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 Dolgoprudny, Moscow Region, Russia 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 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

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

Relativistic generalization Overdense plasma vacuum relativistic electron motion taking into account the magnetic part of Lorentz force laser F

2. Induced inverse bremsstrahlung e Elastic electron-ion scattering in the presence of the intense laser field laser field An electron absorbs this averaged energy at each collision G.M. Fraiman, A.A. Balakin, V.A. Mironov, Phys. Plasmas, 8, 2502 (2001)

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) : this relativistic condition can be fulfilled only for underdense plasma where The heating in the ultra-relativistic case does not depend on the laser intensity! Hot electrons have the energy up to 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: Here Z is the typical charge multiplicity of the atomic ion, and  is the pulse duration (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, (2004): A weak dependence of the typical electron energy E produced during barrier-suppression relativistic ionization of atomic ions on 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 multicharged atomic ion. For example, when laser intensity is one obtains E ~ 10 keV Resonance absorption: when the cluster expands the laser frequency coincides the Mie frequency for a short time instance – then the electric field becomes 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.

Numerical relativistic approach 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 longitudinal drift (in mc) Electron transverse momentum (in mc) Electron kinetic energy (in mc 2 ) Envelope of the laser pulse

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 field in the vacuum, or in the underdense plasmas an electron moves during the laser pulse along the pulse propagation and stops after the end of the laser pulse F(t)cos  t B(t)cos  t 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 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  is the pulse duration; R is the focal radius of 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

2F/  c P x /mc The Ti: sapphire laser intensity of 5  W/cm 2, the pulse duration of 80 fs

P x /mc tt P y /mc Laser pulse envelope

5. Charge separation in thin foils  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 Target Protons Electrons [S.C. Wilks, et al., Phys. Plasmas 8, 542 (2001)]

Rear acceleration mechanisms: charge separation charge separation - At plasma-vacuum interface, quasineutrality NOT valid - A charge separation is established, with an extention ~ e - Charge separation induces a self-consistent electrostatic field E - Self-consistent potential is ~ T e /e (potential-thermal energy balance) Laser-generated electron population, for ultraintense ultrashort laser pulse, has T e ~ MeV, e ~  m E~ MV/  m (!)

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 Shot 12 (10 kG) Shot 26 (10 kG) Shot 29 (5 kG) Shot 33 (5 kG) Shot 39 (2.5 kG) Shot 40 (2.5 kG) Relative # of electrons/MeV/Steradian Electron energy (in MeV) SM-LWFA electron energy spectrum c·  L >> pl = 2  c/  p 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 jet n e ≈10 19 cm -3 NRL The laser pulse is longer than the plasma wavelength

Forced laser wakefield I = 3  W/cm 2 = 820 nm  L ≈ 30 fs He gas jet n e = 2-6  cm -3 W up to 200 MeV V. Malka, et al., Science 298, 1596 (2002) Z. Najimudin, et al., Phys. Plasmas 10, 2071 (2003) n/n 0 c  L ≤ p

7. Electron scattering on potential gradient Here is static electric field gradient produced by outer ionization of the cluster

PRL, 92, (2004)

8. Bubble acceleration A.Pukhov, Rep. Prog. Phys. 66, 47 (2003) 33 fs pulse, W/cm 2 ; cm -3 plasma; time 