared laser is clarified. The results predict the spectrum of
the high energy particle generated in a KrF laser experiment at exceeding 1019 W/cm2
irradiance.
PIC SIMULATION
To investigate hot electron generation for oblique incidence, we use the relativistic 1
and | dimensional PIC simulation with the boost frame moving with csin# parallel
to the target surface, where 0 is an angle of incidence [13, 14]. In the simulation, the
targets are the full ionized plastic (CH) and aluminum, and the electron densities are
neo ~ 3.5 x 1023cm~3 and 8.6 x 1023cm~3, respectively. The densities correspond to
= 20 and 48 for A = 0.25 //in, neo/ncr = 78 and 190 for A = 0.5 /xm, and
cr = 310 and 770 for A = 1/xm, respectively, where ncr is the critical density. The
density profile has a shape density gradient, ne(x) = neo for x > 0 and ne(x) = 0 for
x < 0. The laser intensity rises in 5 fs and remains constant after that. The irradiated
intensity / = 5 x 1019 W/cm2 and the angle of incidence 9 = 30° (p-polarized). 0% = 2.3,
9.2, and 36 for A = 0.25/un, A = 0.5/on, and A = I/an, respectively. The momentum and
energy of electrons, the electromagnetic fields, and the electron and ion densities are
measured after 50 fs.
Figures 1 show snapshots of the electron phase space for neo = 3.5 x 1023cm~3.
Figures l(a-c) and l(d-f) show for A = 0.25 //m and 1 /^m, respectively. The profiles
of the electromagnetic fields and the electron and ion densities at t = 50 fs are shown
in Fig.2. The results show that the electron and ion density profiles of A = 0.25 /^m are
quite different from the profiles of A = 1 /im. The gradient on the surface of the solid
density plasma is still steep for A = 1 //m. However, the gradient for A = 0.25 //m is
gentle compared with one for A = 1 //m. In the case of A = 0.25 /xm, the electric fields
penetrate into dense plasma because of the gentle density gradient. Normalized electron
energy distributions are shown for the plastic (neo — 3.5 x 1023cm~3) and aluminum
(neo = 8.6 x 1023cm~3) in Fig.3(a) and 3(b), respectively. The hot electron temperatures
of the plastic (ne0 - 3.5 x 1023cm~3) are 190 keV, 120 keV, and 60 keV, for 0.25
291
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FIGURE 2. Profiles of the electromagnetic fields and the electron and ion densities at t = 50 fs,
neo — 3.5 x 1023cm~3. The solid and open symbols are for A = 0.25 //m and 1 //m, respectively.
/mi, 0.5 /^m, and 1 //m, respectively. The hot electron temperatures of the aluminum
(ne0 = 8.6 x 1023cm-3) are 170 keV, 80 keV, and 40 keV for 0.25 //m, 0.5 //m, and
1 /xm, respectively. Applying the simulation results of the hot electron temperature to
TLot ~ V Kr/neo)1/2 [(1+«o)1/2 ~ !]mc2' V ~ 2.0 and 2.8 for A - 0.25/xra, 77 ~ 0.95 and
0.98 for A = 0.5//m and 77 ~ 0.41 and 0.43 for A = ljura, respectively. In one dimensional
simulation for normal incidence [9], 77 weekly depend on both /A2 and ne/ncr. 77 oc A"1
in our simulations of p-polarized oblique incidence. It is noted that 77 strongly depends
on the incident angle, polarization, and density scale length, and also depends on ncr/ne
in our simulations.
SUMMARY AND DISCUSSIONS
The hot electron temperature is scaled by 7h0t ~ ^(^cr/^eo)1^2 [(1 + ^o)1//2 ~ I]™?2
rather than Th0t ~ [(1 + &o)^2 ~ l]^c2 at the interaction with overdense plasmas. In the
condition of our simulations, 77 ex A"1. The difference between our results and Wilks's
results may be attributed to the polarization of the laser light. For various laser and
plasma conditions, the more quantitative details of the energy and angular spectrum of
293
0.2
0.4
0.6
mc 2 (y-1)
0.8
0.2
0.4
0.6
mc 2 (y-1)
0.8
FIGURE 3. Electron energy distribution at t = 50 fs and I = 5 x 1019 W/cm2 for (a) n^ = 3.5 x
1023cm~3 and (b) neo = 8.6 x 1023cm~3, respectively. The solid, dashed-doted, and dotted lines are for
A = 0.25 /um, 0.5 /xm, and 1 //m, respectively. The hot electron temperatures are (a) 190, 120, and 60 keV
and (b) 170, 80, and 40 keV for 0.25 //m, 0.5 ^m, and 1 //m, respectively.
the fast particle and the multi-dimensional effects such as surface deformation [10] will
be investigated further in the future.
