VARIOUS MECHANISMS OF ELECTRON HEATING AT THE IRRADIATION OF DENSE

TARGETS BY A SUPER-INTENSE FEMTOSECOND LASER PULSE

Krainov V.P.Moscow Institute of Physics and Technology

141700 Dolgoprudny, Moscow Region, Russiakrainov@online.ru

XX International conference “Elbrus-2005”, 1-6 March 2005

Outlook

1. Vacuum heating

2. Inverse induced bremsstrahlung

3. Stochastic heating

4. Relativistic magnetic force

5. Charge separation in thin foils

6. Longitudinal (wake) plasma waves

7. Electron scattering on potential gradient

8. Bubble acceleration

1. Vacuum (Brunel) heating

Overdense plasma

vacuum

e

cosF t

e e e e e e e e e e e e e e e e e e

F from electrons

Brunel F 1987 Phys. Rev. Lett. 59, 52

2

20.75

2

FE

Applicability

• Overdense plasma target• High contrast of laser• No pre-pulse• Oblique incidence of laser beam• P-polarization of linearly polarized field• Model is applicable also for large atomic

clusters• Non-relativistic laser intensity 18 2( 10 W / cm )

Relativistic generalization

Overdense plasma

vacuum

relativistic electron motiontaking into account themagnetic part of Lorentz force laser

F

19 210 W / cmI cF

E

2. Induced inverse bremsstrahlung

e

A

Elastic electron-ion scattering in thepresence of the intense laser field

laser field

2

22in

e

FE T

An electron absorbs this averaged energyat each collision

G.M. Fraiman, A.A. Balakin, V.A. Mironov, Phys. Plasmas, 8, 2502 (2001)

2;

in

eeiei F

ZnconstE

dt

dE

Applicability

• Overdense plasma, since dE/dt is proportional to plasma density

• Irradiation of solid targets or clusters by very high intensity laser pulse

• Multicharged atomic ions• Irradiation of underdense plasma by a

weak laser pulse resulting in intense electron-ion collisions

• Large pulse duration

Relativistic generalization

A. A. Balakin, G.M. Fraiman, N.J. Fisch, JETP Letters, 81, 3 (2005)

inFc

: this relativistic condition can be fulfilled only for underdense plasma

where 18 2, 10 W / cminF F I The heating in the ultra-relativistic case does not depend on the laser intensity!Hot electrons have the energy up to 1-100 MeV, but the average electron energy in the underdense plasma is of the order of only hundreds of eV!The average electron energy E is determined by simple relation:

2/310 eVE Z

Here Z is the typical charge multiplicity of the atomic ion, and is the pulseduration (in ps).

Electron energy spectra in the underdense plasma

Experiments: S.P. Hatchet, C.G. Brown et al, Phys. Plasmas, 7, 2076 (2000)

Energy spectra at the relativistic ionization

V.P. Krainov, A.V. Sofronov, Phys. Rev. A 69, 015401 (2004):A weak dependence of the typical electron energy Eproduced during barrier-suppression relativistic ionization of atomic ionson the relativistic laser field strength F (before acceleration)

This is a quantum quantity explained by an uncertainty principle.It does not depend on the ionization potential of the multichargedatomic ion. For example, when laser intensity is one obtains E ~ 10 keV

20 210 W / cm

23/1

32 mc

c

mFemcE

Resonance absorption: when the cluster expands the laser frequency coincides the Mie frequency for a short time instance – then the electric fieldbecomes much more than the external laser field

• Laser energy can be transferred to the electrons by the interaction of the incident and reflected electromagnetic wave in underdense pre-plasma.

Y. Sentoku et al., Appl. Phys. B 74, 207 (2002)

They take into account that strong longitudinal electrostatic field is produced by charge separation and apply PIC-simulations

• We show that the dynamic chaos appears without addition of the longitudinal electrostatic field.

• Particle motion becomes stochastic in the field of only standing wave (G.M. Zaslavskii,N.N. Filonenko, Sov. Phys. – JETP 25, 851 (1968)) under some conditions

• The chaotic motion appears due to the magnetic part of the Lorentz force, and it is directed along the pulse propagation.

3. Stochastic heating

Applicability

• Dense targets, femtosecond pulses• Electrons are heated via dynamic chaos

mechanism in underdense pre-plasma, when the laser field is a relativistic one: the laser intensity should be more than

• Electron kinetic energy is a relativistic quantity and increases with the laser intensity .

• The electron motion is similar qualitatively to the Kapitza mathematical pendulum perturbed by the high-frequency field.

218 cm/W10

Numerical relativistic approach

tkxFppc

ptkxF

dt

dp

tkxFppc

p

dt

dp

yx

xy

yx

yx

sincos2

cossin2

sincos2

222

222

Relativistic equations of the electron motion in the field of standing wave in underdense pre-plasma (m = e = 1, smooth turn on and off of the laser field, an electron is initially at rest)

Electron longitudinaldrift (in mc)

Electron transversemomentum(in mc)

Electronkineticenergy(in mc2)

Envelope of the laserpulse

218 cm/W102

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

py

px

Relativistic electron momenta are in units of mc; the begin of the motion is in the origin,Rastunkov V.S., Krainov V.P., Laser Physics, 2005

Electron heating via diffusion mechanism

4. Relativistic magnetic force

Adiabatic relativistic drift of an electron in laser fieldin the vacuum, or in the underdense plasmas

cc

tFtV

2

2

|| 4

)()(

an electron moves during the laser pulse along the pulse propagation and stops after the end of the laser pulse

F(t)cost

B(t)cost

k

F(t) is the envelope of laser pulse

Applicability

• The relativistic electron drift in overdense plasma along the propagation of laser radiation produced by a magnetic part of laser field remains after the end of the laser pulse, unlike the relativistic drift of free electrons in underdense plasma.

• The electron drift velocity in the skin layer is a non-relativistic quantity even at the peak laser intensity of 1022 W/cm².

• The time at which an electron penetrates into field-free matter from the skin layer is much less than the pulse duration. This penetration occurs at the leading edge of the laser pulse.

• The following deep penetration of electrons into field-free matter takes place until their collisions stop this motion.

The axial adiabatic non-relativistic electron ponderomotive drift in the picosecond laser pulse

in underdense plasmas

||

2

2

;4

)()(

VV

cR

tFtV

is the pulse duration;R is the focal radiusof the laser beam. An electron expels from laser beam and stops after end of the pulse

k

F

B

The relativistic longitudinal electron drift in overdense plasma is produced by superintense

femtosecond laser pulse

• The direct solution of relativistic equations for an electron in overdense plasmas perturbed by linearly polarized laser pulse

• Ponderomotive estimate

is incorrect ;)(

)(2

|| c

tFtV

p

2F/c

Px /mc

0 20 40 60 80 100

4.0x10-3

4.5x10-3

5.0x10-3

5.5x10-3

6.0x10-3

6.5x10-3

7.0x10-3

7.5x10-3

8.0x10-3

8.5x10-3

p x

f

The Ti: sapphire laser intensity of 5 1019 W/cm2 , the pulse duration of 80 fs

Px /mc

t

Py /mc

Laserpulseenvelope

-600 -550 -500 -450 -400 -350 -300 -250 -200 -150-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-600 -550 -500 -450 -400 -350 -300 -250 -200 -150-6.0x10-3

-4.0x10-3

-2.0x10-3

0.0

2.0x10-3

4.0x10-3

6.0x10-3

p y

t

-600 -550 -500 -450 -400 -350 -300 -250 -200 -150-1.0x10-3

0.01.0x10-3

2.0x10-3

3.0x10-3

4.0x10-3

5.0x10-3

6.0x10-3

7.0x10-3

px

t

exp

(-t2/2

)

t

5. Charge separation in thin foils

10-100 fs high-intensity laser pulse causes strong charge separation

The protons are accelerated by the electrostatic field set up by fast electrons leaving the target.

Laser Pulse

TargetProtons

Electrons

[S.C. Wilks, et al., Phys. Plasmas 8, 542 (2001)]

Rear acceleration mechanisms:Rear acceleration mechanisms: charge separationcharge separation

- At plasma-vacuum interface, - At plasma-vacuum interface, quasineutrality NOT validquasineutrality NOT valid

- A A chargecharge separation is established, with an separation is established, with an extention ~ extention ~ ee

- Charge separation induces a - Charge separation induces a self-consistent electrostatic field Eself-consistent electrostatic field E

- Self-consistent potential is ~ - Self-consistent potential is ~ TTe e /e (potential-thermal energy balance)/e (potential-thermal energy balance)

e

e

e

TE

~

Laser-generated electron population,Laser-generated electron population,for ultraintense ultrashort laser pulse,for ultraintense ultrashort laser pulse,has has TTee~ MeV, ~ MeV, ee~ ~ mm

E~ MV/E~ MV/mm (!) (!)

6. Longitudinal (wake) plasma waves

Underdense plasma!Ultra-relativistic electrons

T. Tajima, J. Dawson, Phys. Rev. Lett. 43, 262 (1979)J.M. Dawson, Plasma Phys. Contr. Fus. 34, 2039 (1992)C. Joshi, Th. Katsouleas, Physics Today 6, 47 (2003)

Self-modulated laser wakefield

6 8 10 20 40 60 80100 200

103

104

105

106

Sho t 12 (10 kG ) Sho t 26 (10 kG ) Shot 29 (5 kG )Shot 33 (5 kG ) Sho t 39 (2.5 kG) Sho t 40 (2.5 k G)

Re

lativ

e #

of

ele

ctro

ns/

Me

V/S

tera

dia

n

E lectron energy (in M eV)

SM-LWFA electron energy spectrum

c·L >> pl = 2c/p

plc L

Forward Raman scattering inst.

el. density

modulated laser pulse

A. Ting, et al., Bull. A.P.S. 43, 1781 (1998)

2.5 TW, 400 fs

E ≈ 5 GeV/cm , W ≈ 100 MeV

He, H gas jetne ≈1019 cm-3

NRL

The laser pulse is longer than the plasma wavelength

Forced laser wakefield

I = 31018 W/cm2

= 820 nmL ≈ 30 fsHe gas jetne = 2-61019 cm-3

W up to 200 MeVV. Malka, et al., Science 298, 1596 (2002)Z. Najimudin, et al., Phys. Plasmas 10, 2071 (2003)

n/n0 pl

c L

cL≤ p

7. Electron scattering on potential gradient

Here isstatic electricfield gradientproduced byouter ionizationof the cluster

PRL, 92, 133401 (2004)

8. Bubble acceleration

A. Pukhov, Rep. Prog. Phys. 66, 47 (2003)33 fs pulse, 1019 W/cm2; 1019 cm-3 plasma; time