Finally, we discuss the effect of preformed plasma by a prepulse of the intense short
pulse laser that is an essential problem in an actual long wavelength experiment [15,16].
We are afraid of both the absorption of the short pulse in the preformed plasma and the
distance between the ablation surface and critical surface. That prevent the interaction
between intense KrF laser pulse and solid density plasma. Here, we estimate a preformed
plasma profile and volume by the prepulse, the intensity and pulse width of which are
assumed to be 1012 W/cm2 and 2 ns, respectively. Here, we estimate a preformed plasma
profile and volume by the prepulse, assuming the intensity and pulse width are 1012
W/cm2 and 2 ns, respectively. Total particle number and scale length by the ablation
will be 2 x 1020 cm~2 and 40 /^m. The plasma temperature will be greater than 3 keV,
when the intense short pulse energy density > 2J/7r(10/zm)2 in the preformed plasma
and 5% of its energy is absorbed. The absorption in the preformed plasma is negligible,
because the effective absorption length with 3 keV is about 50 jum. Intense laser pulse
interacts with solid density plasmas, since the stand off distance is proportional to A14/4
[17] and short enough compared with wavelength by KrF laser. Therefore, KrF laser is
suitable for the interaction with solid density plasmas even if the prepulses exist.
ACKNOWLEDGMENTS
A part of this study was financially supported by the Budget for Nuclear Research of the
Ministry of Education, Culture, Sports, Science and Technology, based on the screening
and counseling by the Atomic Energy Commission.
294
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Tabak, M., Hammer, J., Glinsky, M. E., Kruer, W. L., Wilks, S. C., Woodworth, J., Campbell, E. M.,
and Perry, M. D., Phys. Plasmas, 1, 1629-1634 (1994).
Maine, P., Stricland, D., Bado, P., Pessot, M., and Mourou, G., IEEE J. Quantum Electron., 24,
398-403 (1988).
Perry, M. D., Pennington, D., Stuart, B. C., Tietbohl, G., Britten, J. A., Brown, C., Herman, S.,
Golick, B., Kartz, M., Miller, J., Powell, H. T., Vergino, M., and Yanovsky, V., Opt. Lett., 24, 160160 (1999).
Shaw, M. J., Ross, I. N., Hooker, C. J., Dodson, J. M., Hirst, G. J., Lister, J. M. D., Divall, E. J., Kidd,
A. K., Hancock, S., Damerell, A. R., and Wyborn, B. E., Fus. Eng. Design, 44, 209-214 (1999).
Teubner, U., Uschmann, I., Gibbon, P., Altenbernd, D., Forster, E., Feurer, T., Theobald, W., Sauerbrey, R., Hirst, G., Key, M. H., Lister, J., and Neely, D., Phys. Rev. E, 54, 4167-4177 (1996).
Borghesi, M., Mackinnon, A. J., Gaillard, R., Willi, O., and Riley, D., Phys. Rev. E, 60, 7374-7381
(1999).
Owadano, Y, "Development of a high-repetition-rate electron-beam-pumped KrF laser," in Second
International Conference on Inertial Fusion Sciences and Applications, 2001, Kyoto, Japan, 2002.
Lefebvre, E., and Bonnaud, G., Phys. Rev. E, 55, 1011-1014 (1997).
Wilks, S. C., and Kruer, W. L., IEEE J. Quantum Electron., 33, 1954-1968 (1997).
Wilks, S. C., Kruer, W. L., Tabak, M., and Langdon, A. B., Phys. Rev. Lett., 69,1383-1386 (1992).
Malka, G., and Miquel, J. L., Phys. Rev. Lett., 77,75-78 (1996).
Oishi, Y, Nayuki, T., Nemoto, K., Okano, Y, Hironaka, Y, Nakamura, K. G., and Kondo, K., Appl.
Phys. Lett., 79, 123^1236 (2001).
Bourdier, A., Phys. Fluids, 26,1804-1807 (1983).
Gibbon, P., and Bell, A. R., Phys. Rev. Lett, 68, 1535-1538 (1992).
Yu, W, Bychenkov, V., Sentoku, Y, Yu, M. Y, Sheng, Z. M., and Mima, K., Phys. Rev. Lett., 85,
570-573 (2000).
Cowan, T. E., Hunt, A. W, Phillips, T. W., Wilks, S. C., Perry, M. D., Brown, C., Fountain, W,
Hatchett, S., Johnson, J., Key, M. H., Parnell, T., Pennington, D. M., Snavely, R. A., and Takahashi,
Y, Phys. Rev. Lett., 84, 903-906 (2000).
Manheimer, W. M., Colombant, D. G., and Gardner, J. H., Phys. Fluids, 25, 1644-1652 (1982).
295